TSTP Solution File: MSC007-2.005 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MSC007-2.005 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 05:34:02 EDT 2022
% Result : Unsatisfiable 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : MSC007-2.005 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Sep 2 03:01:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Unsatisfiable
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(in_type, type, (
% 0.21/0.42 in: ( $i * $i ) > $o)).
% 0.21/0.42 tff(hole_1_type, type, (
% 0.21/0.42 hole_1: $i)).
% 0.21/0.42 tff(pigeon_2_type, type, (
% 0.21/0.42 pigeon_2: $i)).
% 0.21/0.42 tff(hole_of_type, type, (
% 0.21/0.42 hole_of: $i > $i)).
% 0.21/0.42 tff(pigeon_3_type, type, (
% 0.21/0.42 pigeon_3: $i)).
% 0.21/0.42 tff(hole_4_type, type, (
% 0.21/0.42 hole_4: $i)).
% 0.21/0.42 tff(pigeon_4_type, type, (
% 0.21/0.42 pigeon_4: $i)).
% 0.21/0.42 tff(hole_3_type, type, (
% 0.21/0.42 hole_3: $i)).
% 0.21/0.42 tff(pigeon_1_type, type, (
% 0.21/0.42 pigeon_1: $i)).
% 0.21/0.42 tff(hole_2_type, type, (
% 0.21/0.42 hole_2: $i)).
% 0.21/0.42 tff(pigeon_type, type, (
% 0.21/0.42 pigeon: $i > $o)).
% 0.21/0.42 tff(hole_type, type, (
% 0.21/0.42 hole: $i > $o)).
% 0.21/0.42 tff(pigeon_5_type, type, (
% 0.21/0.42 pigeon_5: $i)).
% 0.21/0.42 tff(1,assumption,(~(hole_of(pigeon_2) = hole_1)), introduced(assumption)).
% 0.21/0.42 tff(2,assumption,(~(hole_of(pigeon_4) = hole_4)), introduced(assumption)).
% 0.21/0.42 tff(3,assumption,(in(pigeon_1, hole_2)), introduced(assumption)).
% 0.21/0.42 tff(4,assumption,(hole_of(pigeon_3) = hole_2), introduced(assumption)).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (hole_2 = hole_of(pigeon_3)),
% 0.21/0.42 inference(symmetry,[status(thm)],[4])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (in(pigeon_3, hole_2) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[5])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_2)),
% 0.21/0.42 inference(symmetry,[status(thm)],[6])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (^[X: $i] : refl(((~pigeon(X)) | in(X, hole_of(X))) <=> ((~pigeon(X)) | in(X, hole_of(X))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (![X: $i] : ((~pigeon(X)) | in(X, hole_of(X))) <=> ![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (![X: $i] : ((~pigeon(X)) | in(X, hole_of(X))) <=> ![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(11,axiom,(![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','each_pigeons_hole2')).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.42 tff(13,plain,(
% 0.21/0.42 ![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[12])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (pigeon(pigeon_3) <=> pigeon(pigeon_3)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(16,axiom,(pigeon(pigeon_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_3')).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (pigeon(pigeon_3)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | ((~pigeon(pigeon_3)) | in(pigeon_3, hole_of(pigeon_3)))) <=> ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | (~pigeon(pigeon_3)) | in(pigeon_3, hole_of(pigeon_3)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | ((~pigeon(pigeon_3)) | in(pigeon_3, hole_of(pigeon_3)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | (~pigeon(pigeon_3)) | in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 (in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[20, 17, 14])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 (in(pigeon_3, hole_2)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[21, 7])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (^[Pigeon1: $i, Pigeon2: $i, Hole: $i] : refl(((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1))) <=> ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1))) <=> ![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1))) <=> ![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (^[Pigeon1: $i, Pigeon2: $i, Hole: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~hole(Hole)) | (~pigeon(Pigeon1))) | (~pigeon(Pigeon2))) <=> ((~hole(Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))), (((((~hole(Hole)) | (~pigeon(Pigeon1))) | (~pigeon(Pigeon2))) | (~in(Pigeon1, Hole))) <=> (((~hole(Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1))) | (~in(Pigeon1, Hole))))), rewrite((((~hole(Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1))) | (~in(Pigeon1, Hole))) <=> ((~hole(Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))), (((((~hole(Hole)) | (~pigeon(Pigeon1))) | (~pigeon(Pigeon2))) | (~in(Pigeon1, Hole))) <=> ((~hole(Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1))))), ((((((~hole(Hole)) | (~pigeon(Pigeon1))) | (~pigeon(Pigeon2))) | (~in(Pigeon1, Hole))) | (~in(Pigeon2, Hole))) <=> (((~hole(Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1))) | (~in(Pigeon2, Hole))))), rewrite((((~hole(Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1))) | (~in(Pigeon2, Hole))) <=> ((~hole(Hole)) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))), ((((((~hole(Hole)) | (~pigeon(Pigeon1))) | (~pigeon(Pigeon2))) | (~in(Pigeon1, Hole))) | (~in(Pigeon2, Hole))) <=> ((~hole(Hole)) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1))))), (((((((~hole(Hole)) | (~pigeon(Pigeon1))) | (~pigeon(Pigeon2))) | (~in(Pigeon1, Hole))) | (~in(Pigeon2, Hole))) | (Pigeon1 = Pigeon2)) <=> (((~hole(Hole)) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1))) | (Pigeon1 = Pigeon2)))), rewrite((((~hole(Hole)) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1))) | (Pigeon1 = Pigeon2)) <=> ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))), (((((((~hole(Hole)) | (~pigeon(Pigeon1))) | (~pigeon(Pigeon2))) | (~in(Pigeon1, Hole))) | (~in(Pigeon2, Hole))) | (Pigeon1 = Pigeon2)) <=> ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((((((~hole(Hole)) | (~pigeon(Pigeon1))) | (~pigeon(Pigeon2))) | (~in(Pigeon1, Hole))) | (~in(Pigeon2, Hole))) | (Pigeon1 = Pigeon2)) <=> ![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.42 tff(28,axiom,(![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((((((~hole(Hole)) | (~pigeon(Pigeon1))) | (~pigeon(Pigeon2))) | (~in(Pigeon1, Hole))) | (~in(Pigeon2, Hole))) | (Pigeon1 = Pigeon2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','only_one_per_hole')).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.21/0.42 tff(31,plain,(
% 0.21/0.42 ![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[30])).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (hole(hole_2) <=> hole(hole_2)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(34,axiom,(hole(hole_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hole_2')).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (hole(hole_2)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 ((~(pigeon_1 = pigeon_3)) <=> (~(pigeon_1 = pigeon_3))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(37,axiom,(~(pigeon_1 = pigeon_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_1_is_not_pigeon_3')).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (~(pigeon_1 = pigeon_3)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (pigeon(pigeon_1) <=> pigeon(pigeon_1)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(40,axiom,(pigeon(pigeon_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_1')).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (pigeon(pigeon_1)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_2)) | (~in(pigeon_3, hole_2)) | (~in(pigeon_1, hole_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_2)) | (~in(pigeon_3, hole_2)) | (~in(pigeon_1, hole_2)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 (((~hole(hole_2)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_2)) | (~in(pigeon_3, hole_2)) | (~in(pigeon_1, hole_2)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_2)) | (~in(pigeon_3, hole_2)) | (~in(pigeon_1, hole_2))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_2)) | (~in(pigeon_3, hole_2)) | (~in(pigeon_1, hole_2)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[44, 42])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_2)) | (~in(pigeon_3, hole_2)) | (~in(pigeon_1, hole_2))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (~in(pigeon_3, hole_2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[47, 41, 17, 38, 35, 32, 3])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[48, 22])).
% 0.21/0.42 tff(50,plain,((~(hole_of(pigeon_3) = hole_2)) | (~in(pigeon_1, hole_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (~(hole_of(pigeon_3) = hole_2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[50, 3])).
% 0.21/0.42 tff(52,assumption,(in(pigeon_4, hole_2)), introduced(assumption)).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 ((~(pigeon_1 = pigeon_4)) <=> (~(pigeon_1 = pigeon_4))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(54,axiom,(~(pigeon_1 = pigeon_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_1_is_not_pigeon_4')).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (~(pigeon_1 = pigeon_4)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 (pigeon(pigeon_4) <=> pigeon(pigeon_4)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(57,axiom,(pigeon(pigeon_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_4')).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 (pigeon(pigeon_4)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_4, hole_2)) | (~in(pigeon_1, hole_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_4, hole_2)) | (~in(pigeon_1, hole_2)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (((~hole(hole_2)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_4, hole_2)) | (~in(pigeon_1, hole_2)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_4, hole_2)) | (~in(pigeon_1, hole_2))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[60])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_4, hole_2)) | (~in(pigeon_1, hole_2)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[61, 59])).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_4, hole_2)) | (~in(pigeon_1, hole_2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[64, 41, 58, 55, 35, 32, 52, 3])).
% 0.21/0.43 tff(66,plain,((~in(pigeon_4, hole_2)) | (~in(pigeon_1, hole_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (~in(pigeon_4, hole_2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[66, 3])).
% 0.21/0.43 tff(68,assumption,(hole_of(pigeon_4) = hole_2), introduced(assumption)).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (in(pigeon_4, hole_of(pigeon_4)) <=> in(pigeon_4, hole_2)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[68])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (in(pigeon_4, hole_2) <=> in(pigeon_4, hole_of(pigeon_4))),
% 0.21/0.43 inference(symmetry,[status(thm)],[69])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 ((~in(pigeon_4, hole_2)) <=> (~in(pigeon_4, hole_of(pigeon_4)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[70])).
% 0.21/0.43 tff(72,assumption,(~in(pigeon_4, hole_2)), introduced(assumption)).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (~in(pigeon_4, hole_of(pigeon_4))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | ((~pigeon(pigeon_4)) | in(pigeon_4, hole_of(pigeon_4)))) <=> ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | (~pigeon(pigeon_4)) | in(pigeon_4, hole_of(pigeon_4)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | ((~pigeon(pigeon_4)) | in(pigeon_4, hole_of(pigeon_4)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | (~pigeon(pigeon_4)) | in(pigeon_4, hole_of(pigeon_4))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (in(pigeon_4, hole_of(pigeon_4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[76, 58, 14])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[77, 73])).
% 0.21/0.43 tff(79,plain,((~(hole_of(pigeon_4) = hole_2)) | in(pigeon_4, hole_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (~(hole_of(pigeon_4) = hole_2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[79, 67])).
% 0.21/0.43 tff(81,assumption,(hole_of(pigeon_5) = hole_2), introduced(assumption)).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (hole_2 = hole_of(pigeon_5)),
% 0.21/0.43 inference(symmetry,[status(thm)],[81])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 (in(pigeon_5, hole_2) <=> in(pigeon_5, hole_of(pigeon_5))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[82])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 (in(pigeon_5, hole_of(pigeon_5)) <=> in(pigeon_5, hole_2)),
% 0.21/0.43 inference(symmetry,[status(thm)],[83])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (pigeon(pigeon_5) <=> pigeon(pigeon_5)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(86,axiom,(pigeon(pigeon_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_5')).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (pigeon(pigeon_5)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 (((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | ((~pigeon(pigeon_5)) | in(pigeon_5, hole_of(pigeon_5)))) <=> ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | (~pigeon(pigeon_5)) | in(pigeon_5, hole_of(pigeon_5)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | ((~pigeon(pigeon_5)) | in(pigeon_5, hole_of(pigeon_5)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | (~pigeon(pigeon_5)) | in(pigeon_5, hole_of(pigeon_5))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 (in(pigeon_5, hole_of(pigeon_5))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[90, 87, 14])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 (in(pigeon_5, hole_2)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 ((~(pigeon_1 = pigeon_5)) <=> (~(pigeon_1 = pigeon_5))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(94,axiom,(~(pigeon_1 = pigeon_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_1_is_not_pigeon_5')).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 (~(pigeon_1 = pigeon_5)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_1, hole_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_1, hole_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 (((~hole(hole_2)) | (pigeon_1 = pigeon_5) | (~in(pigeon_5, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_1, hole_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_1 = pigeon_5) | (~in(pigeon_5, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_1, hole_2))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[97])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_1 = pigeon_5) | (~in(pigeon_5, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_1, hole_2)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[98, 96])).
% 0.21/0.43 tff(100,plain,
% 0.21/0.43 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_1 = pigeon_5) | (~in(pigeon_5, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_1)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(101,plain,
% 0.21/0.43 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_1, hole_2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 (~in(pigeon_5, hole_2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[101, 41, 87, 95, 35, 32, 3])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[102, 92])).
% 0.21/0.43 tff(104,plain,((~(hole_of(pigeon_5) = hole_2)) | (~in(pigeon_1, hole_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 (~(hole_of(pigeon_5) = hole_2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[104, 3])).
% 0.21/0.43 tff(106,assumption,(in(pigeon_2, hole_2)), introduced(assumption)).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 ((~(pigeon_1 = pigeon_2)) <=> (~(pigeon_1 = pigeon_2))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(108,axiom,(~(pigeon_1 = pigeon_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_1_is_not_pigeon_2')).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 (~(pigeon_1 = pigeon_2)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 (pigeon(pigeon_2) <=> pigeon(pigeon_2)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(111,axiom,(pigeon(pigeon_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_2')).
% 0.21/0.43 tff(112,plain,
% 0.21/0.43 (pigeon(pigeon_2)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.43 tff(113,plain,
% 0.21/0.43 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_1, hole_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_1, hole_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(114,plain,
% 0.21/0.43 (((~hole(hole_2)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_1, hole_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(115,plain,
% 0.21/0.43 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_1, hole_2))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[114])).
% 0.21/0.43 tff(116,plain,
% 0.21/0.43 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_1, hole_2)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[115, 113])).
% 0.21/0.43 tff(117,plain,
% 0.21/0.43 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_1, hole_2)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(118,plain,
% 0.21/0.43 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_1, hole_2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.43 tff(119,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[118, 41, 112, 109, 35, 32, 106, 3])).
% 0.21/0.43 tff(120,plain,((~in(pigeon_2, hole_2)) | (~in(pigeon_1, hole_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(121,plain,
% 0.21/0.43 (~in(pigeon_2, hole_2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[120, 3])).
% 0.21/0.43 tff(122,assumption,(hole_of(pigeon_2) = hole_2), introduced(assumption)).
% 0.21/0.43 tff(123,plain,
% 0.21/0.43 (in(pigeon_2, hole_of(pigeon_2)) <=> in(pigeon_2, hole_2)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[122])).
% 0.21/0.43 tff(124,plain,
% 0.21/0.43 (in(pigeon_2, hole_2) <=> in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.43 inference(symmetry,[status(thm)],[123])).
% 0.21/0.43 tff(125,plain,
% 0.21/0.43 ((~in(pigeon_2, hole_2)) <=> (~in(pigeon_2, hole_of(pigeon_2)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[124])).
% 0.21/0.43 tff(126,assumption,(~in(pigeon_2, hole_2)), introduced(assumption)).
% 0.21/0.43 tff(127,plain,
% 0.21/0.43 (~in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.21/0.43 tff(128,plain,
% 0.21/0.43 (((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | ((~pigeon(pigeon_2)) | in(pigeon_2, hole_of(pigeon_2)))) <=> ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | (~pigeon(pigeon_2)) | in(pigeon_2, hole_of(pigeon_2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(129,plain,
% 0.21/0.43 ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | ((~pigeon(pigeon_2)) | in(pigeon_2, hole_of(pigeon_2)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(130,plain,
% 0.21/0.43 ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | (~pigeon(pigeon_2)) | in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.43 tff(131,plain,
% 0.21/0.43 (in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[130, 112, 14])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[131, 127])).
% 0.21/0.43 tff(133,plain,((~(hole_of(pigeon_2) = hole_2)) | in(pigeon_2, hole_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 (~(hole_of(pigeon_2) = hole_2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[133, 121])).
% 0.21/0.43 tff(135,assumption,(~(hole_of(pigeon_4) = hole_2)), introduced(assumption)).
% 0.21/0.43 tff(136,assumption,(~(hole_of(pigeon_2) = hole_2)), introduced(assumption)).
% 0.21/0.43 tff(137,assumption,(~(hole_of(pigeon_3) = hole_2)), introduced(assumption)).
% 0.21/0.43 tff(138,assumption,(~(hole_of(pigeon_5) = hole_2)), introduced(assumption)).
% 0.21/0.43 tff(139,assumption,(~(hole_of(pigeon_3) = hole_1)), introduced(assumption)).
% 0.21/0.43 tff(140,assumption,(hole_of(pigeon_2) = hole_1), introduced(assumption)).
% 0.21/0.43 tff(141,assumption,(hole_of(pigeon_4) = hole_1), introduced(assumption)).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 (hole_1 = hole_of(pigeon_4)),
% 0.21/0.43 inference(symmetry,[status(thm)],[141])).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 (in(pigeon_4, hole_1) <=> in(pigeon_4, hole_of(pigeon_4))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[142])).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 (in(pigeon_4, hole_of(pigeon_4)) <=> in(pigeon_4, hole_1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[143])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 (in(pigeon_4, hole_1)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[77, 144])).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 ((pigeon_4 = pigeon_2) <=> (pigeon_2 = pigeon_4)),
% 0.21/0.43 inference(commutativity,[status(thm)],[])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 ((pigeon_2 = pigeon_4) <=> (pigeon_4 = pigeon_2)),
% 0.21/0.43 inference(symmetry,[status(thm)],[146])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 ((~(pigeon_2 = pigeon_4)) <=> (~(pigeon_4 = pigeon_2))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 ((~(pigeon_2 = pigeon_4)) <=> (~(pigeon_2 = pigeon_4))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(150,axiom,(~(pigeon_2 = pigeon_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_2_is_not_pigeon_4')).
% 0.21/0.43 tff(151,plain,
% 0.21/0.43 (~(pigeon_2 = pigeon_4)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.43 tff(152,plain,
% 0.21/0.43 (~(pigeon_4 = pigeon_2)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[151, 148])).
% 0.21/0.43 tff(153,plain,
% 0.21/0.43 (hole_1 = hole_of(pigeon_2)),
% 0.21/0.43 inference(symmetry,[status(thm)],[140])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 (in(pigeon_2, hole_1) <=> in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[153])).
% 0.21/0.43 tff(155,plain,
% 0.21/0.43 (in(pigeon_2, hole_of(pigeon_2)) <=> in(pigeon_2, hole_1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[154])).
% 0.21/0.43 tff(156,plain,
% 0.21/0.43 (in(pigeon_2, hole_1)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[131, 155])).
% 0.21/0.43 tff(157,plain,
% 0.21/0.43 (hole(hole_1) <=> hole(hole_1)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(158,axiom,(hole(hole_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hole_1')).
% 0.21/0.43 tff(159,plain,
% 0.21/0.43 (hole(hole_1)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.21/0.44 tff(160,plain,
% 0.21/0.44 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(161,plain,
% 0.21/0.44 (((~hole(hole_1)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_4, hole_1)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4))) <=> ((~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(162,plain,
% 0.21/0.44 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_4, hole_1)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[161])).
% 0.21/0.44 tff(163,plain,
% 0.21/0.44 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_4, hole_1)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[162, 160])).
% 0.21/0.44 tff(164,plain,
% 0.21/0.44 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_4, hole_1)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(165,plain,
% 0.21/0.44 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.21/0.44 tff(166,plain,
% 0.21/0.44 ((pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_4, hole_1))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[165, 112, 58, 159, 32])).
% 0.21/0.44 tff(167,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[166, 156, 152, 145])).
% 0.21/0.44 tff(168,plain,((~(hole_of(pigeon_2) = hole_1)) | (~(hole_of(pigeon_4) = hole_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(169,plain,
% 0.21/0.44 (~(hole_of(pigeon_4) = hole_1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[168, 140])).
% 0.21/0.44 tff(170,plain,
% 0.21/0.44 (^[X: $i] : refl((hole(hole_of(X)) | (~pigeon(X))) <=> (hole(hole_of(X)) | (~pigeon(X))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(171,plain,
% 0.21/0.44 (![X: $i] : (hole(hole_of(X)) | (~pigeon(X))) <=> ![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[170])).
% 0.21/0.44 tff(172,plain,
% 0.21/0.44 (![X: $i] : (hole(hole_of(X)) | (~pigeon(X))) <=> ![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(173,plain,
% 0.21/0.44 (^[X: $i] : rewrite(((~pigeon(X)) | hole(hole_of(X))) <=> (hole(hole_of(X)) | (~pigeon(X))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(174,plain,
% 0.21/0.44 (![X: $i] : ((~pigeon(X)) | hole(hole_of(X))) <=> ![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[173])).
% 0.21/0.44 tff(175,axiom,(![X: $i] : ((~pigeon(X)) | hole(hole_of(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','each_pigeons_hole1')).
% 0.21/0.44 tff(176,plain,
% 0.21/0.44 (![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.21/0.44 tff(177,plain,
% 0.21/0.44 (![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.21/0.44 tff(178,plain,(
% 0.21/0.44 ![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[177])).
% 0.21/0.44 tff(179,plain,
% 0.21/0.44 (![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.21/0.44 tff(180,plain,
% 0.21/0.44 (((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | (hole(hole_of(pigeon_4)) | (~pigeon(pigeon_4)))) <=> ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | hole(hole_of(pigeon_4)) | (~pigeon(pigeon_4)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(181,plain,
% 0.21/0.44 ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | (hole(hole_of(pigeon_4)) | (~pigeon(pigeon_4)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(182,plain,
% 0.21/0.44 ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | hole(hole_of(pigeon_4)) | (~pigeon(pigeon_4))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.21/0.44 tff(183,plain,
% 0.21/0.44 (hole(hole_of(pigeon_4))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[182, 58, 179])).
% 0.21/0.44 tff(184,plain,
% 0.21/0.44 (^[Hole: $i] : refl(((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole))) <=> ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(185,plain,
% 0.21/0.44 (![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole))) <=> ![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[184])).
% 0.21/0.44 tff(186,plain,
% 0.21/0.44 (![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole))) <=> ![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(187,plain,
% 0.21/0.44 (^[Hole: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~hole(Hole)) | (Hole = hole_1)) | (Hole = hole_2)) <=> ((Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))), (((((~hole(Hole)) | (Hole = hole_1)) | (Hole = hole_2)) | (Hole = hole_3)) <=> (((Hole = hole_2) | (Hole = hole_1) | (~hole(Hole))) | (Hole = hole_3)))), rewrite((((Hole = hole_2) | (Hole = hole_1) | (~hole(Hole))) | (Hole = hole_3)) <=> ((Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))), (((((~hole(Hole)) | (Hole = hole_1)) | (Hole = hole_2)) | (Hole = hole_3)) <=> ((Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole))))), ((((((~hole(Hole)) | (Hole = hole_1)) | (Hole = hole_2)) | (Hole = hole_3)) | (Hole = hole_4)) <=> (((Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole))) | (Hole = hole_4)))), rewrite((((Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole))) | (Hole = hole_4)) <=> ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))), ((((((~hole(Hole)) | (Hole = hole_1)) | (Hole = hole_2)) | (Hole = hole_3)) | (Hole = hole_4)) <=> ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(188,plain,
% 0.21/0.44 (![Hole: $i] : (((((~hole(Hole)) | (Hole = hole_1)) | (Hole = hole_2)) | (Hole = hole_3)) | (Hole = hole_4)) <=> ![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[187])).
% 0.21/0.44 tff(189,axiom,(![Hole: $i] : (((((~hole(Hole)) | (Hole = hole_1)) | (Hole = hole_2)) | (Hole = hole_3)) | (Hole = hole_4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','all_holes')).
% 0.21/0.44 tff(190,plain,
% 0.21/0.44 (![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.21/0.44 tff(191,plain,
% 0.21/0.44 (![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.21/0.44 tff(192,plain,(
% 0.21/0.44 ![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[191])).
% 0.21/0.44 tff(193,plain,
% 0.21/0.44 (![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.21/0.44 tff(194,plain,
% 0.21/0.44 (((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | ((hole_of(pigeon_4) = hole_4) | (hole_of(pigeon_4) = hole_3) | (hole_of(pigeon_4) = hole_2) | (hole_of(pigeon_4) = hole_1) | (~hole(hole_of(pigeon_4))))) <=> ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | (hole_of(pigeon_4) = hole_4) | (hole_of(pigeon_4) = hole_3) | (hole_of(pigeon_4) = hole_2) | (hole_of(pigeon_4) = hole_1) | (~hole(hole_of(pigeon_4))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(195,plain,
% 0.21/0.44 ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | ((hole_of(pigeon_4) = hole_4) | (hole_of(pigeon_4) = hole_3) | (hole_of(pigeon_4) = hole_2) | (hole_of(pigeon_4) = hole_1) | (~hole(hole_of(pigeon_4))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(196,plain,
% 0.21/0.44 ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | (hole_of(pigeon_4) = hole_4) | (hole_of(pigeon_4) = hole_3) | (hole_of(pigeon_4) = hole_2) | (hole_of(pigeon_4) = hole_1) | (~hole(hole_of(pigeon_4)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.21/0.44 tff(197,plain,
% 0.21/0.44 ((hole_of(pigeon_4) = hole_4) | (hole_of(pigeon_4) = hole_3) | (hole_of(pigeon_4) = hole_2) | (hole_of(pigeon_4) = hole_1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[196, 193, 183])).
% 0.21/0.44 tff(198,plain,
% 0.21/0.44 (hole_of(pigeon_4) = hole_3),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[197, 169, 135, 2])).
% 0.21/0.44 tff(199,assumption,(hole_of(pigeon_4) = hole_3), introduced(assumption)).
% 0.21/0.44 tff(200,plain,
% 0.21/0.44 (in(pigeon_4, hole_of(pigeon_4)) <=> in(pigeon_4, hole_3)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[199])).
% 0.21/0.44 tff(201,plain,
% 0.21/0.44 (in(pigeon_4, hole_3) <=> in(pigeon_4, hole_of(pigeon_4))),
% 0.21/0.44 inference(symmetry,[status(thm)],[200])).
% 0.21/0.44 tff(202,plain,
% 0.21/0.44 ((~in(pigeon_4, hole_3)) <=> (~in(pigeon_4, hole_of(pigeon_4)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[201])).
% 0.21/0.44 tff(203,assumption,(~in(pigeon_4, hole_3)), introduced(assumption)).
% 0.21/0.44 tff(204,plain,
% 0.21/0.44 (~in(pigeon_4, hole_of(pigeon_4))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.21/0.44 tff(205,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[77, 204])).
% 0.21/0.44 tff(206,plain,((~(hole_of(pigeon_4) = hole_3)) | in(pigeon_4, hole_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(207,plain,
% 0.21/0.44 (in(pigeon_4, hole_3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[206, 198])).
% 0.21/0.44 tff(208,assumption,(hole_of(pigeon_3) = hole_3), introduced(assumption)).
% 0.21/0.44 tff(209,plain,
% 0.21/0.44 (hole_3 = hole_of(pigeon_3)),
% 0.21/0.44 inference(symmetry,[status(thm)],[208])).
% 0.21/0.44 tff(210,plain,
% 0.21/0.44 (in(pigeon_3, hole_3) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[209])).
% 0.21/0.44 tff(211,plain,
% 0.21/0.44 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_3)),
% 0.21/0.44 inference(symmetry,[status(thm)],[210])).
% 0.21/0.44 tff(212,plain,
% 0.21/0.44 (in(pigeon_3, hole_3)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[21, 211])).
% 0.21/0.44 tff(213,assumption,(in(pigeon_4, hole_3)), introduced(assumption)).
% 0.21/0.44 tff(214,plain,
% 0.21/0.44 (hole(hole_3) <=> hole(hole_3)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(215,axiom,(hole(hole_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hole_3')).
% 0.21/0.44 tff(216,plain,
% 0.21/0.44 (hole(hole_3)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.21/0.44 tff(217,plain,
% 0.21/0.44 ((~(pigeon_3 = pigeon_4)) <=> (~(pigeon_3 = pigeon_4))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(218,axiom,(~(pigeon_3 = pigeon_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_3_is_not_pigeon_4')).
% 0.21/0.44 tff(219,plain,
% 0.21/0.44 (~(pigeon_3 = pigeon_4)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.21/0.44 tff(220,plain,
% 0.21/0.44 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_3 = pigeon_4) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_4) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(221,plain,
% 0.21/0.44 (((~hole(hole_3)) | (pigeon_3 = pigeon_4) | (~in(pigeon_4, hole_3)) | (~in(pigeon_3, hole_3)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_3))) <=> ((pigeon_3 = pigeon_4) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(222,plain,
% 0.21/0.44 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_3 = pigeon_4) | (~in(pigeon_4, hole_3)) | (~in(pigeon_3, hole_3)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_3 = pigeon_4) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[221])).
% 0.21/0.44 tff(223,plain,
% 0.21/0.44 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_3 = pigeon_4) | (~in(pigeon_4, hole_3)) | (~in(pigeon_3, hole_3)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_4) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[222, 220])).
% 0.21/0.44 tff(224,plain,
% 0.21/0.44 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_3 = pigeon_4) | (~in(pigeon_4, hole_3)) | (~in(pigeon_3, hole_3)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_3)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(225,plain,
% 0.21/0.44 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_4) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.21/0.44 tff(226,plain,
% 0.21/0.44 (~in(pigeon_3, hole_3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[225, 17, 58, 219, 216, 32, 213])).
% 0.21/0.44 tff(227,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[226, 212])).
% 0.21/0.44 tff(228,plain,((~(hole_of(pigeon_3) = hole_3)) | (~in(pigeon_4, hole_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(229,plain,
% 0.21/0.44 (~(hole_of(pigeon_3) = hole_3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[228, 207])).
% 0.21/0.45 tff(230,plain,
% 0.21/0.45 (((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | (hole(hole_of(pigeon_3)) | (~pigeon(pigeon_3)))) <=> ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | hole(hole_of(pigeon_3)) | (~pigeon(pigeon_3)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(231,plain,
% 0.21/0.45 ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | (hole(hole_of(pigeon_3)) | (~pigeon(pigeon_3)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(232,plain,
% 0.21/0.45 ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | hole(hole_of(pigeon_3)) | (~pigeon(pigeon_3))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.21/0.45 tff(233,plain,
% 0.21/0.45 (hole(hole_of(pigeon_3))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[232, 17, 179])).
% 0.21/0.45 tff(234,plain,
% 0.21/0.45 (((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | ((hole_of(pigeon_3) = hole_4) | (hole_of(pigeon_3) = hole_3) | (hole_of(pigeon_3) = hole_2) | (hole_of(pigeon_3) = hole_1) | (~hole(hole_of(pigeon_3))))) <=> ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | (hole_of(pigeon_3) = hole_4) | (hole_of(pigeon_3) = hole_3) | (hole_of(pigeon_3) = hole_2) | (hole_of(pigeon_3) = hole_1) | (~hole(hole_of(pigeon_3))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(235,plain,
% 0.21/0.45 ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | ((hole_of(pigeon_3) = hole_4) | (hole_of(pigeon_3) = hole_3) | (hole_of(pigeon_3) = hole_2) | (hole_of(pigeon_3) = hole_1) | (~hole(hole_of(pigeon_3))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(236,plain,
% 0.21/0.45 ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | (hole_of(pigeon_3) = hole_4) | (hole_of(pigeon_3) = hole_3) | (hole_of(pigeon_3) = hole_2) | (hole_of(pigeon_3) = hole_1) | (~hole(hole_of(pigeon_3)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.21/0.45 tff(237,plain,
% 0.21/0.45 ((hole_of(pigeon_3) = hole_4) | (hole_of(pigeon_3) = hole_3) | (hole_of(pigeon_3) = hole_2) | (hole_of(pigeon_3) = hole_1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[236, 193, 233])).
% 0.21/0.45 tff(238,plain,
% 0.21/0.45 (hole_of(pigeon_3) = hole_4),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[237, 229, 137, 139])).
% 0.21/0.45 tff(239,assumption,(hole_of(pigeon_3) = hole_4), introduced(assumption)).
% 0.21/0.45 tff(240,plain,
% 0.21/0.45 (hole_4 = hole_of(pigeon_3)),
% 0.21/0.45 inference(symmetry,[status(thm)],[239])).
% 0.21/0.45 tff(241,plain,
% 0.21/0.45 (in(pigeon_3, hole_4) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[240])).
% 0.21/0.45 tff(242,plain,
% 0.21/0.45 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_4)),
% 0.21/0.45 inference(symmetry,[status(thm)],[241])).
% 0.21/0.45 tff(243,plain,
% 0.21/0.45 (in(pigeon_3, hole_4)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[21, 242])).
% 0.21/0.45 tff(244,assumption,(in(pigeon_5, hole_4)), introduced(assumption)).
% 0.21/0.45 tff(245,plain,
% 0.21/0.45 (hole(hole_4) <=> hole(hole_4)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(246,axiom,(hole(hole_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hole_4')).
% 0.21/0.45 tff(247,plain,
% 0.21/0.45 (hole(hole_4)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.21/0.45 tff(248,plain,
% 0.21/0.45 ((~(pigeon_3 = pigeon_5)) <=> (~(pigeon_3 = pigeon_5))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(249,axiom,(~(pigeon_3 = pigeon_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_3_is_not_pigeon_5')).
% 0.21/0.45 tff(250,plain,
% 0.21/0.45 (~(pigeon_3 = pigeon_5)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.21/0.45 tff(251,plain,
% 0.21/0.45 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_3, hole_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_3, hole_4)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(252,plain,
% 0.21/0.45 (((~hole(hole_4)) | (pigeon_3 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_3, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_3))) <=> ((pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_3, hole_4)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(253,plain,
% 0.21/0.45 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_3 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_3, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_3, hole_4))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[252])).
% 0.21/0.45 tff(254,plain,
% 0.21/0.45 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_3 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_3, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_3, hole_4)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[253, 251])).
% 0.21/0.45 tff(255,plain,
% 0.21/0.45 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_3 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_3, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_3)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(256,plain,
% 0.21/0.45 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_3, hole_4))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.21/0.45 tff(257,plain,
% 0.21/0.45 (~in(pigeon_3, hole_4)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[256, 17, 87, 250, 247, 32, 244])).
% 0.21/0.45 tff(258,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[257, 243])).
% 0.21/0.45 tff(259,plain,((~(hole_of(pigeon_3) = hole_4)) | (~in(pigeon_5, hole_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(260,plain,
% 0.21/0.45 (~in(pigeon_5, hole_4)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[259, 238])).
% 0.21/0.45 tff(261,plain,
% 0.21/0.45 (in(pigeon_2, hole_of(pigeon_2)) <=> in(pigeon_2, hole_1)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[140])).
% 0.21/0.45 tff(262,plain,
% 0.21/0.45 (in(pigeon_2, hole_1) <=> in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.45 inference(symmetry,[status(thm)],[261])).
% 0.21/0.45 tff(263,plain,
% 0.21/0.45 ((~in(pigeon_2, hole_1)) <=> (~in(pigeon_2, hole_of(pigeon_2)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[262])).
% 0.21/0.45 tff(264,assumption,(~in(pigeon_2, hole_1)), introduced(assumption)).
% 0.21/0.45 tff(265,plain,
% 0.21/0.45 (~in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.21/0.45 tff(266,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[131, 265])).
% 0.21/0.45 tff(267,plain,((~(hole_of(pigeon_2) = hole_1)) | in(pigeon_2, hole_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(268,plain,
% 0.21/0.45 (in(pigeon_2, hole_1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[267, 140])).
% 0.21/0.45 tff(269,assumption,(in(pigeon_5, hole_1)), introduced(assumption)).
% 0.21/0.45 tff(270,assumption,(in(pigeon_2, hole_1)), introduced(assumption)).
% 0.21/0.45 tff(271,plain,
% 0.21/0.45 ((~(pigeon_2 = pigeon_5)) <=> (~(pigeon_2 = pigeon_5))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(272,axiom,(~(pigeon_2 = pigeon_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_2_is_not_pigeon_5')).
% 0.21/0.45 tff(273,plain,
% 0.21/0.45 (~(pigeon_2 = pigeon_5)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.21/0.45 tff(274,plain,
% 0.21/0.45 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_5, hole_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_5, hole_1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(275,plain,
% 0.21/0.45 (((~hole(hole_1)) | (pigeon_2 = pigeon_5) | (~in(pigeon_5, hole_1)) | (~in(pigeon_2, hole_1)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_2))) <=> ((pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_5, hole_1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(276,plain,
% 0.21/0.45 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_2 = pigeon_5) | (~in(pigeon_5, hole_1)) | (~in(pigeon_2, hole_1)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_5, hole_1))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[275])).
% 0.21/0.45 tff(277,plain,
% 0.21/0.45 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_2 = pigeon_5) | (~in(pigeon_5, hole_1)) | (~in(pigeon_2, hole_1)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_5, hole_1)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[276, 274])).
% 0.21/0.45 tff(278,plain,
% 0.21/0.45 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_2 = pigeon_5) | (~in(pigeon_5, hole_1)) | (~in(pigeon_2, hole_1)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_2)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(279,plain,
% 0.21/0.45 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_5, hole_1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.21/0.45 tff(280,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[279, 112, 87, 273, 159, 32, 270, 269])).
% 0.21/0.45 tff(281,plain,((~in(pigeon_2, hole_1)) | (~in(pigeon_5, hole_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(282,plain,
% 0.21/0.45 (~in(pigeon_5, hole_1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[281, 268])).
% 0.21/0.45 tff(283,assumption,(hole_of(pigeon_5) = hole_1), introduced(assumption)).
% 0.21/0.45 tff(284,plain,
% 0.21/0.45 (hole_1 = hole_of(pigeon_5)),
% 0.21/0.45 inference(symmetry,[status(thm)],[283])).
% 0.21/0.45 tff(285,plain,
% 0.21/0.45 (in(pigeon_5, hole_1) <=> in(pigeon_5, hole_of(pigeon_5))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[284])).
% 0.21/0.46 tff(286,plain,
% 0.21/0.46 (in(pigeon_5, hole_of(pigeon_5)) <=> in(pigeon_5, hole_1)),
% 0.21/0.46 inference(symmetry,[status(thm)],[285])).
% 0.21/0.46 tff(287,plain,
% 0.21/0.46 (in(pigeon_5, hole_1)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[91, 286])).
% 0.21/0.46 tff(288,assumption,(~in(pigeon_5, hole_1)), introduced(assumption)).
% 0.21/0.46 tff(289,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[288, 287])).
% 0.21/0.46 tff(290,plain,(in(pigeon_5, hole_1) | (~(hole_of(pigeon_5) = hole_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(291,plain,
% 0.21/0.46 (~(hole_of(pigeon_5) = hole_1)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[290, 282])).
% 0.21/0.46 tff(292,assumption,(in(pigeon_5, hole_3)), introduced(assumption)).
% 0.21/0.46 tff(293,plain,
% 0.21/0.46 ((~(pigeon_4 = pigeon_5)) <=> (~(pigeon_4 = pigeon_5))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(294,axiom,(~(pigeon_4 = pigeon_5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_4_is_not_pigeon_5')).
% 0.21/0.46 tff(295,plain,
% 0.21/0.46 (~(pigeon_4 = pigeon_5)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.21/0.46 tff(296,plain,
% 0.21/0.46 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(297,plain,
% 0.21/0.46 (((~hole(hole_3)) | (pigeon_4 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_4, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_4))) <=> ((pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(298,plain,
% 0.21/0.46 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_4 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_4, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[297])).
% 0.21/0.46 tff(299,plain,
% 0.21/0.46 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_4 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_4, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[298, 296])).
% 0.21/0.46 tff(300,plain,
% 0.21/0.46 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_4 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_4, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_4)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(301,plain,
% 0.21/0.46 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.21/0.46 tff(302,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[301, 58, 87, 295, 216, 32, 213, 292])).
% 0.21/0.46 tff(303,plain,((~in(pigeon_4, hole_3)) | (~in(pigeon_5, hole_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(304,plain,
% 0.21/0.46 (~in(pigeon_5, hole_3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[303, 207])).
% 0.21/0.46 tff(305,assumption,(hole_of(pigeon_5) = hole_3), introduced(assumption)).
% 0.21/0.46 tff(306,plain,
% 0.21/0.46 (hole_3 = hole_of(pigeon_5)),
% 0.21/0.46 inference(symmetry,[status(thm)],[305])).
% 0.21/0.46 tff(307,plain,
% 0.21/0.46 (in(pigeon_5, hole_3) <=> in(pigeon_5, hole_of(pigeon_5))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[306])).
% 0.21/0.46 tff(308,plain,
% 0.21/0.46 (in(pigeon_5, hole_of(pigeon_5)) <=> in(pigeon_5, hole_3)),
% 0.21/0.46 inference(symmetry,[status(thm)],[307])).
% 0.21/0.46 tff(309,plain,
% 0.21/0.46 (in(pigeon_5, hole_3)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[91, 308])).
% 0.21/0.46 tff(310,assumption,(~in(pigeon_5, hole_3)), introduced(assumption)).
% 0.21/0.46 tff(311,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[310, 309])).
% 0.21/0.46 tff(312,plain,(in(pigeon_5, hole_3) | (~(hole_of(pigeon_5) = hole_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(313,plain,
% 0.21/0.46 (~(hole_of(pigeon_5) = hole_3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[312, 304])).
% 0.21/0.46 tff(314,plain,
% 0.21/0.46 (((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | (hole(hole_of(pigeon_5)) | (~pigeon(pigeon_5)))) <=> ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | hole(hole_of(pigeon_5)) | (~pigeon(pigeon_5)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(315,plain,
% 0.21/0.46 ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | (hole(hole_of(pigeon_5)) | (~pigeon(pigeon_5)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(316,plain,
% 0.21/0.46 ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | hole(hole_of(pigeon_5)) | (~pigeon(pigeon_5))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.21/0.46 tff(317,plain,
% 0.21/0.46 (hole(hole_of(pigeon_5))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[316, 87, 179])).
% 0.21/0.46 tff(318,plain,
% 0.21/0.46 (((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | ((hole_of(pigeon_5) = hole_4) | (hole_of(pigeon_5) = hole_3) | (hole_of(pigeon_5) = hole_2) | (hole_of(pigeon_5) = hole_1) | (~hole(hole_of(pigeon_5))))) <=> ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | (hole_of(pigeon_5) = hole_4) | (hole_of(pigeon_5) = hole_3) | (hole_of(pigeon_5) = hole_2) | (hole_of(pigeon_5) = hole_1) | (~hole(hole_of(pigeon_5))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(319,plain,
% 0.21/0.46 ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | ((hole_of(pigeon_5) = hole_4) | (hole_of(pigeon_5) = hole_3) | (hole_of(pigeon_5) = hole_2) | (hole_of(pigeon_5) = hole_1) | (~hole(hole_of(pigeon_5))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(320,plain,
% 0.21/0.46 ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | (hole_of(pigeon_5) = hole_4) | (hole_of(pigeon_5) = hole_3) | (hole_of(pigeon_5) = hole_2) | (hole_of(pigeon_5) = hole_1) | (~hole(hole_of(pigeon_5)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.21/0.46 tff(321,plain,
% 0.21/0.46 ((hole_of(pigeon_5) = hole_4) | (hole_of(pigeon_5) = hole_3) | (hole_of(pigeon_5) = hole_2) | (hole_of(pigeon_5) = hole_1)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[320, 193, 317])).
% 0.21/0.46 tff(322,plain,
% 0.21/0.46 (hole_of(pigeon_5) = hole_4),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[321, 313, 138, 291])).
% 0.21/0.46 tff(323,assumption,(hole_of(pigeon_5) = hole_4), introduced(assumption)).
% 0.21/0.46 tff(324,plain,
% 0.21/0.46 (in(pigeon_5, hole_of(pigeon_5)) <=> in(pigeon_5, hole_4)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[323])).
% 0.21/0.46 tff(325,plain,
% 0.21/0.46 (in(pigeon_5, hole_4) <=> in(pigeon_5, hole_of(pigeon_5))),
% 0.21/0.46 inference(symmetry,[status(thm)],[324])).
% 0.21/0.46 tff(326,plain,
% 0.21/0.46 ((~in(pigeon_5, hole_4)) <=> (~in(pigeon_5, hole_of(pigeon_5)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[325])).
% 0.21/0.46 tff(327,assumption,(~in(pigeon_5, hole_4)), introduced(assumption)).
% 0.21/0.46 tff(328,plain,
% 0.21/0.46 (~in(pigeon_5, hole_of(pigeon_5))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.21/0.46 tff(329,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[91, 328])).
% 0.21/0.46 tff(330,plain,((~(hole_of(pigeon_5) = hole_4)) | in(pigeon_5, hole_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(331,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[330, 322, 260])).
% 0.21/0.46 tff(332,plain,((~(hole_of(pigeon_2) = hole_1)) | (hole_of(pigeon_5) = hole_2) | (hole_of(pigeon_3) = hole_2) | (hole_of(pigeon_3) = hole_1) | (hole_of(pigeon_4) = hole_2) | (hole_of(pigeon_4) = hole_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(333,plain,
% 0.21/0.46 (~(hole_of(pigeon_2) = hole_1)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[332, 139, 137, 138, 135, 2])).
% 0.21/0.46 tff(334,assumption,(~(hole_of(pigeon_2) = hole_4)), introduced(assumption)).
% 0.21/0.46 tff(335,plain,
% 0.21/0.46 (((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | (hole(hole_of(pigeon_2)) | (~pigeon(pigeon_2)))) <=> ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | hole(hole_of(pigeon_2)) | (~pigeon(pigeon_2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(336,plain,
% 0.21/0.46 ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | (hole(hole_of(pigeon_2)) | (~pigeon(pigeon_2)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(337,plain,
% 0.21/0.46 ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | hole(hole_of(pigeon_2)) | (~pigeon(pigeon_2))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.21/0.46 tff(338,plain,
% 0.21/0.46 (hole(hole_of(pigeon_2))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[337, 112, 179])).
% 0.21/0.46 tff(339,plain,
% 0.21/0.46 (((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | ((hole_of(pigeon_2) = hole_4) | (hole_of(pigeon_2) = hole_3) | (hole_of(pigeon_2) = hole_2) | (hole_of(pigeon_2) = hole_1) | (~hole(hole_of(pigeon_2))))) <=> ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | (hole_of(pigeon_2) = hole_4) | (hole_of(pigeon_2) = hole_3) | (hole_of(pigeon_2) = hole_2) | (hole_of(pigeon_2) = hole_1) | (~hole(hole_of(pigeon_2))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(340,plain,
% 0.21/0.46 ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | ((hole_of(pigeon_2) = hole_4) | (hole_of(pigeon_2) = hole_3) | (hole_of(pigeon_2) = hole_2) | (hole_of(pigeon_2) = hole_1) | (~hole(hole_of(pigeon_2))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(341,plain,
% 0.21/0.46 ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | (hole_of(pigeon_2) = hole_4) | (hole_of(pigeon_2) = hole_3) | (hole_of(pigeon_2) = hole_2) | (hole_of(pigeon_2) = hole_1) | (~hole(hole_of(pigeon_2)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.21/0.46 tff(342,plain,
% 0.21/0.46 ((hole_of(pigeon_2) = hole_4) | (hole_of(pigeon_2) = hole_3) | (hole_of(pigeon_2) = hole_2) | (hole_of(pigeon_2) = hole_1)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[341, 193, 338])).
% 0.21/0.46 tff(343,plain,
% 0.21/0.46 (hole_of(pigeon_2) = hole_3),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[342, 1, 136, 334])).
% 0.21/0.46 tff(344,assumption,(hole_of(pigeon_2) = hole_3), introduced(assumption)).
% 0.21/0.46 tff(345,plain,
% 0.21/0.46 (hole_3 = hole_of(pigeon_2)),
% 0.21/0.46 inference(symmetry,[status(thm)],[344])).
% 0.21/0.46 tff(346,plain,
% 0.21/0.46 (in(pigeon_2, hole_3) <=> in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[345])).
% 0.21/0.46 tff(347,plain,
% 0.21/0.46 (in(pigeon_2, hole_of(pigeon_2)) <=> in(pigeon_2, hole_3)),
% 0.21/0.46 inference(symmetry,[status(thm)],[346])).
% 0.21/0.46 tff(348,plain,
% 0.21/0.46 (in(pigeon_2, hole_3)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[131, 347])).
% 0.21/0.46 tff(349,assumption,(~(hole_of(pigeon_3) = hole_4)), introduced(assumption)).
% 0.21/0.46 tff(350,plain,
% 0.21/0.46 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(351,plain,
% 0.21/0.46 (((~hole(hole_3)) | (pigeon_2 = pigeon_4) | (~in(pigeon_4, hole_3)) | (~in(pigeon_2, hole_3)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_2))) <=> ((pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(352,plain,
% 0.21/0.46 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_2 = pigeon_4) | (~in(pigeon_4, hole_3)) | (~in(pigeon_2, hole_3)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[351])).
% 0.21/0.46 tff(353,plain,
% 0.21/0.46 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_2 = pigeon_4) | (~in(pigeon_4, hole_3)) | (~in(pigeon_2, hole_3)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[352, 350])).
% 0.21/0.46 tff(354,plain,
% 0.21/0.46 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_2 = pigeon_4) | (~in(pigeon_4, hole_3)) | (~in(pigeon_2, hole_3)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_2)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(355,plain,
% 0.21/0.46 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.21/0.46 tff(356,plain,
% 0.21/0.46 ((~in(pigeon_4, hole_3)) | (~in(pigeon_2, hole_3))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[355, 112, 58, 151, 216, 32])).
% 0.21/0.46 tff(357,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[356, 348, 213])).
% 0.21/0.46 tff(358,plain,((~in(pigeon_4, hole_3)) | (~(hole_of(pigeon_2) = hole_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(359,plain,
% 0.21/0.46 (~in(pigeon_4, hole_3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[358, 344])).
% 0.21/0.46 tff(360,plain,
% 0.21/0.46 (~(hole_of(pigeon_4) = hole_3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[206, 359])).
% 0.21/0.46 tff(361,plain,
% 0.21/0.46 (hole_of(pigeon_4) = hole_1),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[197, 360, 2, 135])).
% 0.21/0.46 tff(362,plain,
% 0.21/0.46 ((pigeon_4 = pigeon_3) <=> (pigeon_3 = pigeon_4)),
% 0.21/0.46 inference(commutativity,[status(thm)],[])).
% 0.21/0.46 tff(363,plain,
% 0.21/0.46 ((pigeon_3 = pigeon_4) <=> (pigeon_4 = pigeon_3)),
% 0.21/0.46 inference(symmetry,[status(thm)],[362])).
% 0.21/0.46 tff(364,plain,
% 0.21/0.46 ((~(pigeon_3 = pigeon_4)) <=> (~(pigeon_4 = pigeon_3))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[363])).
% 0.21/0.46 tff(365,plain,
% 0.21/0.46 (~(pigeon_4 = pigeon_3)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[219, 364])).
% 0.21/0.46 tff(366,assumption,(hole_of(pigeon_3) = hole_1), introduced(assumption)).
% 0.21/0.47 tff(367,plain,
% 0.21/0.47 (hole_1 = hole_of(pigeon_3)),
% 0.21/0.47 inference(symmetry,[status(thm)],[366])).
% 0.21/0.47 tff(368,plain,
% 0.21/0.47 (in(pigeon_3, hole_1) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[367])).
% 0.21/0.47 tff(369,plain,
% 0.21/0.47 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_1)),
% 0.21/0.47 inference(symmetry,[status(thm)],[368])).
% 0.21/0.47 tff(370,plain,
% 0.21/0.47 (in(pigeon_3, hole_1)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[21, 369])).
% 0.21/0.47 tff(371,plain,
% 0.21/0.47 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (pigeon_4 = pigeon_3))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (pigeon_4 = pigeon_3))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(372,plain,
% 0.21/0.47 (((~hole(hole_1)) | (pigeon_4 = pigeon_3) | (~in(pigeon_3, hole_1)) | (~in(pigeon_4, hole_1)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4))) <=> ((~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (pigeon_4 = pigeon_3))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(373,plain,
% 0.21/0.47 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_4 = pigeon_3) | (~in(pigeon_3, hole_1)) | (~in(pigeon_4, hole_1)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (pigeon_4 = pigeon_3)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[372])).
% 0.21/0.47 tff(374,plain,
% 0.21/0.47 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_4 = pigeon_3) | (~in(pigeon_3, hole_1)) | (~in(pigeon_4, hole_1)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (pigeon_4 = pigeon_3))),
% 0.21/0.47 inference(transitivity,[status(thm)],[373, 371])).
% 0.21/0.47 tff(375,plain,
% 0.21/0.47 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_4 = pigeon_3) | (~in(pigeon_3, hole_1)) | (~in(pigeon_4, hole_1)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(376,plain,
% 0.21/0.47 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (pigeon_4 = pigeon_3)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.21/0.47 tff(377,plain,
% 0.21/0.47 ((~in(pigeon_4, hole_1)) | (~in(pigeon_3, hole_1)) | (pigeon_4 = pigeon_3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[376, 17, 58, 159, 32])).
% 0.21/0.47 tff(378,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[377, 370, 145, 365])).
% 0.21/0.47 tff(379,plain,((~(hole_of(pigeon_3) = hole_1)) | (~(hole_of(pigeon_4) = hole_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(380,plain,
% 0.21/0.47 (~(hole_of(pigeon_3) = hole_1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[379, 361])).
% 0.21/0.47 tff(381,plain,
% 0.21/0.47 (hole_of(pigeon_3) = hole_3),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[237, 380, 349, 137])).
% 0.21/0.47 tff(382,plain,
% 0.21/0.47 (hole_3 = hole_of(pigeon_3)),
% 0.21/0.47 inference(symmetry,[status(thm)],[381])).
% 0.21/0.47 tff(383,plain,
% 0.21/0.47 (in(pigeon_3, hole_3) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[382])).
% 0.21/0.47 tff(384,plain,
% 0.21/0.47 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_3)),
% 0.21/0.47 inference(symmetry,[status(thm)],[383])).
% 0.21/0.47 tff(385,plain,
% 0.21/0.47 (in(pigeon_3, hole_3)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[21, 384])).
% 0.21/0.47 tff(386,plain,
% 0.21/0.47 ((~(pigeon_2 = pigeon_3)) <=> (~(pigeon_2 = pigeon_3))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(387,axiom,(~(pigeon_2 = pigeon_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pigeon_2_is_not_pigeon_3')).
% 0.21/0.47 tff(388,plain,
% 0.21/0.47 (~(pigeon_2 = pigeon_3)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[387, 386])).
% 0.21/0.47 tff(389,plain,
% 0.21/0.47 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(390,plain,
% 0.21/0.47 (((~hole(hole_3)) | (pigeon_2 = pigeon_3) | (~in(pigeon_3, hole_3)) | (~in(pigeon_2, hole_3)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_2))) <=> ((pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(391,plain,
% 0.21/0.47 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_2 = pigeon_3) | (~in(pigeon_3, hole_3)) | (~in(pigeon_2, hole_3)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[390])).
% 0.21/0.47 tff(392,plain,
% 0.21/0.47 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_2 = pigeon_3) | (~in(pigeon_3, hole_3)) | (~in(pigeon_2, hole_3)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[391, 389])).
% 0.21/0.47 tff(393,plain,
% 0.21/0.47 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_2 = pigeon_3) | (~in(pigeon_3, hole_3)) | (~in(pigeon_2, hole_3)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_2)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(394,plain,
% 0.21/0.47 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.21/0.47 tff(395,plain,
% 0.21/0.47 ((~in(pigeon_2, hole_3)) | (~in(pigeon_3, hole_3))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[394, 112, 17, 388, 216, 32])).
% 0.21/0.47 tff(396,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[395, 385, 348])).
% 0.21/0.47 tff(397,plain,((~(hole_of(pigeon_2) = hole_3)) | (hole_of(pigeon_3) = hole_4) | (hole_of(pigeon_3) = hole_2) | (hole_of(pigeon_4) = hole_4) | (hole_of(pigeon_4) = hole_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(398,plain,
% 0.21/0.47 (hole_of(pigeon_3) = hole_4),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[397, 343, 137, 2, 135])).
% 0.21/0.47 tff(399,plain,
% 0.21/0.47 (~in(pigeon_5, hole_4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[259, 398])).
% 0.21/0.47 tff(400,plain,
% 0.21/0.47 (~(hole_of(pigeon_5) = hole_4)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[330, 399])).
% 0.21/0.47 tff(401,plain,
% 0.21/0.47 (in(pigeon_2, hole_of(pigeon_2)) <=> in(pigeon_2, hole_3)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[344])).
% 0.21/0.47 tff(402,plain,
% 0.21/0.47 (in(pigeon_2, hole_3) <=> in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.47 inference(symmetry,[status(thm)],[401])).
% 0.21/0.47 tff(403,plain,
% 0.21/0.47 ((~in(pigeon_2, hole_3)) <=> (~in(pigeon_2, hole_of(pigeon_2)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[402])).
% 0.21/0.47 tff(404,assumption,(~in(pigeon_2, hole_3)), introduced(assumption)).
% 0.21/0.47 tff(405,plain,
% 0.21/0.47 (~in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.21/0.47 tff(406,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[131, 405])).
% 0.21/0.47 tff(407,plain,((~(hole_of(pigeon_2) = hole_3)) | in(pigeon_2, hole_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(408,plain,
% 0.21/0.47 (in(pigeon_2, hole_3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[407, 343])).
% 0.21/0.47 tff(409,assumption,(in(pigeon_2, hole_3)), introduced(assumption)).
% 0.21/0.47 tff(410,plain,
% 0.21/0.47 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(411,plain,
% 0.21/0.47 (((~hole(hole_3)) | (pigeon_2 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_2, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_2))) <=> ((pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(412,plain,
% 0.21/0.47 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_2 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_2, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[411])).
% 0.21/0.47 tff(413,plain,
% 0.21/0.47 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_2 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_2, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[412, 410])).
% 0.21/0.47 tff(414,plain,
% 0.21/0.47 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_2 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_2, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_2)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(415,plain,
% 0.21/0.47 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.21/0.47 tff(416,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[415, 112, 87, 273, 216, 32, 409, 292])).
% 0.21/0.47 tff(417,plain,((~in(pigeon_2, hole_3)) | (~in(pigeon_5, hole_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(418,plain,
% 0.21/0.47 (~in(pigeon_5, hole_3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[417, 408])).
% 0.21/0.47 tff(419,plain,
% 0.21/0.47 (~(hole_of(pigeon_5) = hole_3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[312, 418])).
% 0.21/0.47 tff(420,plain,
% 0.21/0.47 (hole_of(pigeon_5) = hole_1),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[321, 419, 138, 400])).
% 0.21/0.47 tff(421,plain,
% 0.21/0.47 (in(pigeon_5, hole_1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[290, 420])).
% 0.21/0.47 tff(422,plain,
% 0.21/0.47 (~(hole_of(pigeon_2) = hole_3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[358, 213])).
% 0.21/0.47 tff(423,plain,
% 0.21/0.47 (hole_of(pigeon_2) = hole_4),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[342, 422, 1, 136])).
% 0.21/0.47 tff(424,plain,
% 0.21/0.47 (hole_4 = hole_of(pigeon_2)),
% 0.21/0.47 inference(symmetry,[status(thm)],[423])).
% 0.21/0.47 tff(425,plain,
% 0.21/0.47 (in(pigeon_2, hole_4) <=> in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[424])).
% 0.21/0.47 tff(426,plain,
% 0.21/0.47 (in(pigeon_2, hole_of(pigeon_2)) <=> in(pigeon_2, hole_4)),
% 0.21/0.47 inference(symmetry,[status(thm)],[425])).
% 0.21/0.47 tff(427,plain,
% 0.21/0.47 (in(pigeon_2, hole_4)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[131, 426])).
% 0.21/0.47 tff(428,plain,
% 0.21/0.47 (~(hole_of(pigeon_3) = hole_3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[228, 213])).
% 0.21/0.47 tff(429,plain,
% 0.21/0.47 (hole_of(pigeon_3) = hole_4),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[237, 428, 139, 137])).
% 0.21/0.47 tff(430,plain,
% 0.21/0.47 (hole_4 = hole_of(pigeon_3)),
% 0.21/0.47 inference(symmetry,[status(thm)],[429])).
% 0.21/0.47 tff(431,plain,
% 0.21/0.47 (in(pigeon_3, hole_4) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[430])).
% 0.21/0.47 tff(432,plain,
% 0.21/0.47 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_4)),
% 0.21/0.47 inference(symmetry,[status(thm)],[431])).
% 0.21/0.47 tff(433,plain,
% 0.21/0.47 (in(pigeon_3, hole_4)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[21, 432])).
% 0.21/0.47 tff(434,plain,
% 0.21/0.47 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(435,plain,
% 0.21/0.48 (((~hole(hole_4)) | (pigeon_2 = pigeon_3) | (~in(pigeon_3, hole_4)) | (~in(pigeon_2, hole_4)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_2))) <=> ((pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(436,plain,
% 0.21/0.48 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_2 = pigeon_3) | (~in(pigeon_3, hole_4)) | (~in(pigeon_2, hole_4)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[435])).
% 0.21/0.48 tff(437,plain,
% 0.21/0.48 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_2 = pigeon_3) | (~in(pigeon_3, hole_4)) | (~in(pigeon_2, hole_4)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[436, 434])).
% 0.21/0.48 tff(438,plain,
% 0.21/0.48 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_2 = pigeon_3) | (~in(pigeon_3, hole_4)) | (~in(pigeon_2, hole_4)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_2)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(439,plain,
% 0.21/0.48 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.21/0.48 tff(440,plain,
% 0.21/0.48 ((~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[439, 112, 17, 388, 247, 32])).
% 0.21/0.48 tff(441,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[440, 433, 427])).
% 0.21/0.48 tff(442,plain,((~in(pigeon_4, hole_3)) | (hole_of(pigeon_3) = hole_1) | (hole_of(pigeon_3) = hole_2) | (hole_of(pigeon_2) = hole_1) | (hole_of(pigeon_2) = hole_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(443,plain,
% 0.21/0.48 (~in(pigeon_4, hole_3)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[442, 1, 136, 137, 139])).
% 0.21/0.48 tff(444,plain,
% 0.21/0.48 (~(hole_of(pigeon_4) = hole_3)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[206, 443])).
% 0.21/0.48 tff(445,plain,
% 0.21/0.48 (hole_of(pigeon_4) = hole_1),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[197, 444, 135, 2])).
% 0.21/0.48 tff(446,plain,
% 0.21/0.48 (in(pigeon_4, hole_of(pigeon_4)) <=> in(pigeon_4, hole_1)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[141])).
% 0.21/0.48 tff(447,plain,
% 0.21/0.48 (in(pigeon_4, hole_1) <=> in(pigeon_4, hole_of(pigeon_4))),
% 0.21/0.48 inference(symmetry,[status(thm)],[446])).
% 0.21/0.48 tff(448,plain,
% 0.21/0.48 ((~in(pigeon_4, hole_1)) <=> (~in(pigeon_4, hole_of(pigeon_4)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[447])).
% 0.21/0.48 tff(449,assumption,(~in(pigeon_4, hole_1)), introduced(assumption)).
% 0.21/0.48 tff(450,plain,
% 0.21/0.48 (~in(pigeon_4, hole_of(pigeon_4))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.21/0.48 tff(451,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[77, 450])).
% 0.21/0.48 tff(452,plain,((~(hole_of(pigeon_4) = hole_1)) | in(pigeon_4, hole_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(453,plain,
% 0.21/0.48 (in(pigeon_4, hole_1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[452, 445])).
% 0.21/0.48 tff(454,plain,
% 0.21/0.48 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_5, hole_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_5, hole_1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(455,plain,
% 0.21/0.48 (((~hole(hole_1)) | (pigeon_4 = pigeon_5) | (~in(pigeon_5, hole_1)) | (~in(pigeon_4, hole_1)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_4))) <=> ((pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_5, hole_1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(456,plain,
% 0.21/0.48 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_4 = pigeon_5) | (~in(pigeon_5, hole_1)) | (~in(pigeon_4, hole_1)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_5, hole_1))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[455])).
% 0.21/0.48 tff(457,plain,
% 0.21/0.48 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_4 = pigeon_5) | (~in(pigeon_5, hole_1)) | (~in(pigeon_4, hole_1)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_5, hole_1)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[456, 454])).
% 0.21/0.48 tff(458,plain,
% 0.21/0.48 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_4 = pigeon_5) | (~in(pigeon_5, hole_1)) | (~in(pigeon_4, hole_1)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_4)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(459,plain,
% 0.21/0.48 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_5, hole_1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.21/0.48 tff(460,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[459, 58, 87, 295, 159, 32, 453, 421])).
% 0.21/0.48 tff(461,plain,((hole_of(pigeon_2) = hole_1) | (hole_of(pigeon_5) = hole_2) | (hole_of(pigeon_4) = hole_2) | (hole_of(pigeon_4) = hole_4) | (hole_of(pigeon_3) = hole_2) | (hole_of(pigeon_2) = hole_2) | (hole_of(pigeon_3) = hole_1) | (hole_of(pigeon_2) = hole_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(462,plain,
% 0.21/0.48 (hole_of(pigeon_2) = hole_4),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[461, 333, 135, 2, 137, 136, 139, 138])).
% 0.21/0.48 tff(463,plain,
% 0.21/0.48 (hole_4 = hole_of(pigeon_2)),
% 0.21/0.48 inference(symmetry,[status(thm)],[462])).
% 0.21/0.48 tff(464,plain,
% 0.21/0.48 (in(pigeon_2, hole_4) <=> in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[463])).
% 0.21/0.48 tff(465,plain,
% 0.21/0.48 (in(pigeon_2, hole_of(pigeon_2)) <=> in(pigeon_2, hole_4)),
% 0.21/0.48 inference(symmetry,[status(thm)],[464])).
% 0.21/0.48 tff(466,plain,
% 0.21/0.48 (in(pigeon_2, hole_4)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[131, 465])).
% 0.21/0.48 tff(467,assumption,(hole_of(pigeon_2) = hole_4), introduced(assumption)).
% 0.21/0.48 tff(468,plain,
% 0.21/0.48 (hole_4 = hole_of(pigeon_2)),
% 0.21/0.48 inference(symmetry,[status(thm)],[467])).
% 0.21/0.48 tff(469,plain,
% 0.21/0.48 (in(pigeon_2, hole_4) <=> in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[468])).
% 0.21/0.48 tff(470,plain,
% 0.21/0.48 (in(pigeon_2, hole_of(pigeon_2)) <=> in(pigeon_2, hole_4)),
% 0.21/0.48 inference(symmetry,[status(thm)],[469])).
% 0.21/0.48 tff(471,plain,
% 0.21/0.48 (in(pigeon_2, hole_4)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[131, 470])).
% 0.21/0.48 tff(472,plain,
% 0.21/0.48 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_2, hole_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_2, hole_4)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(473,plain,
% 0.21/0.48 (((~hole(hole_4)) | (pigeon_2 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_2, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_2))) <=> ((pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_2, hole_4)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(474,plain,
% 0.21/0.48 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_2 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_2, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_2, hole_4))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[473])).
% 0.21/0.48 tff(475,plain,
% 0.21/0.48 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_2 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_2, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_2, hole_4)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[474, 472])).
% 0.21/0.48 tff(476,plain,
% 0.21/0.48 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_2 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_2, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_2)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(477,plain,
% 0.21/0.48 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_5) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_2, hole_4))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.21/0.48 tff(478,plain,
% 0.21/0.48 (~in(pigeon_2, hole_4)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[477, 112, 87, 273, 247, 32, 244])).
% 0.21/0.48 tff(479,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[478, 471])).
% 0.21/0.48 tff(480,plain,((~(hole_of(pigeon_2) = hole_4)) | (~in(pigeon_5, hole_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(481,plain,
% 0.21/0.48 (~in(pigeon_5, hole_4)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[480, 462])).
% 0.21/0.48 tff(482,plain,
% 0.21/0.48 (~(hole_of(pigeon_5) = hole_4)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[330, 481])).
% 0.21/0.48 tff(483,plain,
% 0.21/0.48 (~in(pigeon_4, hole_3)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[442, 333, 136, 137, 139])).
% 0.21/0.48 tff(484,plain,
% 0.21/0.48 (~(hole_of(pigeon_4) = hole_3)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[206, 483])).
% 0.21/0.49 tff(485,plain,
% 0.21/0.49 (hole_of(pigeon_4) = hole_1),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[197, 484, 135, 2])).
% 0.21/0.49 tff(486,plain,
% 0.21/0.49 (in(pigeon_4, hole_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[452, 485])).
% 0.21/0.49 tff(487,assumption,(in(pigeon_4, hole_1)), introduced(assumption)).
% 0.21/0.49 tff(488,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[459, 58, 87, 295, 159, 32, 487, 269])).
% 0.21/0.49 tff(489,plain,((~in(pigeon_5, hole_1)) | (~in(pigeon_4, hole_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(490,plain,
% 0.21/0.49 (~in(pigeon_5, hole_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[489, 486])).
% 0.21/0.49 tff(491,plain,
% 0.21/0.49 (~(hole_of(pigeon_5) = hole_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[290, 490])).
% 0.21/0.49 tff(492,plain,
% 0.21/0.49 (hole_of(pigeon_5) = hole_3),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[321, 491, 138, 482])).
% 0.21/0.49 tff(493,plain,
% 0.21/0.49 (in(pigeon_5, hole_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[312, 492])).
% 0.21/0.49 tff(494,plain,
% 0.21/0.49 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (~in(pigeon_5, hole_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (~in(pigeon_5, hole_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(495,plain,
% 0.21/0.49 (((~hole(hole_3)) | (pigeon_3 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_3, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_3))) <=> ((pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (~in(pigeon_5, hole_3)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(496,plain,
% 0.21/0.49 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_3 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_3, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (~in(pigeon_5, hole_3))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[495])).
% 0.21/0.49 tff(497,plain,
% 0.21/0.49 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_3 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_3, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (~in(pigeon_5, hole_3)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[496, 494])).
% 0.21/0.49 tff(498,plain,
% 0.21/0.49 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_3 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_3, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_3)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(499,plain,
% 0.21/0.49 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (~in(pigeon_5, hole_3))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.21/0.49 tff(500,plain,
% 0.21/0.49 (~in(pigeon_3, hole_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[499, 17, 87, 250, 216, 32, 292])).
% 0.21/0.49 tff(501,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[500, 212])).
% 0.21/0.49 tff(502,plain,((~(hole_of(pigeon_3) = hole_3)) | (~in(pigeon_5, hole_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(503,plain,
% 0.21/0.49 (~(hole_of(pigeon_3) = hole_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[502, 493])).
% 0.21/0.49 tff(504,plain,
% 0.21/0.49 (hole_of(pigeon_3) = hole_4),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[237, 503, 137, 139])).
% 0.21/0.49 tff(505,plain,
% 0.21/0.49 (hole_4 = hole_of(pigeon_3)),
% 0.21/0.49 inference(symmetry,[status(thm)],[504])).
% 0.21/0.49 tff(506,plain,
% 0.21/0.49 (in(pigeon_3, hole_4) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[505])).
% 0.21/0.49 tff(507,plain,
% 0.21/0.49 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_4)),
% 0.21/0.49 inference(symmetry,[status(thm)],[506])).
% 0.21/0.49 tff(508,plain,
% 0.21/0.49 (in(pigeon_3, hole_4)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[21, 507])).
% 0.21/0.49 tff(509,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[440, 508, 466])).
% 0.21/0.49 tff(510,plain,((hole_of(pigeon_3) = hole_1) | (hole_of(pigeon_3) = hole_2) | (hole_of(pigeon_5) = hole_2) | (hole_of(pigeon_4) = hole_2) | (hole_of(pigeon_4) = hole_4) | (hole_of(pigeon_2) = hole_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(511,plain,
% 0.21/0.49 (hole_of(pigeon_3) = hole_1),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[510, 2, 138, 135, 137, 136])).
% 0.21/0.49 tff(512,plain,
% 0.21/0.49 (~(hole_of(pigeon_4) = hole_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[379, 511])).
% 0.21/0.49 tff(513,plain,
% 0.21/0.49 (hole_of(pigeon_4) = hole_3),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[197, 512, 135, 2])).
% 0.21/0.49 tff(514,plain,
% 0.21/0.49 (in(pigeon_4, hole_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[206, 513])).
% 0.21/0.49 tff(515,plain,
% 0.21/0.49 (~(hole_of(pigeon_2) = hole_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[358, 514])).
% 0.21/0.49 tff(516,plain,
% 0.21/0.49 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_1)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[366])).
% 0.21/0.49 tff(517,plain,
% 0.21/0.49 (in(pigeon_3, hole_1) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.49 inference(symmetry,[status(thm)],[516])).
% 0.21/0.49 tff(518,plain,
% 0.21/0.49 ((~in(pigeon_3, hole_1)) <=> (~in(pigeon_3, hole_of(pigeon_3)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[517])).
% 0.21/0.49 tff(519,assumption,(~in(pigeon_3, hole_1)), introduced(assumption)).
% 0.21/0.49 tff(520,plain,
% 0.21/0.49 (~in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[519, 518])).
% 0.21/0.49 tff(521,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[21, 520])).
% 0.21/0.49 tff(522,plain,((~(hole_of(pigeon_3) = hole_1)) | in(pigeon_3, hole_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(523,plain,
% 0.21/0.49 (in(pigeon_3, hole_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[522, 511])).
% 0.21/0.49 tff(524,assumption,(in(pigeon_3, hole_1)), introduced(assumption)).
% 0.21/0.49 tff(525,plain,
% 0.21/0.49 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (~in(pigeon_5, hole_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (~in(pigeon_5, hole_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(526,plain,
% 0.21/0.49 (((~hole(hole_1)) | (pigeon_3 = pigeon_5) | (~in(pigeon_5, hole_1)) | (~in(pigeon_3, hole_1)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_3))) <=> ((pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (~in(pigeon_5, hole_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(527,plain,
% 0.21/0.49 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_3 = pigeon_5) | (~in(pigeon_5, hole_1)) | (~in(pigeon_3, hole_1)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (~in(pigeon_5, hole_1))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[526])).
% 0.21/0.49 tff(528,plain,
% 0.21/0.49 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_3 = pigeon_5) | (~in(pigeon_5, hole_1)) | (~in(pigeon_3, hole_1)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (~in(pigeon_5, hole_1)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[527, 525])).
% 0.21/0.49 tff(529,plain,
% 0.21/0.49 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_3 = pigeon_5) | (~in(pigeon_5, hole_1)) | (~in(pigeon_3, hole_1)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_3)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(530,plain,
% 0.21/0.49 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_5) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (~in(pigeon_5, hole_1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.21/0.49 tff(531,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[530, 17, 87, 250, 159, 32, 524, 269])).
% 0.21/0.49 tff(532,plain,((~in(pigeon_3, hole_1)) | (~in(pigeon_5, hole_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(533,plain,
% 0.21/0.49 (~in(pigeon_5, hole_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[532, 523])).
% 0.21/0.49 tff(534,plain,
% 0.21/0.49 (~(hole_of(pigeon_5) = hole_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[290, 533])).
% 0.21/0.49 tff(535,plain,
% 0.21/0.49 (~in(pigeon_5, hole_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[303, 514])).
% 0.21/0.49 tff(536,plain,
% 0.21/0.49 (~(hole_of(pigeon_5) = hole_3)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[312, 535])).
% 0.21/0.49 tff(537,plain,
% 0.21/0.49 (hole_of(pigeon_5) = hole_4),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[321, 536, 138, 534])).
% 0.21/0.49 tff(538,plain,
% 0.21/0.49 (in(pigeon_5, hole_4)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[330, 537])).
% 0.21/0.49 tff(539,plain,
% 0.21/0.49 (~(hole_of(pigeon_2) = hole_4)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[480, 538])).
% 0.21/0.49 tff(540,plain,
% 0.21/0.49 (hole_of(pigeon_2) = hole_1),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[342, 539, 136, 515])).
% 0.21/0.49 tff(541,plain,
% 0.21/0.49 (in(pigeon_2, hole_1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[267, 540])).
% 0.21/0.49 tff(542,plain,
% 0.21/0.49 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(543,plain,
% 0.21/0.49 (((~hole(hole_1)) | (pigeon_2 = pigeon_3) | (~in(pigeon_3, hole_1)) | (~in(pigeon_2, hole_1)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_2))) <=> ((pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(544,plain,
% 0.21/0.49 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_2 = pigeon_3) | (~in(pigeon_3, hole_1)) | (~in(pigeon_2, hole_1)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[543])).
% 0.21/0.49 tff(545,plain,
% 0.21/0.49 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_2 = pigeon_3) | (~in(pigeon_3, hole_1)) | (~in(pigeon_2, hole_1)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[544, 542])).
% 0.21/0.49 tff(546,plain,
% 0.21/0.49 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_2 = pigeon_3) | (~in(pigeon_3, hole_1)) | (~in(pigeon_2, hole_1)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_2)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(547,plain,
% 0.21/0.49 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_3) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.21/0.49 tff(548,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[547, 112, 17, 388, 159, 32, 523, 541])).
% 0.21/0.49 tff(549,plain,((hole_of(pigeon_4) = hole_4) | (hole_of(pigeon_2) = hole_2) | (hole_of(pigeon_5) = hole_2) | (hole_of(pigeon_4) = hole_2) | (hole_of(pigeon_3) = hole_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(550,plain,
% 0.21/0.49 (hole_of(pigeon_4) = hole_4),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[549, 134, 105, 80, 51])).
% 0.21/0.49 tff(551,assumption,(hole_of(pigeon_4) = hole_4), introduced(assumption)).
% 0.21/0.49 tff(552,plain,
% 0.21/0.49 (hole_4 = hole_of(pigeon_4)),
% 0.21/0.49 inference(symmetry,[status(thm)],[551])).
% 0.21/0.49 tff(553,plain,
% 0.21/0.49 (in(pigeon_4, hole_4) <=> in(pigeon_4, hole_of(pigeon_4))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[552])).
% 0.21/0.49 tff(554,plain,
% 0.21/0.49 (in(pigeon_4, hole_of(pigeon_4)) <=> in(pigeon_4, hole_4)),
% 0.21/0.49 inference(symmetry,[status(thm)],[553])).
% 0.21/0.49 tff(555,plain,
% 0.21/0.49 (in(pigeon_4, hole_4)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[77, 554])).
% 0.21/0.49 tff(556,plain,
% 0.21/0.49 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(557,plain,
% 0.21/0.49 (((~hole(hole_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_4)) | (~in(pigeon_4, hole_4)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4))) <=> ((~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(558,plain,
% 0.21/0.50 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_4)) | (~in(pigeon_4, hole_4)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[557])).
% 0.21/0.50 tff(559,plain,
% 0.21/0.50 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_4)) | (~in(pigeon_4, hole_4)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[558, 556])).
% 0.21/0.50 tff(560,plain,
% 0.21/0.50 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_2, hole_4)) | (~in(pigeon_4, hole_4)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(561,plain,
% 0.21/0.50 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (pigeon_4 = pigeon_2) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.21/0.50 tff(562,plain,
% 0.21/0.50 ((pigeon_4 = pigeon_2) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[561, 112, 58, 247, 32])).
% 0.21/0.50 tff(563,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[562, 555, 152, 471])).
% 0.21/0.50 tff(564,plain,((~(hole_of(pigeon_2) = hole_4)) | (~(hole_of(pigeon_4) = hole_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(565,plain,
% 0.21/0.50 (~(hole_of(pigeon_2) = hole_4)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[564, 550])).
% 0.21/0.50 tff(566,plain,
% 0.21/0.50 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_4, hole_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_4, hole_4)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(567,plain,
% 0.21/0.50 (((~hole(hole_4)) | (pigeon_4 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_4, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_4))) <=> ((pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_4, hole_4)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(568,plain,
% 0.21/0.50 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_4 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_4, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_4, hole_4))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[567])).
% 0.21/0.50 tff(569,plain,
% 0.21/0.50 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_4 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_4, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_4, hole_4)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[568, 566])).
% 0.21/0.50 tff(570,plain,
% 0.21/0.50 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_4 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_4, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_4)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(571,plain,
% 0.21/0.50 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_4 = pigeon_5) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_4, hole_4))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.21/0.50 tff(572,plain,
% 0.21/0.50 (~in(pigeon_4, hole_4)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[571, 58, 87, 295, 247, 32, 244])).
% 0.21/0.50 tff(573,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[572, 555])).
% 0.21/0.50 tff(574,plain,((~(hole_of(pigeon_4) = hole_4)) | (~in(pigeon_5, hole_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(575,plain,
% 0.21/0.50 (~in(pigeon_5, hole_4)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[574, 550])).
% 0.21/0.50 tff(576,plain,
% 0.21/0.50 (~(hole_of(pigeon_5) = hole_4)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[330, 575])).
% 0.21/0.50 tff(577,plain,
% 0.21/0.50 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_4, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_4 = pigeon_3))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_4, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_4 = pigeon_3))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(578,plain,
% 0.21/0.50 (((~hole(hole_4)) | (pigeon_4 = pigeon_3) | (~in(pigeon_3, hole_4)) | (~in(pigeon_4, hole_4)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4))) <=> ((~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_4, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_4 = pigeon_3))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(579,plain,
% 0.21/0.50 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_4 = pigeon_3) | (~in(pigeon_3, hole_4)) | (~in(pigeon_4, hole_4)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_4, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_4 = pigeon_3)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[578])).
% 0.21/0.50 tff(580,plain,
% 0.21/0.50 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_4 = pigeon_3) | (~in(pigeon_3, hole_4)) | (~in(pigeon_4, hole_4)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_4, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_4 = pigeon_3))),
% 0.21/0.50 inference(transitivity,[status(thm)],[579, 577])).
% 0.21/0.50 tff(581,plain,
% 0.21/0.50 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_4 = pigeon_3) | (~in(pigeon_3, hole_4)) | (~in(pigeon_4, hole_4)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(582,plain,
% 0.21/0.50 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_4, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_4 = pigeon_3)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.21/0.50 tff(583,plain,
% 0.21/0.50 ((~in(pigeon_4, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_4 = pigeon_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[582, 17, 58, 247, 32])).
% 0.21/0.50 tff(584,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[583, 243, 555, 365])).
% 0.21/0.50 tff(585,plain,((~(hole_of(pigeon_3) = hole_4)) | (~(hole_of(pigeon_4) = hole_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(586,plain,
% 0.21/0.50 (~(hole_of(pigeon_3) = hole_4)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[585, 550])).
% 0.21/0.50 tff(587,plain,
% 0.21/0.50 ((pigeon_3 = pigeon_2) <=> (pigeon_2 = pigeon_3)),
% 0.21/0.50 inference(commutativity,[status(thm)],[])).
% 0.21/0.50 tff(588,plain,
% 0.21/0.50 ((pigeon_2 = pigeon_3) <=> (pigeon_3 = pigeon_2)),
% 0.21/0.50 inference(symmetry,[status(thm)],[587])).
% 0.21/0.50 tff(589,plain,
% 0.21/0.50 ((~(pigeon_2 = pigeon_3)) <=> (~(pigeon_3 = pigeon_2))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[588])).
% 0.21/0.50 tff(590,plain,
% 0.21/0.50 (~(pigeon_3 = pigeon_2)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[388, 589])).
% 0.21/0.50 tff(591,plain,
% 0.21/0.50 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (pigeon_3 = pigeon_2))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (pigeon_3 = pigeon_2))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(592,plain,
% 0.21/0.50 (((~hole(hole_3)) | (pigeon_3 = pigeon_2) | (~in(pigeon_2, hole_3)) | (~in(pigeon_3, hole_3)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3))) <=> ((~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (pigeon_3 = pigeon_2))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(593,plain,
% 0.21/0.50 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_3 = pigeon_2) | (~in(pigeon_2, hole_3)) | (~in(pigeon_3, hole_3)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (pigeon_3 = pigeon_2)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[592])).
% 0.21/0.50 tff(594,plain,
% 0.21/0.50 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_3 = pigeon_2) | (~in(pigeon_2, hole_3)) | (~in(pigeon_3, hole_3)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (pigeon_3 = pigeon_2))),
% 0.21/0.50 inference(transitivity,[status(thm)],[593, 591])).
% 0.21/0.50 tff(595,plain,
% 0.21/0.50 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_3 = pigeon_2) | (~in(pigeon_2, hole_3)) | (~in(pigeon_3, hole_3)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(596,plain,
% 0.21/0.50 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (pigeon_3 = pigeon_2)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[595, 594])).
% 0.21/0.50 tff(597,plain,
% 0.21/0.50 ((~in(pigeon_2, hole_3)) | (~in(pigeon_3, hole_3)) | (pigeon_3 = pigeon_2)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[596, 112, 17, 216, 32])).
% 0.21/0.50 tff(598,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[597, 212, 409, 590])).
% 0.21/0.50 tff(599,plain,((~in(pigeon_2, hole_3)) | (~(hole_of(pigeon_3) = hole_3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(600,plain,
% 0.21/0.50 (~in(pigeon_2, hole_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[599, 208])).
% 0.21/0.50 tff(601,plain,
% 0.21/0.50 (~(hole_of(pigeon_2) = hole_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[407, 600])).
% 0.21/0.50 tff(602,plain,
% 0.21/0.50 (hole_of(pigeon_2) = hole_1),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[342, 601, 136, 334])).
% 0.21/0.50 tff(603,plain,
% 0.21/0.50 (in(pigeon_2, hole_1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[267, 602])).
% 0.21/0.50 tff(604,assumption,(~(hole_of(pigeon_5) = hole_4)), introduced(assumption)).
% 0.21/0.50 tff(605,plain,
% 0.21/0.50 (~in(pigeon_5, hole_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[502, 208])).
% 0.21/0.50 tff(606,plain,
% 0.21/0.50 (~(hole_of(pigeon_5) = hole_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[312, 605])).
% 0.21/0.50 tff(607,plain,
% 0.21/0.50 (hole_of(pigeon_5) = hole_1),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[321, 606, 138, 604])).
% 0.21/0.50 tff(608,plain,
% 0.21/0.50 (in(pigeon_5, hole_1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[290, 607])).
% 0.21/0.50 tff(609,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[281, 608, 603])).
% 0.21/0.50 tff(610,plain,((~(hole_of(pigeon_3) = hole_3)) | (hole_of(pigeon_5) = hole_2) | (hole_of(pigeon_5) = hole_4) | (hole_of(pigeon_2) = hole_2) | (hole_of(pigeon_2) = hole_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(611,plain,
% 0.21/0.50 (~(hole_of(pigeon_3) = hole_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[610, 105, 576, 134, 565])).
% 0.21/0.50 tff(612,plain,
% 0.21/0.50 (hole_of(pigeon_3) = hole_1),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[237, 611, 51, 586])).
% 0.21/0.50 tff(613,plain,
% 0.21/0.50 (in(pigeon_3, hole_1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[522, 612])).
% 0.21/0.50 tff(614,plain,
% 0.21/0.50 (~in(pigeon_5, hole_1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[532, 613])).
% 0.21/0.50 tff(615,plain,
% 0.21/0.50 (~(hole_of(pigeon_5) = hole_1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[290, 614])).
% 0.21/0.50 tff(616,plain,
% 0.21/0.50 (hole_of(pigeon_5) = hole_3),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[321, 615, 105, 576])).
% 0.21/0.50 tff(617,plain,
% 0.21/0.50 (in(pigeon_5, hole_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[312, 616])).
% 0.21/0.50 tff(618,plain,
% 0.21/0.50 (~in(pigeon_2, hole_3)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[417, 617])).
% 0.21/0.51 tff(619,plain,
% 0.21/0.51 (~(hole_of(pigeon_2) = hole_3)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[407, 618])).
% 0.21/0.51 tff(620,plain,
% 0.21/0.51 (hole_of(pigeon_2) = hole_1),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[342, 619, 134, 565])).
% 0.21/0.51 tff(621,plain,
% 0.21/0.51 (in(pigeon_2, hole_1)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[267, 620])).
% 0.21/0.51 tff(622,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[547, 112, 17, 388, 159, 32, 613, 621])).
% 0.21/0.51 tff(623,plain,(~in(pigeon_1, hole_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(624,assumption,(hole_of(pigeon_1) = hole_2), introduced(assumption)).
% 0.21/0.51 tff(625,plain,
% 0.21/0.51 (hole_2 = hole_of(pigeon_1)),
% 0.21/0.51 inference(symmetry,[status(thm)],[624])).
% 0.21/0.51 tff(626,plain,
% 0.21/0.51 (in(pigeon_1, hole_2) <=> in(pigeon_1, hole_of(pigeon_1))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[625])).
% 0.21/0.51 tff(627,plain,
% 0.21/0.51 (in(pigeon_1, hole_of(pigeon_1)) <=> in(pigeon_1, hole_2)),
% 0.21/0.51 inference(symmetry,[status(thm)],[626])).
% 0.21/0.51 tff(628,plain,
% 0.21/0.51 (((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | ((~pigeon(pigeon_1)) | in(pigeon_1, hole_of(pigeon_1)))) <=> ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | (~pigeon(pigeon_1)) | in(pigeon_1, hole_of(pigeon_1)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(629,plain,
% 0.21/0.51 ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | ((~pigeon(pigeon_1)) | in(pigeon_1, hole_of(pigeon_1)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(630,plain,
% 0.21/0.51 ((~![X: $i] : ((~pigeon(X)) | in(X, hole_of(X)))) | (~pigeon(pigeon_1)) | in(pigeon_1, hole_of(pigeon_1))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.21/0.51 tff(631,plain,
% 0.21/0.51 (in(pigeon_1, hole_of(pigeon_1))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[630, 41, 14])).
% 0.21/0.51 tff(632,plain,
% 0.21/0.51 (in(pigeon_1, hole_2)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[631, 627])).
% 0.21/0.51 tff(633,assumption,(~in(pigeon_1, hole_2)), introduced(assumption)).
% 0.21/0.51 tff(634,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[633, 632])).
% 0.21/0.51 tff(635,plain,(in(pigeon_1, hole_2) | (~(hole_of(pigeon_1) = hole_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(636,plain,
% 0.21/0.51 (~(hole_of(pigeon_1) = hole_2)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[635, 623])).
% 0.21/0.51 tff(637,assumption,(~(hole_of(pigeon_1) = hole_2)), introduced(assumption)).
% 0.21/0.51 tff(638,assumption,(~(hole_of(pigeon_1) = hole_3)), introduced(assumption)).
% 0.21/0.51 tff(639,plain,
% 0.21/0.51 (in(pigeon_5, hole_1)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[290, 283])).
% 0.21/0.51 tff(640,plain,
% 0.21/0.51 (~in(pigeon_3, hole_1)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[532, 639])).
% 0.21/0.51 tff(641,plain,
% 0.21/0.51 (~(hole_of(pigeon_3) = hole_1)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[522, 640])).
% 0.21/0.51 tff(642,plain,
% 0.21/0.51 ((pigeon_5 = pigeon_1) <=> (pigeon_1 = pigeon_5)),
% 0.21/0.51 inference(commutativity,[status(thm)],[])).
% 0.21/0.51 tff(643,plain,
% 0.21/0.51 ((pigeon_1 = pigeon_5) <=> (pigeon_5 = pigeon_1)),
% 0.21/0.51 inference(symmetry,[status(thm)],[642])).
% 0.21/0.51 tff(644,plain,
% 0.21/0.51 ((~(pigeon_1 = pigeon_5)) <=> (~(pigeon_5 = pigeon_1))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[643])).
% 0.21/0.51 tff(645,plain,
% 0.21/0.51 (~(pigeon_5 = pigeon_1)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[95, 644])).
% 0.21/0.51 tff(646,assumption,(hole_of(pigeon_1) = hole_1), introduced(assumption)).
% 0.21/0.51 tff(647,plain,
% 0.21/0.51 (hole_1 = hole_of(pigeon_1)),
% 0.21/0.51 inference(symmetry,[status(thm)],[646])).
% 0.21/0.51 tff(648,plain,
% 0.21/0.51 (in(pigeon_1, hole_1) <=> in(pigeon_1, hole_of(pigeon_1))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[647])).
% 0.21/0.51 tff(649,plain,
% 0.21/0.51 (in(pigeon_1, hole_of(pigeon_1)) <=> in(pigeon_1, hole_1)),
% 0.21/0.51 inference(symmetry,[status(thm)],[648])).
% 0.21/0.51 tff(650,plain,
% 0.21/0.51 (in(pigeon_1, hole_1)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[631, 649])).
% 0.21/0.51 tff(651,plain,
% 0.21/0.51 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (pigeon_5 = pigeon_1) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)) | (~in(pigeon_5, hole_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (pigeon_5 = pigeon_1) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)) | (~in(pigeon_5, hole_1)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(652,plain,
% 0.21/0.51 (((~hole(hole_1)) | (pigeon_5 = pigeon_1) | (~in(pigeon_1, hole_1)) | (~in(pigeon_5, hole_1)) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5))) <=> ((~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (pigeon_5 = pigeon_1) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)) | (~in(pigeon_5, hole_1)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(653,plain,
% 0.21/0.51 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_5 = pigeon_1) | (~in(pigeon_1, hole_1)) | (~in(pigeon_5, hole_1)) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (pigeon_5 = pigeon_1) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)) | (~in(pigeon_5, hole_1))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[652])).
% 0.21/0.51 tff(654,plain,
% 0.21/0.51 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_5 = pigeon_1) | (~in(pigeon_1, hole_1)) | (~in(pigeon_5, hole_1)) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (pigeon_5 = pigeon_1) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)) | (~in(pigeon_5, hole_1)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[653, 651])).
% 0.21/0.51 tff(655,plain,
% 0.21/0.51 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_5 = pigeon_1) | (~in(pigeon_1, hole_1)) | (~in(pigeon_5, hole_1)) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(656,plain,
% 0.21/0.51 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (pigeon_5 = pigeon_1) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)) | (~in(pigeon_5, hole_1))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[655, 654])).
% 0.21/0.51 tff(657,plain,
% 0.21/0.51 ((pigeon_5 = pigeon_1) | (~in(pigeon_1, hole_1)) | (~in(pigeon_5, hole_1))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[656, 41, 87, 159, 32])).
% 0.21/0.51 tff(658,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[657, 650, 645, 287])).
% 0.21/0.51 tff(659,plain,((~(hole_of(pigeon_1) = hole_1)) | (~(hole_of(pigeon_5) = hole_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(660,plain,
% 0.21/0.51 (~(hole_of(pigeon_1) = hole_1)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[659, 283])).
% 0.21/0.51 tff(661,plain,
% 0.21/0.51 (((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | (hole(hole_of(pigeon_1)) | (~pigeon(pigeon_1)))) <=> ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | hole(hole_of(pigeon_1)) | (~pigeon(pigeon_1)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(662,plain,
% 0.21/0.51 ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | (hole(hole_of(pigeon_1)) | (~pigeon(pigeon_1)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(663,plain,
% 0.21/0.51 ((~![X: $i] : (hole(hole_of(X)) | (~pigeon(X)))) | hole(hole_of(pigeon_1)) | (~pigeon(pigeon_1))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.21/0.51 tff(664,plain,
% 0.21/0.51 (hole(hole_of(pigeon_1))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[663, 41, 179])).
% 0.21/0.51 tff(665,plain,
% 0.21/0.51 (((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | ((hole_of(pigeon_1) = hole_4) | (hole_of(pigeon_1) = hole_3) | (hole_of(pigeon_1) = hole_2) | (hole_of(pigeon_1) = hole_1) | (~hole(hole_of(pigeon_1))))) <=> ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | (hole_of(pigeon_1) = hole_4) | (hole_of(pigeon_1) = hole_3) | (hole_of(pigeon_1) = hole_2) | (hole_of(pigeon_1) = hole_1) | (~hole(hole_of(pigeon_1))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(666,plain,
% 0.21/0.51 ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | ((hole_of(pigeon_1) = hole_4) | (hole_of(pigeon_1) = hole_3) | (hole_of(pigeon_1) = hole_2) | (hole_of(pigeon_1) = hole_1) | (~hole(hole_of(pigeon_1))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(667,plain,
% 0.21/0.51 ((~![Hole: $i] : ((Hole = hole_4) | (Hole = hole_3) | (Hole = hole_2) | (Hole = hole_1) | (~hole(Hole)))) | (hole_of(pigeon_1) = hole_4) | (hole_of(pigeon_1) = hole_3) | (hole_of(pigeon_1) = hole_2) | (hole_of(pigeon_1) = hole_1) | (~hole(hole_of(pigeon_1)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[666, 665])).
% 0.21/0.51 tff(668,plain,
% 0.21/0.51 ((hole_of(pigeon_1) = hole_4) | (hole_of(pigeon_1) = hole_3) | (hole_of(pigeon_1) = hole_2) | (hole_of(pigeon_1) = hole_1)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[667, 193, 664])).
% 0.21/0.51 tff(669,plain,
% 0.21/0.51 (hole_of(pigeon_1) = hole_4),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[668, 660, 638, 637])).
% 0.21/0.51 tff(670,assumption,(hole_of(pigeon_1) = hole_4), introduced(assumption)).
% 0.21/0.51 tff(671,plain,
% 0.21/0.51 (hole_4 = hole_of(pigeon_1)),
% 0.21/0.51 inference(symmetry,[status(thm)],[670])).
% 0.21/0.51 tff(672,plain,
% 0.21/0.51 (in(pigeon_1, hole_4) <=> in(pigeon_1, hole_of(pigeon_1))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[671])).
% 0.21/0.51 tff(673,plain,
% 0.21/0.51 (in(pigeon_1, hole_of(pigeon_1)) <=> in(pigeon_1, hole_4)),
% 0.21/0.51 inference(symmetry,[status(thm)],[672])).
% 0.21/0.51 tff(674,plain,
% 0.21/0.51 (in(pigeon_1, hole_4)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[631, 673])).
% 0.21/0.51 tff(675,plain,
% 0.21/0.51 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_3, hole_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_3, hole_4)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(676,plain,
% 0.21/0.51 (((~hole(hole_4)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_3, hole_4)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(677,plain,
% 0.21/0.51 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_3, hole_4))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[676])).
% 0.21/0.51 tff(678,plain,
% 0.21/0.51 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_3, hole_4)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[677, 675])).
% 0.21/0.51 tff(679,plain,
% 0.21/0.51 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(680,plain,
% 0.21/0.51 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_3, hole_4))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[679, 678])).
% 0.21/0.51 tff(681,plain,
% 0.21/0.51 ((~in(pigeon_1, hole_4)) | (~in(pigeon_3, hole_4))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[680, 41, 17, 38, 247, 32])).
% 0.21/0.51 tff(682,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[681, 243, 674])).
% 0.21/0.51 tff(683,plain,((~(hole_of(pigeon_3) = hole_4)) | (~(hole_of(pigeon_1) = hole_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(684,plain,
% 0.21/0.51 (~(hole_of(pigeon_3) = hole_4)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[683, 669])).
% 0.21/0.51 tff(685,plain,
% 0.21/0.51 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_4, hole_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_4, hole_4)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(686,plain,
% 0.21/0.51 (((~hole(hole_4)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_4, hole_4)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(687,plain,
% 0.21/0.51 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_4, hole_4))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[686])).
% 0.21/0.51 tff(688,plain,
% 0.21/0.51 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_4, hole_4)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[687, 685])).
% 0.21/0.51 tff(689,plain,
% 0.21/0.51 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(690,plain,
% 0.21/0.52 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_4, hole_4))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.21/0.52 tff(691,plain,
% 0.21/0.52 ((~in(pigeon_1, hole_4)) | (~in(pigeon_4, hole_4))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[690, 41, 58, 55, 247, 32])).
% 0.21/0.52 tff(692,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[691, 555, 674])).
% 0.21/0.52 tff(693,plain,((~(hole_of(pigeon_4) = hole_4)) | (~(hole_of(pigeon_1) = hole_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(694,plain,
% 0.21/0.52 (~(hole_of(pigeon_4) = hole_4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[693, 669])).
% 0.21/0.52 tff(695,plain,
% 0.21/0.52 (~in(pigeon_2, hole_1)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[281, 639])).
% 0.21/0.52 tff(696,plain,
% 0.21/0.52 (~(hole_of(pigeon_2) = hole_1)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[267, 695])).
% 0.21/0.52 tff(697,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_2, hole_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_2, hole_4)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(698,plain,
% 0.21/0.52 (((~hole(hole_4)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_2, hole_4)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(699,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_2, hole_4))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[698])).
% 0.21/0.52 tff(700,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_2, hole_4)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[699, 697])).
% 0.21/0.52 tff(701,plain,
% 0.21/0.52 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(702,plain,
% 0.21/0.52 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~hole(hole_4)) | (~in(pigeon_1, hole_4)) | (~in(pigeon_2, hole_4))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[701, 700])).
% 0.21/0.52 tff(703,plain,
% 0.21/0.52 ((~in(pigeon_1, hole_4)) | (~in(pigeon_2, hole_4))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[702, 41, 112, 109, 247, 32])).
% 0.21/0.52 tff(704,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[703, 471, 674])).
% 0.21/0.52 tff(705,plain,((~(hole_of(pigeon_2) = hole_4)) | (~(hole_of(pigeon_1) = hole_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(706,plain,
% 0.21/0.52 (~(hole_of(pigeon_2) = hole_4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[705, 669])).
% 0.21/0.52 tff(707,assumption,(~(hole_of(pigeon_4) = hole_1)), introduced(assumption)).
% 0.21/0.52 tff(708,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_3 = pigeon_4) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_4, hole_2)) | (~in(pigeon_3, hole_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_4) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_4, hole_2)) | (~in(pigeon_3, hole_2)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(709,plain,
% 0.21/0.52 (((~hole(hole_2)) | (pigeon_3 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_3, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_3))) <=> ((pigeon_3 = pigeon_4) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_4, hole_2)) | (~in(pigeon_3, hole_2)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(710,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_3 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_3, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_3 = pigeon_4) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_4, hole_2)) | (~in(pigeon_3, hole_2))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[709])).
% 0.21/0.52 tff(711,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_3 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_3, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_4) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_4, hole_2)) | (~in(pigeon_3, hole_2)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[710, 708])).
% 0.21/0.52 tff(712,plain,
% 0.21/0.52 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_3 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_3, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_3)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(713,plain,
% 0.21/0.52 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_3 = pigeon_4) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_4, hole_2)) | (~in(pigeon_3, hole_2))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[712, 711])).
% 0.21/0.52 tff(714,plain,
% 0.21/0.52 ((~in(pigeon_4, hole_2)) | (~in(pigeon_3, hole_2))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[713, 17, 58, 219, 35, 32])).
% 0.21/0.52 tff(715,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[714, 22, 52])).
% 0.21/0.52 tff(716,plain,((~in(pigeon_4, hole_2)) | (~(hole_of(pigeon_3) = hole_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(717,plain,
% 0.21/0.52 (~in(pigeon_4, hole_2)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[716, 4])).
% 0.21/0.52 tff(718,plain,
% 0.21/0.52 (~(hole_of(pigeon_4) = hole_2)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[79, 717])).
% 0.21/0.52 tff(719,plain,
% 0.21/0.52 (hole_of(pigeon_4) = hole_3),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[197, 718, 2, 707])).
% 0.21/0.52 tff(720,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_3 = pigeon_2))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_3 = pigeon_2))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(721,plain,
% 0.21/0.52 (((~hole(hole_2)) | (pigeon_3 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_3, hole_2)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3))) <=> ((~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_3 = pigeon_2))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(722,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_3 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_3, hole_2)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_3 = pigeon_2)))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[721])).
% 0.21/0.52 tff(723,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_3 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_3, hole_2)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_3 = pigeon_2))),
% 0.21/0.52 inference(transitivity,[status(thm)],[722, 720])).
% 0.21/0.52 tff(724,plain,
% 0.21/0.52 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_3 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_3, hole_2)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(725,plain,
% 0.21/0.52 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_3 = pigeon_2)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.21/0.52 tff(726,plain,
% 0.21/0.52 ((~in(pigeon_2, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_3 = pigeon_2)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[725, 112, 17, 35, 32])).
% 0.21/0.52 tff(727,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[726, 22, 106, 590])).
% 0.21/0.52 tff(728,plain,((~in(pigeon_2, hole_2)) | (~(hole_of(pigeon_3) = hole_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(729,plain,
% 0.21/0.52 (~in(pigeon_2, hole_2)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[728, 4])).
% 0.21/0.52 tff(730,plain,
% 0.21/0.52 (~(hole_of(pigeon_2) = hole_2)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[133, 729])).
% 0.21/0.52 tff(731,plain,
% 0.21/0.52 (hole_of(pigeon_2) = hole_3),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[342, 730, 334, 1])).
% 0.21/0.52 tff(732,plain,
% 0.21/0.52 (~in(pigeon_4, hole_3)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[358, 731])).
% 0.21/0.52 tff(733,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[206, 732, 719])).
% 0.21/0.52 tff(734,plain,((~(hole_of(pigeon_3) = hole_2)) | (hole_of(pigeon_4) = hole_4) | (hole_of(pigeon_4) = hole_1) | (hole_of(pigeon_2) = hole_4) | (hole_of(pigeon_2) = hole_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(735,plain,
% 0.21/0.52 (~(hole_of(pigeon_3) = hole_2)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[734, 707, 2, 334, 1])).
% 0.21/0.52 tff(736,plain,
% 0.21/0.52 (hole_of(pigeon_3) = hole_3),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[237, 735, 349, 139])).
% 0.21/0.52 tff(737,plain,
% 0.21/0.52 (~in(pigeon_4, hole_3)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[228, 736])).
% 0.21/0.52 tff(738,plain,
% 0.21/0.52 (~(hole_of(pigeon_4) = hole_3)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[206, 737])).
% 0.21/0.52 tff(739,plain,
% 0.21/0.52 (hole_of(pigeon_4) = hole_2),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[197, 738, 2, 707])).
% 0.21/0.52 tff(740,plain,
% 0.21/0.52 (in(pigeon_4, hole_2)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[79, 739])).
% 0.21/0.52 tff(741,plain,
% 0.21/0.52 (~in(pigeon_2, hole_3)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[599, 736])).
% 0.21/0.52 tff(742,plain,
% 0.21/0.52 (~(hole_of(pigeon_2) = hole_3)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[407, 741])).
% 0.21/0.52 tff(743,plain,
% 0.21/0.52 (hole_of(pigeon_2) = hole_2),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[342, 742, 334, 1])).
% 0.21/0.52 tff(744,plain,
% 0.21/0.52 (in(pigeon_2, hole_2)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[133, 743])).
% 0.21/0.52 tff(745,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_4, hole_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_4, hole_2)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(746,plain,
% 0.21/0.52 (((~hole(hole_2)) | (pigeon_2 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_2, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_2))) <=> ((pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_4, hole_2)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(747,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_2 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_2, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_4, hole_2))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[746])).
% 0.21/0.52 tff(748,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_2 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_2, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_4, hole_2)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[747, 745])).
% 0.21/0.52 tff(749,plain,
% 0.21/0.52 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_2 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_2, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_2)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(750,plain,
% 0.21/0.52 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_2)) | (~in(pigeon_2, hole_2)) | (~in(pigeon_4, hole_2))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[749, 748])).
% 0.21/0.52 tff(751,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[750, 112, 58, 151, 35, 32, 744, 740])).
% 0.21/0.52 tff(752,plain,((hole_of(pigeon_4) = hole_1) | (hole_of(pigeon_2) = hole_4) | (hole_of(pigeon_2) = hole_1) | (hole_of(pigeon_4) = hole_4) | (hole_of(pigeon_3) = hole_4) | (hole_of(pigeon_3) = hole_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(753,plain,
% 0.21/0.52 (hole_of(pigeon_4) = hole_1),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[752, 706, 696, 694, 684, 641])).
% 0.21/0.52 tff(754,plain,
% 0.21/0.52 (in(pigeon_4, hole_1)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[452, 753])).
% 0.21/0.52 tff(755,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[459, 58, 87, 295, 159, 32, 754, 639])).
% 0.21/0.52 tff(756,plain,((~(hole_of(pigeon_5) = hole_1)) | (hole_of(pigeon_1) = hole_3) | (hole_of(pigeon_1) = hole_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(757,plain,
% 0.21/0.52 (~(hole_of(pigeon_5) = hole_1)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[756, 637, 638])).
% 0.21/0.52 tff(758,assumption,(~(hole_of(pigeon_5) = hole_3)), introduced(assumption)).
% 0.21/0.52 tff(759,assumption,(~(hole_of(pigeon_5) = hole_1)), introduced(assumption)).
% 0.21/0.52 tff(760,plain,
% 0.21/0.52 (~(hole_of(pigeon_2) = hole_4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[705, 670])).
% 0.21/0.52 tff(761,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_1, hole_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_1, hole_4)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(762,plain,
% 0.21/0.52 (((~hole(hole_4)) | (pigeon_1 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_1, hole_4)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(763,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_1 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_1, hole_4))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[762])).
% 0.21/0.52 tff(764,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_1 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_1, hole_4)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[763, 761])).
% 0.21/0.52 tff(765,plain,
% 0.21/0.52 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_1 = pigeon_5) | (~in(pigeon_5, hole_4)) | (~in(pigeon_1, hole_4)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_1)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(766,plain,
% 0.21/0.52 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_4)) | (~in(pigeon_5, hole_4)) | (~in(pigeon_1, hole_4))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[765, 764])).
% 0.21/0.52 tff(767,plain,
% 0.21/0.52 ((~in(pigeon_5, hole_4)) | (~in(pigeon_1, hole_4))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[766, 41, 87, 95, 247, 32])).
% 0.21/0.52 tff(768,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[767, 674, 244])).
% 0.21/0.52 tff(769,plain,((~in(pigeon_5, hole_4)) | (~(hole_of(pigeon_1) = hole_4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(770,plain,
% 0.21/0.52 (~in(pigeon_5, hole_4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[769, 670])).
% 0.21/0.52 tff(771,plain,
% 0.21/0.52 (~(hole_of(pigeon_5) = hole_4)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[330, 770])).
% 0.21/0.52 tff(772,plain,
% 0.21/0.52 (hole_of(pigeon_5) = hole_2),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[321, 771, 758, 759])).
% 0.21/0.52 tff(773,plain,
% 0.21/0.52 ((pigeon_5 = pigeon_2) <=> (pigeon_2 = pigeon_5)),
% 0.21/0.52 inference(commutativity,[status(thm)],[])).
% 0.21/0.52 tff(774,plain,
% 0.21/0.52 ((pigeon_2 = pigeon_5) <=> (pigeon_5 = pigeon_2)),
% 0.21/0.52 inference(symmetry,[status(thm)],[773])).
% 0.21/0.52 tff(775,plain,
% 0.21/0.52 ((~(pigeon_2 = pigeon_5)) <=> (~(pigeon_5 = pigeon_2))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[774])).
% 0.21/0.52 tff(776,plain,
% 0.21/0.52 (~(pigeon_5 = pigeon_2)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[273, 775])).
% 0.21/0.52 tff(777,plain,
% 0.21/0.52 (hole_2 = hole_of(pigeon_2)),
% 0.21/0.52 inference(symmetry,[status(thm)],[122])).
% 0.21/0.52 tff(778,plain,
% 0.21/0.52 (in(pigeon_2, hole_2) <=> in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[777])).
% 0.21/0.52 tff(779,plain,
% 0.21/0.52 (in(pigeon_2, hole_of(pigeon_2)) <=> in(pigeon_2, hole_2)),
% 0.21/0.52 inference(symmetry,[status(thm)],[778])).
% 0.21/0.52 tff(780,plain,
% 0.21/0.52 (in(pigeon_2, hole_2)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[131, 779])).
% 0.21/0.52 tff(781,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (pigeon_5 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_5, hole_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (pigeon_5 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_5, hole_2)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(782,plain,
% 0.21/0.52 (((~hole(hole_2)) | (pigeon_5 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_5, hole_2)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5))) <=> ((~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (pigeon_5 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_5, hole_2)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(783,plain,
% 0.21/0.52 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_5 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_5, hole_2)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (pigeon_5 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_5, hole_2))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[782])).
% 0.21/0.53 tff(784,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_5 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_5, hole_2)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (pigeon_5 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_5, hole_2)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[783, 781])).
% 0.21/0.53 tff(785,plain,
% 0.21/0.53 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_5 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_5, hole_2)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(786,plain,
% 0.21/0.53 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (pigeon_5 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_5, hole_2))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[785, 784])).
% 0.21/0.53 tff(787,plain,
% 0.21/0.53 ((pigeon_5 = pigeon_2) | (~in(pigeon_2, hole_2)) | (~in(pigeon_5, hole_2))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[786, 112, 87, 35, 32])).
% 0.21/0.53 tff(788,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[787, 780, 776, 92])).
% 0.21/0.53 tff(789,plain,((~(hole_of(pigeon_2) = hole_2)) | (~(hole_of(pigeon_5) = hole_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(790,plain,
% 0.21/0.53 (~(hole_of(pigeon_2) = hole_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[789, 772])).
% 0.21/0.53 tff(791,plain,
% 0.21/0.53 ((pigeon_5 = pigeon_4) <=> (pigeon_4 = pigeon_5)),
% 0.21/0.53 inference(commutativity,[status(thm)],[])).
% 0.21/0.53 tff(792,plain,
% 0.21/0.53 ((pigeon_4 = pigeon_5) <=> (pigeon_5 = pigeon_4)),
% 0.21/0.53 inference(symmetry,[status(thm)],[791])).
% 0.21/0.53 tff(793,plain,
% 0.21/0.53 ((~(pigeon_4 = pigeon_5)) <=> (~(pigeon_5 = pigeon_4))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[792])).
% 0.21/0.53 tff(794,plain,
% 0.21/0.53 (~(pigeon_5 = pigeon_4)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[295, 793])).
% 0.21/0.53 tff(795,plain,
% 0.21/0.53 (hole_2 = hole_of(pigeon_4)),
% 0.21/0.53 inference(symmetry,[status(thm)],[68])).
% 0.21/0.53 tff(796,plain,
% 0.21/0.53 (in(pigeon_4, hole_2) <=> in(pigeon_4, hole_of(pigeon_4))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[795])).
% 0.21/0.53 tff(797,plain,
% 0.21/0.53 (in(pigeon_4, hole_of(pigeon_4)) <=> in(pigeon_4, hole_2)),
% 0.21/0.53 inference(symmetry,[status(thm)],[796])).
% 0.21/0.53 tff(798,plain,
% 0.21/0.53 (in(pigeon_4, hole_2)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[77, 797])).
% 0.21/0.53 tff(799,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_4, hole_2)) | (pigeon_5 = pigeon_4))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_4, hole_2)) | (pigeon_5 = pigeon_4))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(800,plain,
% 0.21/0.53 (((~hole(hole_2)) | (pigeon_5 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_5, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5))) <=> ((~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_4, hole_2)) | (pigeon_5 = pigeon_4))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(801,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_5 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_5, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_4, hole_2)) | (pigeon_5 = pigeon_4)))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[800])).
% 0.21/0.53 tff(802,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_5 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_5, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_4, hole_2)) | (pigeon_5 = pigeon_4))),
% 0.21/0.53 inference(transitivity,[status(thm)],[801, 799])).
% 0.21/0.53 tff(803,plain,
% 0.21/0.53 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_5 = pigeon_4) | (~in(pigeon_4, hole_2)) | (~in(pigeon_5, hole_2)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(804,plain,
% 0.21/0.53 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_4, hole_2)) | (pigeon_5 = pigeon_4)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[803, 802])).
% 0.21/0.53 tff(805,plain,
% 0.21/0.53 ((~in(pigeon_5, hole_2)) | (~in(pigeon_4, hole_2)) | (pigeon_5 = pigeon_4)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[804, 58, 87, 35, 32])).
% 0.21/0.53 tff(806,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[805, 798, 92, 794])).
% 0.21/0.53 tff(807,plain,((~(hole_of(pigeon_4) = hole_2)) | (~(hole_of(pigeon_5) = hole_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(808,plain,
% 0.21/0.53 (~(hole_of(pigeon_4) = hole_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[807, 772])).
% 0.21/0.53 tff(809,plain,
% 0.21/0.53 (~(hole_of(pigeon_4) = hole_4)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[693, 670])).
% 0.21/0.53 tff(810,plain,
% 0.21/0.53 ((pigeon_5 = pigeon_3) <=> (pigeon_3 = pigeon_5)),
% 0.21/0.53 inference(commutativity,[status(thm)],[])).
% 0.21/0.53 tff(811,plain,
% 0.21/0.53 ((pigeon_3 = pigeon_5) <=> (pigeon_5 = pigeon_3)),
% 0.21/0.53 inference(symmetry,[status(thm)],[810])).
% 0.21/0.53 tff(812,plain,
% 0.21/0.53 ((~(pigeon_3 = pigeon_5)) <=> (~(pigeon_5 = pigeon_3))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[811])).
% 0.21/0.53 tff(813,plain,
% 0.21/0.53 (~(pigeon_5 = pigeon_3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[250, 812])).
% 0.21/0.53 tff(814,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_5 = pigeon_3))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_5 = pigeon_3))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(815,plain,
% 0.21/0.53 (((~hole(hole_2)) | (pigeon_5 = pigeon_3) | (~in(pigeon_3, hole_2)) | (~in(pigeon_5, hole_2)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5))) <=> ((~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_5 = pigeon_3))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(816,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_5 = pigeon_3) | (~in(pigeon_3, hole_2)) | (~in(pigeon_5, hole_2)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_5 = pigeon_3)))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[815])).
% 0.21/0.53 tff(817,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_5 = pigeon_3) | (~in(pigeon_3, hole_2)) | (~in(pigeon_5, hole_2)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_5 = pigeon_3))),
% 0.21/0.53 inference(transitivity,[status(thm)],[816, 814])).
% 0.21/0.53 tff(818,plain,
% 0.21/0.53 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_2)) | (pigeon_5 = pigeon_3) | (~in(pigeon_3, hole_2)) | (~in(pigeon_5, hole_2)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(819,plain,
% 0.21/0.53 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_5)) | (~hole(hole_2)) | (~in(pigeon_5, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_5 = pigeon_3)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[818, 817])).
% 0.21/0.53 tff(820,plain,
% 0.21/0.53 ((~in(pigeon_5, hole_2)) | (~in(pigeon_3, hole_2)) | (pigeon_5 = pigeon_3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[819, 17, 87, 35, 32])).
% 0.21/0.53 tff(821,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[820, 22, 92, 813])).
% 0.21/0.53 tff(822,plain,((~(hole_of(pigeon_3) = hole_2)) | (~(hole_of(pigeon_5) = hole_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(823,plain,
% 0.21/0.53 (~(hole_of(pigeon_3) = hole_2)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[822, 772])).
% 0.21/0.53 tff(824,plain,
% 0.21/0.53 (~(hole_of(pigeon_3) = hole_4)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[683, 670])).
% 0.21/0.53 tff(825,plain,
% 0.21/0.53 (~(hole_of(pigeon_2) = hole_3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[397, 824, 823, 809, 808])).
% 0.21/0.53 tff(826,plain,
% 0.21/0.53 (hole_of(pigeon_2) = hole_1),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[342, 825, 790, 760])).
% 0.21/0.53 tff(827,plain,
% 0.21/0.53 (hole_1 = hole_of(pigeon_2)),
% 0.21/0.53 inference(symmetry,[status(thm)],[826])).
% 0.21/0.53 tff(828,plain,
% 0.21/0.53 (in(pigeon_2, hole_1) <=> in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[827])).
% 0.21/0.53 tff(829,plain,
% 0.21/0.53 (in(pigeon_2, hole_of(pigeon_2)) <=> in(pigeon_2, hole_1)),
% 0.21/0.53 inference(symmetry,[status(thm)],[828])).
% 0.21/0.53 tff(830,plain,
% 0.21/0.53 (in(pigeon_2, hole_1)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[131, 829])).
% 0.21/0.53 tff(831,plain,
% 0.21/0.53 (~(hole_of(pigeon_4) = hole_1)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[168, 826])).
% 0.21/0.53 tff(832,plain,
% 0.21/0.53 (hole_of(pigeon_4) = hole_3),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[197, 831, 809, 808])).
% 0.21/0.53 tff(833,plain,
% 0.21/0.53 (in(pigeon_4, hole_3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[206, 832])).
% 0.21/0.53 tff(834,plain,
% 0.21/0.53 (~(hole_of(pigeon_3) = hole_3)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[228, 833])).
% 0.21/0.53 tff(835,plain,
% 0.21/0.53 (hole_of(pigeon_3) = hole_1),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[237, 834, 824, 823])).
% 0.21/0.53 tff(836,plain,
% 0.21/0.53 (hole_1 = hole_of(pigeon_3)),
% 0.21/0.53 inference(symmetry,[status(thm)],[835])).
% 0.21/0.53 tff(837,plain,
% 0.21/0.53 (in(pigeon_3, hole_1) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[836])).
% 0.21/0.53 tff(838,plain,
% 0.21/0.53 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_1)),
% 0.21/0.53 inference(symmetry,[status(thm)],[837])).
% 0.21/0.53 tff(839,plain,
% 0.21/0.53 (in(pigeon_3, hole_1)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[21, 838])).
% 0.21/0.53 tff(840,plain,
% 0.21/0.53 ((~in(pigeon_2, hole_1)) | (~in(pigeon_3, hole_1))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[547, 112, 17, 388, 159, 32])).
% 0.21/0.53 tff(841,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[840, 839, 830])).
% 0.21/0.53 tff(842,plain,((~(hole_of(pigeon_1) = hole_4)) | (hole_of(pigeon_5) = hole_3) | (hole_of(pigeon_5) = hole_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(843,plain,
% 0.21/0.53 (~(hole_of(pigeon_1) = hole_4)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[842, 759, 758])).
% 0.21/0.53 tff(844,plain,
% 0.21/0.53 (hole_of(pigeon_1) = hole_1),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[668, 843, 638, 637])).
% 0.21/0.53 tff(845,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (~in(pigeon_1, hole_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (~in(pigeon_1, hole_1)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(846,plain,
% 0.21/0.53 (((~hole(hole_1)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_1)) | (~in(pigeon_1, hole_1)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (~in(pigeon_1, hole_1)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(847,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_1)) | (~in(pigeon_1, hole_1)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (~in(pigeon_1, hole_1))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[846])).
% 0.21/0.53 tff(848,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_1)) | (~in(pigeon_1, hole_1)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (~in(pigeon_1, hole_1)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[847, 845])).
% 0.21/0.53 tff(849,plain,
% 0.21/0.53 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_1)) | (~in(pigeon_1, hole_1)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(850,plain,
% 0.21/0.53 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_1)) | (~in(pigeon_3, hole_1)) | (~in(pigeon_1, hole_1))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[849, 848])).
% 0.21/0.53 tff(851,plain,
% 0.21/0.53 ((~in(pigeon_3, hole_1)) | (~in(pigeon_1, hole_1))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[850, 41, 17, 38, 159, 32])).
% 0.21/0.53 tff(852,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[851, 650, 524])).
% 0.21/0.53 tff(853,plain,((~in(pigeon_3, hole_1)) | (~(hole_of(pigeon_1) = hole_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(854,plain,
% 0.21/0.53 (~in(pigeon_3, hole_1)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[853, 844])).
% 0.21/0.53 tff(855,plain,
% 0.21/0.53 (~(hole_of(pigeon_3) = hole_1)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[522, 854])).
% 0.21/0.53 tff(856,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(857,plain,
% 0.21/0.53 (((~hole(hole_1)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_1, hole_1)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(858,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_1, hole_1)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_1, hole_1))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[857])).
% 0.21/0.53 tff(859,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_1, hole_1)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[858, 856])).
% 0.21/0.53 tff(860,plain,
% 0.21/0.53 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_1)) | (~in(pigeon_1, hole_1)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(861,plain,
% 0.21/0.53 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~in(pigeon_2, hole_1)) | (~hole(hole_1)) | (~in(pigeon_1, hole_1))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[860, 859])).
% 0.21/0.53 tff(862,plain,
% 0.21/0.53 ((~in(pigeon_2, hole_1)) | (~in(pigeon_1, hole_1))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[861, 41, 112, 109, 159, 32])).
% 0.21/0.53 tff(863,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[862, 650, 270])).
% 0.21/0.53 tff(864,plain,((~in(pigeon_2, hole_1)) | (~(hole_of(pigeon_1) = hole_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(865,plain,
% 0.21/0.53 (~in(pigeon_2, hole_1)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[864, 844])).
% 0.21/0.53 tff(866,plain,
% 0.21/0.53 (~(hole_of(pigeon_2) = hole_1)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[267, 865])).
% 0.21/0.53 tff(867,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(868,plain,
% 0.21/0.53 (((~hole(hole_1)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_1)) | (~in(pigeon_1, hole_1)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(869,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_1)) | (~in(pigeon_1, hole_1)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_1, hole_1))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[868])).
% 0.21/0.53 tff(870,plain,
% 0.21/0.53 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_1)) | (~in(pigeon_1, hole_1)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_1, hole_1)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[869, 867])).
% 0.21/0.53 tff(871,plain,
% 0.21/0.53 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_1)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_1)) | (~in(pigeon_1, hole_1)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(872,plain,
% 0.21/0.53 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_1)) | (~hole(hole_1)) | (~in(pigeon_1, hole_1))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[871, 870])).
% 0.21/0.53 tff(873,plain,
% 0.21/0.53 ((~in(pigeon_4, hole_1)) | (~in(pigeon_1, hole_1))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[872, 41, 58, 55, 159, 32])).
% 0.21/0.53 tff(874,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[873, 650, 487])).
% 0.21/0.53 tff(875,plain,((~in(pigeon_4, hole_1)) | (~(hole_of(pigeon_1) = hole_1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(876,plain,
% 0.21/0.53 (~in(pigeon_4, hole_1)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[875, 844])).
% 0.21/0.53 tff(877,plain,
% 0.21/0.53 (~(hole_of(pigeon_4) = hole_1)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[452, 876])).
% 0.21/0.53 tff(878,assumption,(~(hole_of(pigeon_2) = hole_3)), introduced(assumption)).
% 0.21/0.53 tff(879,assumption,(~(hole_of(pigeon_3) = hole_3)), introduced(assumption)).
% 0.21/0.53 tff(880,plain,
% 0.21/0.53 (~in(pigeon_5, hole_4)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[259, 239])).
% 0.21/0.53 tff(881,plain,
% 0.21/0.53 (~(hole_of(pigeon_5) = hole_4)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[330, 880])).
% 0.21/0.53 tff(882,plain,
% 0.21/0.53 (hole_of(pigeon_5) = hole_2),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[321, 881, 758, 759])).
% 0.21/0.53 tff(883,plain,
% 0.21/0.53 (~(hole_of(pigeon_2) = hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[789, 882])).
% 0.21/0.54 tff(884,plain,
% 0.21/0.54 (hole_of(pigeon_2) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[342, 883, 1, 878])).
% 0.21/0.54 tff(885,plain,
% 0.21/0.54 (hole_4 = hole_of(pigeon_2)),
% 0.21/0.54 inference(symmetry,[status(thm)],[884])).
% 0.21/0.54 tff(886,plain,
% 0.21/0.54 (in(pigeon_2, hole_4) <=> in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[885])).
% 0.21/0.54 tff(887,plain,
% 0.21/0.54 (in(pigeon_2, hole_of(pigeon_2)) <=> in(pigeon_2, hole_4)),
% 0.21/0.54 inference(symmetry,[status(thm)],[886])).
% 0.21/0.54 tff(888,plain,
% 0.21/0.54 (in(pigeon_2, hole_4)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[131, 887])).
% 0.21/0.54 tff(889,plain,
% 0.21/0.54 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_3 = pigeon_2))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_3 = pigeon_2))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(890,plain,
% 0.21/0.54 (((~hole(hole_4)) | (pigeon_3 = pigeon_2) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3))) <=> ((~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_3 = pigeon_2))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(891,plain,
% 0.21/0.54 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_3 = pigeon_2) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_3 = pigeon_2)))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[890])).
% 0.21/0.54 tff(892,plain,
% 0.21/0.54 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_3 = pigeon_2) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_3 = pigeon_2))),
% 0.21/0.54 inference(transitivity,[status(thm)],[891, 889])).
% 0.21/0.54 tff(893,plain,
% 0.21/0.54 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_3 = pigeon_2) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(894,plain,
% 0.21/0.54 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_3)) | (~hole(hole_4)) | (~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_3 = pigeon_2)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[893, 892])).
% 0.21/0.54 tff(895,plain,
% 0.21/0.54 ((~in(pigeon_2, hole_4)) | (~in(pigeon_3, hole_4)) | (pigeon_3 = pigeon_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[894, 112, 17, 247, 32])).
% 0.21/0.54 tff(896,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[895, 243, 888, 590])).
% 0.21/0.54 tff(897,plain,((~(hole_of(pigeon_3) = hole_4)) | (hole_of(pigeon_2) = hole_1) | (hole_of(pigeon_2) = hole_3) | (hole_of(pigeon_5) = hole_3) | (hole_of(pigeon_5) = hole_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(898,plain,
% 0.21/0.54 (~(hole_of(pigeon_3) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[897, 878, 1, 758, 759])).
% 0.21/0.54 tff(899,plain,
% 0.21/0.54 (hole_of(pigeon_3) = hole_2),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[237, 898, 139, 879])).
% 0.21/0.54 tff(900,plain,
% 0.21/0.54 (~(hole_of(pigeon_5) = hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[822, 899])).
% 0.21/0.54 tff(901,plain,
% 0.21/0.54 (hole_of(pigeon_5) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[321, 900, 758, 759])).
% 0.21/0.54 tff(902,plain,
% 0.21/0.54 (in(pigeon_5, hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[330, 901])).
% 0.21/0.54 tff(903,plain,
% 0.21/0.54 (~in(pigeon_2, hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[728, 899])).
% 0.21/0.54 tff(904,plain,
% 0.21/0.54 (~(hole_of(pigeon_2) = hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[133, 903])).
% 0.21/0.54 tff(905,plain,
% 0.21/0.54 (hole_of(pigeon_2) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[342, 904, 1, 878])).
% 0.21/0.54 tff(906,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[480, 905, 902])).
% 0.21/0.54 tff(907,plain,((hole_of(pigeon_2) = hole_3) | (hole_of(pigeon_2) = hole_1) | (hole_of(pigeon_5) = hole_3) | (hole_of(pigeon_5) = hole_1) | (hole_of(pigeon_3) = hole_1) | (hole_of(pigeon_3) = hole_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(908,plain,
% 0.21/0.54 (hole_of(pigeon_3) = hole_3),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[907, 878, 758, 759, 139, 1])).
% 0.21/0.54 tff(909,plain,
% 0.21/0.54 (~in(pigeon_4, hole_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[228, 908])).
% 0.21/0.54 tff(910,plain,
% 0.21/0.54 (~(hole_of(pigeon_4) = hole_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[206, 909])).
% 0.21/0.54 tff(911,assumption,(~(hole_of(pigeon_4) = hole_3)), introduced(assumption)).
% 0.21/0.54 tff(912,plain,
% 0.21/0.54 (~(hole_of(pigeon_5) = hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[789, 122])).
% 0.21/0.54 tff(913,plain,
% 0.21/0.54 (hole_of(pigeon_5) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[321, 912, 758, 759])).
% 0.21/0.54 tff(914,plain,
% 0.21/0.54 (in(pigeon_5, hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[330, 913])).
% 0.21/0.54 tff(915,plain,
% 0.21/0.54 (~(hole_of(pigeon_4) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[574, 914])).
% 0.21/0.54 tff(916,plain,
% 0.21/0.54 (hole_of(pigeon_4) = hole_2),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[197, 915, 707, 911])).
% 0.21/0.54 tff(917,plain,
% 0.21/0.54 (in(pigeon_4, hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[79, 916])).
% 0.21/0.54 tff(918,plain,
% 0.21/0.54 (in(pigeon_2, hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[133, 122])).
% 0.21/0.54 tff(919,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[750, 112, 58, 151, 35, 32, 918, 917])).
% 0.21/0.54 tff(920,plain,((~(hole_of(pigeon_2) = hole_2)) | (hole_of(pigeon_4) = hole_1) | (hole_of(pigeon_4) = hole_3) | (hole_of(pigeon_5) = hole_3) | (hole_of(pigeon_5) = hole_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(921,plain,
% 0.21/0.54 (~(hole_of(pigeon_2) = hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[920, 910, 707, 758, 759])).
% 0.21/0.54 tff(922,plain,
% 0.21/0.54 (hole_of(pigeon_2) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[342, 921, 1, 878])).
% 0.21/0.54 tff(923,plain,
% 0.21/0.54 (~in(pigeon_5, hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[480, 922])).
% 0.21/0.54 tff(924,plain,
% 0.21/0.54 (~(hole_of(pigeon_5) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[330, 923])).
% 0.21/0.54 tff(925,plain,
% 0.21/0.54 (hole_of(pigeon_5) = hole_2),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[321, 924, 758, 759])).
% 0.21/0.54 tff(926,plain,
% 0.21/0.54 (~(hole_of(pigeon_4) = hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[807, 925])).
% 0.21/0.54 tff(927,plain,
% 0.21/0.54 (hole_of(pigeon_4) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[197, 926, 707, 910])).
% 0.21/0.54 tff(928,plain,
% 0.21/0.54 (hole_4 = hole_of(pigeon_4)),
% 0.21/0.54 inference(symmetry,[status(thm)],[927])).
% 0.21/0.54 tff(929,plain,
% 0.21/0.54 (in(pigeon_4, hole_4) <=> in(pigeon_4, hole_of(pigeon_4))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[928])).
% 0.21/0.54 tff(930,plain,
% 0.21/0.54 (in(pigeon_4, hole_of(pigeon_4)) <=> in(pigeon_4, hole_4)),
% 0.21/0.54 inference(symmetry,[status(thm)],[929])).
% 0.21/0.54 tff(931,plain,
% 0.21/0.54 (in(pigeon_4, hole_4)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[77, 930])).
% 0.21/0.54 tff(932,plain,
% 0.21/0.54 (hole_4 = hole_of(pigeon_2)),
% 0.21/0.54 inference(symmetry,[status(thm)],[922])).
% 0.21/0.54 tff(933,plain,
% 0.21/0.54 (in(pigeon_2, hole_4) <=> in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[932])).
% 0.21/0.54 tff(934,plain,
% 0.21/0.54 (in(pigeon_2, hole_of(pigeon_2)) <=> in(pigeon_2, hole_4)),
% 0.21/0.54 inference(symmetry,[status(thm)],[933])).
% 0.21/0.54 tff(935,plain,
% 0.21/0.54 (in(pigeon_2, hole_4)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[131, 934])).
% 0.21/0.54 tff(936,plain,
% 0.21/0.54 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(937,plain,
% 0.21/0.54 (((~hole(hole_4)) | (pigeon_2 = pigeon_4) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_2))) <=> ((pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(938,plain,
% 0.21/0.54 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_2 = pigeon_4) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[937])).
% 0.21/0.54 tff(939,plain,
% 0.21/0.54 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_2 = pigeon_4) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_2)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4)))),
% 0.21/0.54 inference(transitivity,[status(thm)],[938, 936])).
% 0.21/0.54 tff(940,plain,
% 0.21/0.54 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_4)) | (pigeon_2 = pigeon_4) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_2)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(941,plain,
% 0.21/0.54 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_2 = pigeon_4) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_4)) | (~hole(hole_4)) | (~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[940, 939])).
% 0.21/0.54 tff(942,plain,
% 0.21/0.54 ((~in(pigeon_4, hole_4)) | (~in(pigeon_2, hole_4))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[941, 112, 58, 151, 247, 32])).
% 0.21/0.54 tff(943,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[942, 935, 931])).
% 0.21/0.54 tff(944,plain,((hole_of(pigeon_2) = hole_3) | (hole_of(pigeon_4) = hole_1) | (hole_of(pigeon_5) = hole_3) | (hole_of(pigeon_5) = hole_1) | (hole_of(pigeon_2) = hole_1) | (hole_of(pigeon_3) = hole_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(945,plain,
% 0.21/0.54 (hole_of(pigeon_2) = hole_3),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[944, 877, 758, 759, 866, 855])).
% 0.21/0.54 tff(946,plain,
% 0.21/0.54 (~in(pigeon_4, hole_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[358, 945])).
% 0.21/0.54 tff(947,plain,
% 0.21/0.54 (~(hole_of(pigeon_4) = hole_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[206, 946])).
% 0.21/0.54 tff(948,plain,
% 0.21/0.54 (in(pigeon_2, hole_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[407, 945])).
% 0.21/0.54 tff(949,plain,
% 0.21/0.54 (~(hole_of(pigeon_3) = hole_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[599, 948])).
% 0.21/0.54 tff(950,plain,
% 0.21/0.54 (~(hole_of(pigeon_4) = hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[807, 81])).
% 0.21/0.54 tff(951,plain,
% 0.21/0.54 (hole_of(pigeon_4) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[197, 950, 707, 911])).
% 0.21/0.54 tff(952,plain,
% 0.21/0.54 (hole_4 = hole_of(pigeon_4)),
% 0.21/0.54 inference(symmetry,[status(thm)],[951])).
% 0.21/0.54 tff(953,plain,
% 0.21/0.54 (in(pigeon_4, hole_4) <=> in(pigeon_4, hole_of(pigeon_4))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[952])).
% 0.21/0.54 tff(954,plain,
% 0.21/0.54 (in(pigeon_4, hole_of(pigeon_4)) <=> in(pigeon_4, hole_4)),
% 0.21/0.54 inference(symmetry,[status(thm)],[953])).
% 0.21/0.54 tff(955,plain,
% 0.21/0.54 (in(pigeon_4, hole_4)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[77, 954])).
% 0.21/0.54 tff(956,plain,
% 0.21/0.54 (~(hole_of(pigeon_3) = hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[822, 81])).
% 0.21/0.54 tff(957,plain,
% 0.21/0.54 (hole_of(pigeon_3) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[237, 956, 139, 879])).
% 0.21/0.54 tff(958,plain,
% 0.21/0.54 (hole_4 = hole_of(pigeon_3)),
% 0.21/0.54 inference(symmetry,[status(thm)],[957])).
% 0.21/0.54 tff(959,plain,
% 0.21/0.54 (in(pigeon_3, hole_4) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[958])).
% 0.21/0.54 tff(960,plain,
% 0.21/0.54 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_4)),
% 0.21/0.54 inference(symmetry,[status(thm)],[959])).
% 0.21/0.54 tff(961,plain,
% 0.21/0.54 (in(pigeon_3, hole_4)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[21, 960])).
% 0.21/0.54 tff(962,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[583, 961, 955, 365])).
% 0.21/0.54 tff(963,plain,((~(hole_of(pigeon_5) = hole_2)) | (hole_of(pigeon_3) = hole_1) | (hole_of(pigeon_3) = hole_3) | (hole_of(pigeon_4) = hole_1) | (hole_of(pigeon_4) = hole_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(964,plain,
% 0.21/0.54 (~(hole_of(pigeon_5) = hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[963, 855, 949, 877, 947])).
% 0.21/0.54 tff(965,plain,
% 0.21/0.54 (hole_of(pigeon_5) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[321, 964, 758, 759])).
% 0.21/0.54 tff(966,plain,
% 0.21/0.54 (in(pigeon_5, hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[330, 965])).
% 0.21/0.54 tff(967,plain,
% 0.21/0.54 (~(hole_of(pigeon_4) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[574, 966])).
% 0.21/0.54 tff(968,plain,
% 0.21/0.54 (hole_of(pigeon_4) = hole_2),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[197, 967, 877, 947])).
% 0.21/0.54 tff(969,plain,
% 0.21/0.54 (~(hole_of(pigeon_3) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[259, 966])).
% 0.21/0.54 tff(970,plain,
% 0.21/0.54 (hole_of(pigeon_3) = hole_2),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[237, 969, 855, 949])).
% 0.21/0.54 tff(971,plain,
% 0.21/0.54 (~in(pigeon_4, hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[716, 970])).
% 0.21/0.54 tff(972,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[79, 971, 968])).
% 0.21/0.54 tff(973,plain,((hole_of(pigeon_5) = hole_1) | (hole_of(pigeon_5) = hole_3) | (hole_of(pigeon_1) = hole_3) | (hole_of(pigeon_1) = hole_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(974,plain,
% 0.21/0.54 (hole_of(pigeon_5) = hole_3),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[973, 757, 638, 637])).
% 0.21/0.54 tff(975,plain,
% 0.21/0.54 (in(pigeon_5, hole_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[312, 974])).
% 0.21/0.54 tff(976,plain,
% 0.21/0.54 (~(hole_of(pigeon_3) = hole_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[502, 975])).
% 0.21/0.54 tff(977,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[750, 112, 58, 151, 35, 32, 106, 52])).
% 0.21/0.54 tff(978,plain,((~in(pigeon_2, hole_2)) | (~in(pigeon_4, hole_2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(979,plain,
% 0.21/0.54 (~in(pigeon_2, hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[978, 52])).
% 0.21/0.54 tff(980,plain,
% 0.21/0.54 (~(hole_of(pigeon_2) = hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[133, 979])).
% 0.21/0.54 tff(981,plain,
% 0.21/0.54 (~in(pigeon_2, hole_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[417, 975])).
% 0.21/0.54 tff(982,plain,
% 0.21/0.54 (~(hole_of(pigeon_2) = hole_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[407, 981])).
% 0.21/0.54 tff(983,plain,
% 0.21/0.54 (~(hole_of(pigeon_3) = hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[716, 52])).
% 0.21/0.54 tff(984,plain,
% 0.21/0.54 (~(hole_of(pigeon_1) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[705, 467])).
% 0.21/0.54 tff(985,plain,
% 0.21/0.54 (hole_of(pigeon_1) = hole_1),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[668, 984, 638, 637])).
% 0.21/0.54 tff(986,plain,
% 0.21/0.54 (~in(pigeon_3, hole_1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[853, 985])).
% 0.21/0.54 tff(987,plain,
% 0.21/0.54 (~(hole_of(pigeon_3) = hole_1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[522, 986])).
% 0.21/0.54 tff(988,plain,
% 0.21/0.54 (hole_of(pigeon_3) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[237, 987, 976, 137])).
% 0.21/0.54 tff(989,plain,
% 0.21/0.54 (hole_4 = hole_of(pigeon_3)),
% 0.21/0.54 inference(symmetry,[status(thm)],[988])).
% 0.21/0.54 tff(990,plain,
% 0.21/0.54 (in(pigeon_3, hole_4) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[989])).
% 0.21/0.54 tff(991,plain,
% 0.21/0.54 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_4)),
% 0.21/0.54 inference(symmetry,[status(thm)],[990])).
% 0.21/0.54 tff(992,plain,
% 0.21/0.54 (in(pigeon_3, hole_4)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[21, 991])).
% 0.21/0.54 tff(993,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[440, 992, 471])).
% 0.21/0.54 tff(994,plain,((~(hole_of(pigeon_2) = hole_4)) | (hole_of(pigeon_3) = hole_2) | (hole_of(pigeon_1) = hole_3) | (hole_of(pigeon_1) = hole_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(995,plain,
% 0.21/0.54 (~(hole_of(pigeon_2) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[994, 983, 638, 637])).
% 0.21/0.54 tff(996,plain,
% 0.21/0.54 (hole_of(pigeon_2) = hole_1),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[342, 995, 982, 980])).
% 0.21/0.54 tff(997,plain,
% 0.21/0.54 (in(pigeon_2, hole_1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[267, 996])).
% 0.21/0.54 tff(998,plain,
% 0.21/0.54 (~(hole_of(pigeon_1) = hole_1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[864, 997])).
% 0.21/0.54 tff(999,plain,
% 0.21/0.54 (hole_of(pigeon_1) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[668, 998, 638, 637])).
% 0.21/0.54 tff(1000,plain,
% 0.21/0.54 (~(hole_of(pigeon_3) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[683, 999])).
% 0.21/0.54 tff(1001,plain,
% 0.21/0.54 (hole_of(pigeon_3) = hole_1),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[237, 1000, 976, 983])).
% 0.21/0.54 tff(1002,plain,
% 0.21/0.54 (in(pigeon_3, hole_1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[522, 1001])).
% 0.21/0.54 tff(1003,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[547, 112, 17, 388, 159, 32, 1002, 997])).
% 0.21/0.54 tff(1004,plain,((~in(pigeon_4, hole_2)) | (hole_of(pigeon_1) = hole_3) | (hole_of(pigeon_1) = hole_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(1005,plain,
% 0.21/0.54 (~in(pigeon_4, hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[1004, 637, 638])).
% 0.21/0.54 tff(1006,plain,
% 0.21/0.54 (~(hole_of(pigeon_4) = hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[79, 1005])).
% 0.21/0.54 tff(1007,plain,
% 0.21/0.54 (~in(pigeon_4, hole_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[303, 975])).
% 0.21/0.54 tff(1008,plain,
% 0.21/0.54 (~(hole_of(pigeon_4) = hole_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[206, 1007])).
% 0.21/0.54 tff(1009,plain,
% 0.21/0.54 (~(hole_of(pigeon_1) = hole_1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[864, 268])).
% 0.21/0.54 tff(1010,plain,
% 0.21/0.54 (hole_of(pigeon_4) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[197, 169, 1008, 1006])).
% 0.21/0.54 tff(1011,plain,
% 0.21/0.54 (~(hole_of(pigeon_1) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[693, 1010])).
% 0.21/0.54 tff(1012,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[668, 1011, 1009, 638, 637])).
% 0.21/0.54 tff(1013,plain,((~(hole_of(pigeon_2) = hole_1)) | (hole_of(pigeon_1) = hole_3) | (hole_of(pigeon_1) = hole_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(1014,plain,
% 0.21/0.54 (~(hole_of(pigeon_2) = hole_1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[1013, 637, 638])).
% 0.21/0.54 tff(1015,plain,
% 0.21/0.54 (~(hole_of(pigeon_2) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[564, 551])).
% 0.21/0.54 tff(1016,plain,
% 0.21/0.54 (hole_of(pigeon_2) = hole_2),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[342, 1015, 878, 1])).
% 0.21/0.54 tff(1017,plain,
% 0.21/0.54 (in(pigeon_2, hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[133, 1016])).
% 0.21/0.54 tff(1018,plain,
% 0.21/0.54 (~(hole_of(pigeon_3) = hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[728, 1017])).
% 0.21/0.54 tff(1019,plain,
% 0.21/0.54 (hole_of(pigeon_3) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[237, 1018, 879, 139])).
% 0.21/0.54 tff(1020,plain,
% 0.21/0.54 (hole_4 = hole_of(pigeon_3)),
% 0.21/0.54 inference(symmetry,[status(thm)],[1019])).
% 0.21/0.54 tff(1021,plain,
% 0.21/0.54 (in(pigeon_3, hole_4) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[1020])).
% 0.21/0.54 tff(1022,plain,
% 0.21/0.54 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_4)),
% 0.21/0.54 inference(symmetry,[status(thm)],[1021])).
% 0.21/0.54 tff(1023,plain,
% 0.21/0.54 (in(pigeon_3, hole_4)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[21, 1022])).
% 0.21/0.54 tff(1024,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[583, 1023, 555, 365])).
% 0.21/0.54 tff(1025,plain,((~(hole_of(pigeon_4) = hole_4)) | (hole_of(pigeon_3) = hole_3) | (hole_of(pigeon_3) = hole_1) | (hole_of(pigeon_2) = hole_3) | (hole_of(pigeon_2) = hole_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(1026,plain,
% 0.21/0.54 (~(hole_of(pigeon_4) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[1025, 139, 976, 982, 1014])).
% 0.21/0.54 tff(1027,plain,
% 0.21/0.54 (hole_of(pigeon_4) = hole_1),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[197, 1026, 1008, 1006])).
% 0.21/0.54 tff(1028,plain,
% 0.21/0.54 (in(pigeon_4, hole_1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[452, 1027])).
% 0.21/0.54 tff(1029,plain,
% 0.21/0.54 (~(hole_of(pigeon_1) = hole_1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[875, 1028])).
% 0.21/0.54 tff(1030,plain,
% 0.21/0.54 (hole_of(pigeon_1) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[668, 1029, 638, 637])).
% 0.21/0.54 tff(1031,plain,
% 0.21/0.54 (~(hole_of(pigeon_3) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[683, 1030])).
% 0.21/0.54 tff(1032,plain,
% 0.21/0.54 (hole_of(pigeon_3) = hole_2),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[237, 1031, 976, 139])).
% 0.21/0.54 tff(1033,plain,
% 0.21/0.54 (~(hole_of(pigeon_2) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[705, 1030])).
% 0.21/0.54 tff(1034,plain,
% 0.21/0.54 (hole_of(pigeon_2) = hole_2),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[342, 1033, 982, 1014])).
% 0.21/0.54 tff(1035,plain,
% 0.21/0.54 (in(pigeon_2, hole_2)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[133, 1034])).
% 0.21/0.54 tff(1036,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[728, 1035, 1032])).
% 0.21/0.54 tff(1037,plain,((hole_of(pigeon_3) = hole_1) | (hole_of(pigeon_1) = hole_3) | (hole_of(pigeon_1) = hole_2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(1038,plain,
% 0.21/0.54 (hole_of(pigeon_3) = hole_1),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[1037, 637, 638])).
% 0.21/0.54 tff(1039,plain,
% 0.21/0.54 (in(pigeon_3, hole_1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[522, 1038])).
% 0.21/0.54 tff(1040,plain,
% 0.21/0.54 (~(hole_of(pigeon_1) = hole_1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[853, 1039])).
% 0.21/0.54 tff(1041,plain,
% 0.21/0.54 (~(hole_of(pigeon_4) = hole_1)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[379, 1038])).
% 0.21/0.54 tff(1042,plain,
% 0.21/0.54 (hole_of(pigeon_4) = hole_4),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[197, 1041, 1008, 1006])).
% 0.21/0.54 tff(1043,plain,
% 0.21/0.54 (~(hole_of(pigeon_1) = hole_4)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[693, 1042])).
% 0.21/0.54 tff(1044,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[668, 1043, 1040, 638, 637])).
% 0.21/0.54 tff(1045,plain,((hole_of(pigeon_1) = hole_2) | (hole_of(pigeon_1) = hole_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(1046,plain,
% 0.21/0.54 (hole_of(pigeon_1) = hole_3),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[1045, 636])).
% 0.21/0.54 tff(1047,plain,
% 0.21/0.54 (hole_3 = hole_of(pigeon_1)),
% 0.21/0.54 inference(symmetry,[status(thm)],[1046])).
% 0.21/0.54 tff(1048,plain,
% 0.21/0.54 (in(pigeon_1, hole_3) <=> in(pigeon_1, hole_of(pigeon_1))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[1047])).
% 0.21/0.54 tff(1049,plain,
% 0.21/0.54 (in(pigeon_1, hole_of(pigeon_1)) <=> in(pigeon_1, hole_3)),
% 0.21/0.54 inference(symmetry,[status(thm)],[1048])).
% 0.21/0.54 tff(1050,plain,
% 0.21/0.54 (in(pigeon_1, hole_3)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[631, 1049])).
% 0.21/0.54 tff(1051,assumption,(~in(pigeon_1, hole_3)), introduced(assumption)).
% 0.21/0.54 tff(1052,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[1051, 1050])).
% 0.21/0.54 tff(1053,plain,(in(pigeon_1, hole_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(1054,plain,
% 0.21/0.54 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_1, hole_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_1, hole_3)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(1055,plain,
% 0.21/0.54 (((~hole(hole_3)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_1, hole_3)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(1056,plain,
% 0.21/0.54 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_1, hole_3))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[1055])).
% 0.21/0.54 tff(1057,plain,
% 0.21/0.54 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_1, hole_3)))),
% 0.21/0.54 inference(transitivity,[status(thm)],[1056, 1054])).
% 0.21/0.54 tff(1058,plain,
% 0.21/0.54 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_1 = pigeon_2) | (~in(pigeon_2, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_2)) | (~pigeon(pigeon_1)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(1059,plain,
% 0.21/0.54 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_2) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_2)) | (~in(pigeon_2, hole_3)) | (~hole(hole_3)) | (~in(pigeon_1, hole_3))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 0.21/0.54 tff(1060,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[1059, 41, 112, 109, 216, 32, 409, 1053])).
% 0.21/0.54 tff(1061,plain,(~in(pigeon_2, hole_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(1062,plain,
% 0.21/0.54 (~(hole_of(pigeon_2) = hole_3)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[407, 1061])).
% 0.21/0.54 tff(1063,plain,
% 0.21/0.54 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_1, hole_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_1, hole_3)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(1064,plain,
% 0.21/0.54 (((~hole(hole_3)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_1, hole_3)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(1065,plain,
% 0.21/0.54 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_1, hole_3))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[1064])).
% 0.21/0.54 tff(1066,plain,
% 0.21/0.54 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_1, hole_3)))),
% 0.21/0.54 inference(transitivity,[status(thm)],[1065, 1063])).
% 0.21/0.54 tff(1067,plain,
% 0.21/0.54 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_1 = pigeon_4) | (~in(pigeon_4, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_4)) | (~pigeon(pigeon_1)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(1068,plain,
% 0.21/0.54 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_4) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_4)) | (~in(pigeon_4, hole_3)) | (~hole(hole_3)) | (~in(pigeon_1, hole_3))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 0.21/0.54 tff(1069,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[1068, 41, 58, 55, 216, 32, 213, 1053])).
% 0.21/0.54 tff(1070,plain,(~in(pigeon_4, hole_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(1071,plain,
% 0.21/0.55 (~(hole_of(pigeon_4) = hole_3)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[206, 1070])).
% 0.21/0.55 tff(1072,plain,
% 0.21/0.55 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)) | (~in(pigeon_1, hole_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)) | (~in(pigeon_1, hole_3)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(1073,plain,
% 0.21/0.55 (((~hole(hole_3)) | (pigeon_1 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)) | (~in(pigeon_1, hole_3)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(1074,plain,
% 0.21/0.55 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_1 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)) | (~in(pigeon_1, hole_3))))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[1073])).
% 0.21/0.55 tff(1075,plain,
% 0.21/0.55 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_1 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)) | (~in(pigeon_1, hole_3)))),
% 0.21/0.55 inference(transitivity,[status(thm)],[1074, 1072])).
% 0.21/0.55 tff(1076,plain,
% 0.21/0.55 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_1 = pigeon_5) | (~in(pigeon_5, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_5)) | (~pigeon(pigeon_1)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(1077,plain,
% 0.21/0.55 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_5) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_5)) | (~hole(hole_3)) | (~in(pigeon_5, hole_3)) | (~in(pigeon_1, hole_3))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 0.21/0.55 tff(1078,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[1077, 41, 87, 95, 216, 32, 292, 1053])).
% 0.21/0.55 tff(1079,plain,(~in(pigeon_5, hole_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(1080,plain,
% 0.21/0.55 (~(hole_of(pigeon_5) = hole_3)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[312, 1079])).
% 0.21/0.55 tff(1081,plain,
% 0.21/0.55 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_3)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[208])).
% 0.21/0.55 tff(1082,plain,
% 0.21/0.55 (in(pigeon_3, hole_3) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.55 inference(symmetry,[status(thm)],[1081])).
% 0.21/0.55 tff(1083,plain,
% 0.21/0.55 ((~in(pigeon_3, hole_3)) <=> (~in(pigeon_3, hole_of(pigeon_3)))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[1082])).
% 0.21/0.55 tff(1084,assumption,(in(pigeon_3, hole_3)), introduced(assumption)).
% 0.21/0.55 tff(1085,plain,
% 0.21/0.55 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (~in(pigeon_1, hole_3)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (~in(pigeon_1, hole_3)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(1086,plain,
% 0.21/0.55 (((~hole(hole_3)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1))) <=> ((pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (~in(pigeon_1, hole_3)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(1087,plain,
% 0.21/0.55 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (~in(pigeon_1, hole_3))))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[1086])).
% 0.21/0.55 tff(1088,plain,
% 0.21/0.55 (((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1)))) <=> ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (~in(pigeon_1, hole_3)))),
% 0.21/0.55 inference(transitivity,[status(thm)],[1087, 1085])).
% 0.21/0.55 tff(1089,plain,
% 0.21/0.55 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | ((~hole(hole_3)) | (pigeon_1 = pigeon_3) | (~in(pigeon_3, hole_3)) | (~in(pigeon_1, hole_3)) | (~pigeon(pigeon_3)) | (~pigeon(pigeon_1)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(1090,plain,
% 0.21/0.55 ((~![Pigeon1: $i, Pigeon2: $i, Hole: $i] : ((~hole(Hole)) | (Pigeon1 = Pigeon2) | (~in(Pigeon2, Hole)) | (~in(Pigeon1, Hole)) | (~pigeon(Pigeon2)) | (~pigeon(Pigeon1)))) | (pigeon_1 = pigeon_3) | (~pigeon(pigeon_1)) | (~pigeon(pigeon_3)) | (~hole(hole_3)) | (~in(pigeon_3, hole_3)) | (~in(pigeon_1, hole_3))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[1089, 1088])).
% 0.21/0.55 tff(1091,plain,
% 0.21/0.55 ((~in(pigeon_3, hole_3)) | (~in(pigeon_1, hole_3))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[1090, 41, 17, 38, 216, 32])).
% 0.21/0.55 tff(1092,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[1091, 1050, 1084])).
% 0.21/0.55 tff(1093,plain,(~in(pigeon_3, hole_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(1094,plain,
% 0.21/0.55 (~in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[1093, 1083])).
% 0.21/0.55 tff(1095,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[21, 1094])).
% 0.21/0.55 tff(1096,plain,(~(hole_of(pigeon_3) = hole_3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(1097,plain,
% 0.21/0.55 (~(hole_of(pigeon_3) = hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[379, 141])).
% 0.21/0.55 tff(1098,plain,
% 0.21/0.55 (hole_of(pigeon_5) = hole_1),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[907, 1097, 1096, 1062, 1080, 1])).
% 0.21/0.55 tff(1099,plain,
% 0.21/0.55 (in(pigeon_4, hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[452, 141])).
% 0.21/0.55 tff(1100,plain,
% 0.21/0.55 (~in(pigeon_5, hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[489, 1099])).
% 0.21/0.55 tff(1101,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[290, 1100, 1098])).
% 0.21/0.55 tff(1102,plain,((~(hole_of(pigeon_4) = hole_1)) | (hole_of(pigeon_2) = hole_1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(1103,plain,
% 0.21/0.55 (~(hole_of(pigeon_4) = hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[1102, 1])).
% 0.21/0.55 tff(1104,plain,
% 0.21/0.55 (hole_of(pigeon_4) = hole_2),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[197, 1103, 1071, 2])).
% 0.21/0.55 tff(1105,plain,
% 0.21/0.55 (in(pigeon_4, hole_2)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[79, 1104])).
% 0.21/0.55 tff(1106,plain,
% 0.21/0.55 (~in(pigeon_2, hole_2)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[978, 1105])).
% 0.21/0.55 tff(1107,plain,
% 0.21/0.55 (~(hole_of(pigeon_2) = hole_2)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[133, 1106])).
% 0.21/0.55 tff(1108,plain,
% 0.21/0.55 (hole_of(pigeon_2) = hole_4),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[342, 1107, 1062, 1])).
% 0.21/0.55 tff(1109,plain,
% 0.21/0.55 (hole_4 = hole_of(pigeon_2)),
% 0.21/0.55 inference(symmetry,[status(thm)],[1108])).
% 0.21/0.55 tff(1110,plain,
% 0.21/0.55 (in(pigeon_2, hole_4) <=> in(pigeon_2, hole_of(pigeon_2))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[1109])).
% 0.21/0.55 tff(1111,plain,
% 0.21/0.55 (in(pigeon_2, hole_of(pigeon_2)) <=> in(pigeon_2, hole_4)),
% 0.21/0.55 inference(symmetry,[status(thm)],[1110])).
% 0.21/0.55 tff(1112,plain,
% 0.21/0.55 (in(pigeon_2, hole_4)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[131, 1111])).
% 0.21/0.55 tff(1113,plain,
% 0.21/0.55 (~(hole_of(pigeon_3) = hole_2)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[716, 1105])).
% 0.21/0.55 tff(1114,plain,
% 0.21/0.55 (~(hole_of(pigeon_5) = hole_2)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[807, 1104])).
% 0.21/0.55 tff(1115,plain,
% 0.21/0.55 (~in(pigeon_5, hole_4)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[480, 1108])).
% 0.21/0.55 tff(1116,plain,
% 0.21/0.55 (~(hole_of(pigeon_5) = hole_4)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[330, 1115])).
% 0.21/0.55 tff(1117,plain,
% 0.21/0.55 (hole_of(pigeon_5) = hole_1),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[321, 1116, 1080, 1114])).
% 0.21/0.55 tff(1118,plain,
% 0.21/0.55 (in(pigeon_5, hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[290, 1117])).
% 0.21/0.55 tff(1119,plain,
% 0.21/0.55 (~in(pigeon_3, hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[532, 1118])).
% 0.21/0.55 tff(1120,plain,
% 0.21/0.55 (~(hole_of(pigeon_3) = hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[522, 1119])).
% 0.21/0.55 tff(1121,plain,
% 0.21/0.55 (hole_of(pigeon_3) = hole_4),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[237, 1120, 1096, 1113])).
% 0.21/0.55 tff(1122,plain,
% 0.21/0.55 (hole_4 = hole_of(pigeon_3)),
% 0.21/0.55 inference(symmetry,[status(thm)],[1121])).
% 0.21/0.55 tff(1123,plain,
% 0.21/0.55 (in(pigeon_3, hole_4) <=> in(pigeon_3, hole_of(pigeon_3))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[1122])).
% 0.21/0.55 tff(1124,plain,
% 0.21/0.55 (in(pigeon_3, hole_of(pigeon_3)) <=> in(pigeon_3, hole_4)),
% 0.21/0.55 inference(symmetry,[status(thm)],[1123])).
% 0.21/0.55 tff(1125,plain,
% 0.21/0.55 (in(pigeon_3, hole_4)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[21, 1124])).
% 0.21/0.55 tff(1126,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[440, 1125, 1112])).
% 0.21/0.55 tff(1127,plain,((hole_of(pigeon_2) = hole_1) | (hole_of(pigeon_4) = hole_4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(1128,plain,
% 0.21/0.55 (hole_of(pigeon_2) = hole_1),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[1127, 2])).
% 0.21/0.55 tff(1129,plain,
% 0.21/0.55 (in(pigeon_2, hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[267, 1128])).
% 0.21/0.55 tff(1130,plain,
% 0.21/0.55 (~(hole_of(pigeon_4) = hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[168, 1128])).
% 0.21/0.55 tff(1131,plain,
% 0.21/0.55 (hole_of(pigeon_4) = hole_2),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[197, 1130, 1071, 2])).
% 0.21/0.55 tff(1132,plain,
% 0.21/0.55 (in(pigeon_4, hole_2)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[79, 1131])).
% 0.21/0.55 tff(1133,plain,
% 0.21/0.55 (~(hole_of(pigeon_3) = hole_2)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[716, 1132])).
% 0.21/0.55 tff(1134,plain,
% 0.21/0.55 (~(hole_of(pigeon_5) = hole_2)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[807, 1131])).
% 0.21/0.55 tff(1135,plain,
% 0.21/0.55 (~in(pigeon_5, hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[281, 1129])).
% 0.21/0.55 tff(1136,plain,
% 0.21/0.55 (~(hole_of(pigeon_5) = hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[290, 1135])).
% 0.21/0.55 tff(1137,plain,
% 0.21/0.55 (hole_of(pigeon_5) = hole_4),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[321, 1136, 1080, 1134])).
% 0.21/0.55 tff(1138,plain,
% 0.21/0.55 (in(pigeon_5, hole_4)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[330, 1137])).
% 0.21/0.55 tff(1139,plain,
% 0.21/0.55 (~(hole_of(pigeon_3) = hole_4)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[259, 1138])).
% 0.21/0.55 tff(1140,plain,
% 0.21/0.55 (hole_of(pigeon_3) = hole_1),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[237, 1139, 1096, 1133])).
% 0.21/0.55 tff(1141,plain,
% 0.21/0.55 (in(pigeon_3, hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[522, 1140])).
% 0.21/0.55 tff(1142,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[547, 112, 17, 388, 159, 32, 1141, 1129])).
% 0.21/0.55 tff(1143,plain,(hole_of(pigeon_4) = hole_4), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(1144,plain,
% 0.21/0.55 ((hole_of(pigeon_3) = hole_1) | (hole_of(pigeon_2) = hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[1025, 1062, 1096, 1143])).
% 0.21/0.55 tff(1145,plain,
% 0.21/0.55 (hole_of(pigeon_3) = hole_1),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[1144, 1])).
% 0.21/0.55 tff(1146,plain,
% 0.21/0.55 (in(pigeon_3, hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[522, 1145])).
% 0.21/0.55 tff(1147,plain,
% 0.21/0.55 (~(hole_of(pigeon_2) = hole_4)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[564, 1143])).
% 0.21/0.55 tff(1148,plain,
% 0.21/0.55 ((hole_of(pigeon_2) = hole_2) | (hole_of(pigeon_2) = hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[342, 1062, 1147])).
% 0.21/0.55 tff(1149,plain,
% 0.21/0.55 (hole_of(pigeon_2) = hole_2),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[1148, 1])).
% 0.21/0.55 tff(1150,plain,
% 0.21/0.55 ((hole_4 = hole_1) <=> (hole_1 = hole_4)),
% 0.21/0.55 inference(commutativity,[status(thm)],[])).
% 0.21/0.55 tff(1151,plain,
% 0.21/0.55 ((hole_of(pigeon_4) = hole_1) <=> (hole_4 = hole_1)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[1143])).
% 0.21/0.55 tff(1152,plain,
% 0.21/0.55 ((hole_of(pigeon_4) = hole_1) <=> (hole_1 = hole_4)),
% 0.21/0.55 inference(transitivity,[status(thm)],[1151, 1150])).
% 0.21/0.55 tff(1153,plain,
% 0.21/0.55 ((hole_1 = hole_4) <=> (hole_of(pigeon_4) = hole_1)),
% 0.21/0.55 inference(symmetry,[status(thm)],[1152])).
% 0.21/0.55 tff(1154,plain,
% 0.21/0.55 ((~(hole_1 = hole_4)) <=> (~(hole_of(pigeon_4) = hole_1))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[1153])).
% 0.21/0.55 tff(1155,plain,
% 0.21/0.55 ((~(hole_1 = hole_4)) <=> (~(hole_1 = hole_4))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(1156,axiom,(~(hole_1 = hole_4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hole_1_is_not_hole_4')).
% 0.21/0.55 tff(1157,plain,
% 0.21/0.55 (~(hole_1 = hole_4)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 0.21/0.55 tff(1158,plain,
% 0.21/0.55 (~(hole_of(pigeon_4) = hole_1)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[1157, 1154])).
% 0.21/0.55 tff(1159,plain,
% 0.21/0.55 ((~(hole_of(pigeon_2) = hole_2)) | (hole_of(pigeon_5) = hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[920, 1080, 1158, 1071])).
% 0.21/0.55 tff(1160,plain,
% 0.21/0.55 (hole_of(pigeon_5) = hole_1),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[1159, 1149])).
% 0.21/0.55 tff(1161,plain,
% 0.21/0.55 (in(pigeon_5, hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[290, 1160])).
% 0.21/0.55 tff(1162,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[532, 1161, 1146])).
% 0.21/0.55 tff(1163,plain,(hole_of(pigeon_2) = hole_1), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(1164,plain,
% 0.21/0.55 (in(pigeon_2, hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[267, 1163])).
% 0.21/0.55 tff(1165,plain,
% 0.21/0.55 (~in(pigeon_5, hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[281, 1164])).
% 0.21/0.55 tff(1166,plain,
% 0.21/0.55 (~(hole_of(pigeon_5) = hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[290, 1165])).
% 0.21/0.55 tff(1167,plain,
% 0.21/0.55 (~in(pigeon_5, hole_4)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[574, 1143])).
% 0.21/0.55 tff(1168,plain,
% 0.21/0.55 (~(hole_of(pigeon_5) = hole_4)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[330, 1167])).
% 0.21/0.55 tff(1169,plain,
% 0.21/0.55 ((hole_of(pigeon_5) = hole_2) | (hole_of(pigeon_5) = hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[321, 1080, 1168])).
% 0.21/0.55 tff(1170,plain,
% 0.21/0.55 (hole_of(pigeon_5) = hole_2),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[1169, 1166])).
% 0.21/0.55 tff(1171,plain,
% 0.21/0.55 ((~(hole_of(pigeon_5) = hole_2)) | (hole_of(pigeon_3) = hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[963, 1071, 1096, 1158])).
% 0.21/0.55 tff(1172,plain,
% 0.21/0.55 (hole_of(pigeon_3) = hole_1),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[1171, 1170])).
% 0.21/0.55 tff(1173,plain,
% 0.21/0.55 (in(pigeon_3, hole_1)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[522, 1172])).
% 0.21/0.55 tff(1174,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[547, 112, 17, 388, 159, 32, 1173, 1164])).
% 0.21/0.55 % SZS output end Proof
%------------------------------------------------------------------------------