TSTP Solution File: SET611+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET611+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 : Tue Sep 20 05:07:18 EDT 2022
% Result : Theorem 0.57s 0.69s
% Output : Proof 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET611+3 : TPTP v8.1.0. Released v2.2.0.
% 0.05/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n007.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Sep 3 06:40:04 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.57/0.69 % SZS status Theorem
% 0.57/0.69 % SZS output start Proof
% 0.57/0.69 tff(member_type, type, (
% 0.57/0.69 member: ( $i * $i ) > $o)).
% 0.57/0.69 tff(tptp_fun_C_3_type, type, (
% 0.57/0.69 tptp_fun_C_3: $i)).
% 0.57/0.69 tff(tptp_fun_D_0_type, type, (
% 0.57/0.69 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.57/0.69 tff(difference_type, type, (
% 0.57/0.69 difference: ( $i * $i ) > $i)).
% 0.57/0.69 tff(tptp_fun_B_4_type, type, (
% 0.57/0.69 tptp_fun_B_4: $i)).
% 0.57/0.69 tff(intersection_type, type, (
% 0.57/0.69 intersection: ( $i * $i ) > $i)).
% 0.57/0.69 tff(empty_set_type, type, (
% 0.57/0.69 empty_set: $i)).
% 0.57/0.69 tff(1,plain,
% 0.57/0.69 (^[B: $i, C: $i, D: $i] : refl((member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))))),
% 0.57/0.69 inference(bind,[status(th)],[])).
% 0.57/0.69 tff(2,plain,
% 0.57/0.69 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.57/0.69 inference(quant_intro,[status(thm)],[1])).
% 0.57/0.69 tff(3,plain,
% 0.57/0.69 (^[B: $i, C: $i, D: $i] : rewrite((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))))),
% 0.57/0.69 inference(bind,[status(th)],[])).
% 0.57/0.69 tff(4,plain,
% 0.57/0.69 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.57/0.69 inference(quant_intro,[status(thm)],[3])).
% 0.57/0.69 tff(5,plain,
% 0.57/0.69 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(6,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_defn')).
% 0.57/0.69 tff(7,plain,
% 0.57/0.69 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.57/0.69 tff(8,plain,(
% 0.57/0.69 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.57/0.69 inference(skolemize,[status(sab)],[7])).
% 0.57/0.69 tff(9,plain,
% 0.57/0.69 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.57/0.69 tff(10,plain,
% 0.57/0.69 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.57/0.69 tff(11,plain,
% 0.57/0.69 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_0(B!4, difference(B!4, C!3)), intersection(C!3, B!4)) <=> (~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3)))))),
% 0.57/0.69 inference(quant_inst,[status(thm)],[])).
% 0.57/0.69 tff(12,plain,
% 0.57/0.69 (member(tptp_fun_D_0(B!4, difference(B!4, C!3)), intersection(C!3, B!4)) <=> (~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3))))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.57/0.69 tff(13,plain,
% 0.57/0.69 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.57/0.69 inference(bind,[status(th)],[])).
% 0.57/0.69 tff(14,plain,
% 0.57/0.69 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.57/0.69 inference(quant_intro,[status(thm)],[13])).
% 0.57/0.69 tff(15,plain,
% 0.57/0.69 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(16,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.57/0.69 tff(17,plain,
% 0.57/0.69 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.57/0.69 tff(18,plain,(
% 0.57/0.69 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.57/0.69 inference(skolemize,[status(sab)],[17])).
% 0.57/0.69 tff(19,plain,
% 0.57/0.69 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.57/0.69 tff(20,plain,
% 0.57/0.69 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!4, C!3) = intersection(C!3, B!4))),
% 0.57/0.69 inference(quant_inst,[status(thm)],[])).
% 0.57/0.69 tff(21,plain,
% 0.57/0.69 (intersection(B!4, C!3) = intersection(C!3, B!4)),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.57/0.69 tff(22,assumption,(~(intersection(B!4, C!3) = empty_set)), introduced(assumption)).
% 0.57/0.69 tff(23,plain,
% 0.57/0.69 ((~((intersection(B!4, C!3) = empty_set) <=> (difference(B!4, C!3) = B!4))) <=> ((~(intersection(B!4, C!3) = empty_set)) <=> (difference(B!4, C!3) = B!4))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(24,plain,
% 0.57/0.69 ((~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))) <=> (~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B)))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(25,axiom,(~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th84')).
% 0.57/0.69 tff(26,plain,
% 0.57/0.69 (~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.57/0.69 tff(27,plain,
% 0.57/0.69 (~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[26, 24])).
% 0.57/0.69 tff(28,plain,
% 0.57/0.69 (~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.57/0.69 tff(29,plain,
% 0.57/0.69 (~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.57/0.69 tff(30,plain,
% 0.57/0.69 (~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.57/0.69 tff(31,plain,
% 0.57/0.69 (~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.57/0.69 tff(32,plain,
% 0.57/0.69 (~![B: $i, C: $i] : ((intersection(B, C) = empty_set) <=> (difference(B, C) = B))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.57/0.69 tff(33,plain,(
% 0.57/0.69 ~((intersection(B!4, C!3) = empty_set) <=> (difference(B!4, C!3) = B!4))),
% 0.57/0.69 inference(skolemize,[status(sab)],[32])).
% 0.57/0.69 tff(34,plain,
% 0.57/0.69 ((~(intersection(B!4, C!3) = empty_set)) <=> (difference(B!4, C!3) = B!4)),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.57/0.69 tff(35,plain,
% 0.57/0.69 ((intersection(B!4, C!3) = empty_set) | (difference(B!4, C!3) = B!4) | (~((~(intersection(B!4, C!3) = empty_set)) <=> (difference(B!4, C!3) = B!4)))),
% 0.57/0.69 inference(tautology,[status(thm)],[])).
% 0.57/0.69 tff(36,plain,
% 0.57/0.69 ((intersection(B!4, C!3) = empty_set) | (difference(B!4, C!3) = B!4)),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.57/0.69 tff(37,plain,
% 0.57/0.69 (difference(B!4, C!3) = B!4),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[36, 22])).
% 0.57/0.69 tff(38,plain,
% 0.57/0.69 (member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)),
% 0.57/0.69 inference(monotonicity,[status(thm)],[37])).
% 0.57/0.69 tff(39,plain,
% 0.57/0.69 (member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4) <=> member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), difference(B!4, C!3))),
% 0.57/0.69 inference(symmetry,[status(thm)],[38])).
% 0.57/0.69 tff(40,plain,
% 0.57/0.69 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), intersection(C!3, B!4)) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3)))))),
% 0.57/0.69 inference(quant_inst,[status(thm)],[])).
% 0.57/0.69 tff(41,plain,
% 0.57/0.69 (member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), intersection(C!3, B!4)) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3))))),
% 0.57/0.69 inference(unit_resolution,[status(thm)],[40, 10])).
% 0.57/0.69 tff(42,plain,
% 0.57/0.69 (intersection(C!3, B!4) = intersection(B!4, C!3)),
% 0.57/0.69 inference(symmetry,[status(thm)],[21])).
% 0.57/0.69 tff(43,plain,
% 0.57/0.69 ((intersection(C!3, B!4) = empty_set) <=> (intersection(B!4, C!3) = empty_set)),
% 0.57/0.69 inference(monotonicity,[status(thm)],[42])).
% 0.57/0.69 tff(44,plain,
% 0.57/0.69 ((intersection(B!4, C!3) = empty_set) <=> (intersection(C!3, B!4) = empty_set)),
% 0.57/0.69 inference(symmetry,[status(thm)],[43])).
% 0.57/0.69 tff(45,plain,
% 0.57/0.69 ((~(intersection(B!4, C!3) = empty_set)) <=> (~(intersection(C!3, B!4) = empty_set))),
% 0.57/0.69 inference(monotonicity,[status(thm)],[44])).
% 0.57/0.69 tff(46,plain,
% 0.57/0.69 (~(intersection(C!3, B!4) = empty_set)),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[22, 45])).
% 0.57/0.69 tff(47,plain,
% 0.57/0.69 (^[B: $i, C: $i] : trans(monotonicity(rewrite((~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))) <=> ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))), (((~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))) | (B = C)) <=> (((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)) | (B = C)))), rewrite((((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)) | (B = C)) <=> ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))), (((~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))) | (B = C)) <=> ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))),
% 0.57/0.69 inference(bind,[status(th)],[])).
% 0.57/0.69 tff(48,plain,
% 0.57/0.69 (![B: $i, C: $i] : ((~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))) | (B = C)) <=> ![B: $i, C: $i] : ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))),
% 0.57/0.69 inference(quant_intro,[status(thm)],[47])).
% 0.57/0.69 tff(49,plain,
% 0.57/0.69 (![B: $i, C: $i] : ((~![D: $i] : (member(D, B) <=> member(D, C))) | (B = C)) <=> ![B: $i, C: $i] : ((~![D: $i] : (member(D, B) <=> member(D, C))) | (B = C))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(50,plain,
% 0.57/0.69 (^[B: $i, C: $i] : rewrite((![D: $i] : (member(D, B) <=> member(D, C)) => (B = C)) <=> ((~![D: $i] : (member(D, B) <=> member(D, C))) | (B = C)))),
% 0.57/0.69 inference(bind,[status(th)],[])).
% 0.57/0.69 tff(51,plain,
% 0.57/0.69 (![B: $i, C: $i] : (![D: $i] : (member(D, B) <=> member(D, C)) => (B = C)) <=> ![B: $i, C: $i] : ((~![D: $i] : (member(D, B) <=> member(D, C))) | (B = C))),
% 0.57/0.69 inference(quant_intro,[status(thm)],[50])).
% 0.57/0.69 tff(52,axiom,(![B: $i, C: $i] : (![D: $i] : (member(D, B) <=> member(D, C)) => (B = C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','member_equal')).
% 0.57/0.69 tff(53,plain,
% 0.57/0.69 (![B: $i, C: $i] : ((~![D: $i] : (member(D, B) <=> member(D, C))) | (B = C))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.57/0.69 tff(54,plain,
% 0.57/0.69 (![B: $i, C: $i] : ((~![D: $i] : (member(D, B) <=> member(D, C))) | (B = C))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.57/0.69 tff(55,plain,(
% 0.57/0.69 ![B: $i, C: $i] : ((~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))) | (B = C))),
% 0.57/0.69 inference(skolemize,[status(sab)],[54])).
% 0.57/0.69 tff(56,plain,
% 0.57/0.69 (![B: $i, C: $i] : ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))),
% 0.57/0.69 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.57/0.69 tff(57,plain,
% 0.57/0.69 (((~![B: $i, C: $i] : ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) | ((intersection(C!3, B!4) = empty_set) | ((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), empty_set)))) <=> ((~![B: $i, C: $i] : ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) | (intersection(C!3, B!4) = empty_set) | ((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), empty_set)))),
% 0.57/0.69 inference(rewrite,[status(thm)],[])).
% 0.57/0.69 tff(58,plain,
% 0.57/0.69 ((~![B: $i, C: $i] : ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) | ((intersection(C!3, B!4) = empty_set) | ((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), empty_set)))),
% 0.57/0.70 inference(quant_inst,[status(thm)],[])).
% 0.57/0.70 tff(59,plain,
% 0.57/0.70 ((~![B: $i, C: $i] : ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) | (intersection(C!3, B!4) = empty_set) | ((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), empty_set))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.57/0.70 tff(60,plain,
% 0.57/0.70 ((intersection(C!3, B!4) = empty_set) | ((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), empty_set))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.57/0.70 tff(61,plain,
% 0.57/0.70 ((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), empty_set)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[60, 46])).
% 0.57/0.70 tff(62,plain,
% 0.57/0.70 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.57/0.70 inference(bind,[status(th)],[])).
% 0.57/0.70 tff(63,plain,
% 0.57/0.70 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.57/0.70 inference(quant_intro,[status(thm)],[62])).
% 0.57/0.70 tff(64,plain,
% 0.57/0.70 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.57/0.70 inference(rewrite,[status(thm)],[])).
% 0.57/0.70 tff(65,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_defn')).
% 0.57/0.70 tff(66,plain,
% 0.57/0.70 (![B: $i] : (~member(B, empty_set))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.57/0.70 tff(67,plain,(
% 0.57/0.70 ![B: $i] : (~member(B, empty_set))),
% 0.57/0.70 inference(skolemize,[status(sab)],[66])).
% 0.57/0.70 tff(68,plain,
% 0.57/0.70 (![B: $i] : (~member(B, empty_set))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.57/0.70 tff(69,plain,
% 0.57/0.70 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), empty_set))),
% 0.57/0.70 inference(quant_inst,[status(thm)],[])).
% 0.57/0.70 tff(70,plain,
% 0.57/0.70 (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), empty_set)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.57/0.70 tff(71,plain,
% 0.57/0.70 ((~((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), intersection(C!3, B!4))) <=> member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), empty_set))) | member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), intersection(C!3, B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), empty_set)),
% 0.57/0.70 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(72,plain,
% 0.57/0.70 (member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), intersection(C!3, B!4))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[71, 70, 61])).
% 0.57/0.70 tff(73,plain,
% 0.57/0.70 ((~(member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), intersection(C!3, B!4)) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3)))))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), intersection(C!3, B!4))) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3))))),
% 0.57/0.70 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(74,plain,
% 0.57/0.70 (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3)))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[73, 72, 41])).
% 0.57/0.70 tff(75,plain,
% 0.57/0.70 (((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3))) | member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)),
% 0.57/0.70 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(76,plain,
% 0.57/0.70 (member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.57/0.70 tff(77,plain,
% 0.57/0.70 (member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), difference(B!4, C!3))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[76, 39])).
% 0.57/0.70 tff(78,plain,
% 0.57/0.70 (^[B: $i, C: $i, D: $i] : refl((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))),
% 0.57/0.70 inference(bind,[status(th)],[])).
% 0.57/0.70 tff(79,plain,
% 0.57/0.70 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.57/0.70 inference(quant_intro,[status(thm)],[78])).
% 0.57/0.70 tff(80,plain,
% 0.57/0.70 (^[B: $i, C: $i, D: $i] : rewrite((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))),
% 0.57/0.70 inference(bind,[status(th)],[])).
% 0.57/0.70 tff(81,plain,
% 0.57/0.70 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.57/0.70 inference(quant_intro,[status(thm)],[80])).
% 0.57/0.70 tff(82,plain,
% 0.57/0.70 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.57/0.70 inference(rewrite,[status(thm)],[])).
% 0.57/0.70 tff(83,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_defn')).
% 0.57/0.70 tff(84,plain,
% 0.57/0.70 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.57/0.70 tff(85,plain,(
% 0.57/0.70 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.57/0.70 inference(skolemize,[status(sab)],[84])).
% 0.57/0.70 tff(86,plain,
% 0.57/0.70 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.57/0.70 tff(87,plain,
% 0.57/0.70 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.57/0.70 tff(88,plain,
% 0.57/0.70 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3))))),
% 0.57/0.70 inference(quant_inst,[status(thm)],[])).
% 0.57/0.70 tff(89,plain,
% 0.57/0.70 (member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3)))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.57/0.70 tff(90,plain,
% 0.57/0.70 (((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3))) | member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3)),
% 0.57/0.70 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(91,plain,
% 0.57/0.70 (member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[90, 74])).
% 0.57/0.70 tff(92,plain,
% 0.57/0.70 (((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3)) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3))),
% 0.57/0.70 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(93,plain,
% 0.57/0.70 ((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.57/0.70 tff(94,plain,
% 0.57/0.70 ((~(member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3))))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3)))),
% 0.57/0.70 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(95,plain,
% 0.57/0.70 ((~(member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), C!3))))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), difference(B!4, C!3)))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.57/0.70 tff(96,plain,
% 0.57/0.70 (~member(tptp_fun_D_0(empty_set, intersection(C!3, B!4)), difference(B!4, C!3))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[95, 89])).
% 0.57/0.70 tff(97,plain,
% 0.57/0.70 ($false),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[96, 77])).
% 0.57/0.70 tff(98,plain,(intersection(B!4, C!3) = empty_set), inference(lemma,lemma(discharge,[]))).
% 0.57/0.70 tff(99,plain,
% 0.57/0.70 (empty_set = intersection(B!4, C!3)),
% 0.57/0.70 inference(symmetry,[status(thm)],[98])).
% 0.57/0.70 tff(100,plain,
% 0.57/0.70 (empty_set = intersection(C!3, B!4)),
% 0.57/0.70 inference(transitivity,[status(thm)],[99, 21])).
% 0.57/0.70 tff(101,plain,
% 0.57/0.70 (member(tptp_fun_D_0(B!4, difference(B!4, C!3)), empty_set) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), intersection(C!3, B!4))),
% 0.57/0.70 inference(monotonicity,[status(thm)],[100])).
% 0.57/0.70 tff(102,plain,
% 0.57/0.70 ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), empty_set)) <=> (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), intersection(C!3, B!4)))),
% 0.57/0.70 inference(monotonicity,[status(thm)],[101])).
% 0.57/0.70 tff(103,plain,
% 0.57/0.70 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), empty_set))),
% 0.57/0.70 inference(quant_inst,[status(thm)],[])).
% 0.57/0.70 tff(104,plain,
% 0.57/0.70 (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), empty_set)),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[103, 68])).
% 0.57/0.70 tff(105,plain,
% 0.57/0.70 (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), intersection(C!3, B!4))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[104, 102])).
% 0.57/0.70 tff(106,plain,
% 0.57/0.70 ((~(member(tptp_fun_D_0(B!4, difference(B!4, C!3)), intersection(C!3, B!4)) <=> (~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3)))))) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), intersection(C!3, B!4)) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3)))),
% 0.57/0.70 inference(tautology,[status(thm)],[])).
% 0.57/0.70 tff(107,plain,
% 0.57/0.70 ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[106, 105, 12])).
% 0.57/0.70 tff(108,plain,
% 0.57/0.70 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3))))),
% 0.57/0.70 inference(quant_inst,[status(thm)],[])).
% 0.57/0.70 tff(109,plain,
% 0.57/0.70 (member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3)))),
% 0.57/0.70 inference(unit_resolution,[status(thm)],[108, 87])).
% 0.57/0.70 tff(110,plain,
% 0.57/0.70 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.57/0.70 inference(bind,[status(th)],[])).
% 0.57/0.70 tff(111,plain,
% 0.57/0.70 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.57/0.70 inference(quant_intro,[status(thm)],[110])).
% 0.57/0.70 tff(112,plain,
% 0.57/0.70 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.57/0.70 inference(pull_quant,[status(thm)],[])).
% 0.57/0.70 tff(113,plain,
% 0.57/0.70 (^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> (~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))))), pull_quant((~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C))))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 0.57/0.70 inference(bind,[status(th)],[])).
% 0.57/0.70 tff(114,plain,
% 0.57/0.70 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.57/0.70 inference(quant_intro,[status(thm)],[113])).
% 0.57/0.70 tff(115,plain,
% 0.57/0.70 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.57/0.70 inference(transitivity,[status(thm)],[114, 112])).
% 0.57/0.70 tff(116,plain,
% 0.57/0.70 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.57/0.70 inference(transitivity,[status(thm)],[115, 111])).
% 0.57/0.70 tff(117,plain,
% 0.57/0.70 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.57/0.70 inference(bind,[status(th)],[])).
% 0.57/0.70 tff(118,plain,
% 0.57/0.70 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.57/0.70 inference(quant_intro,[status(thm)],[117])).
% 0.57/0.70 tff(119,plain,
% 0.57/0.70 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.57/0.70 inference(transitivity,[status(thm)],[118, 116])).
% 0.57/0.70 tff(120,plain,
% 0.57/0.70 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 0.57/0.70 inference(bind,[status(th)],[])).
% 0.57/0.70 tff(121,plain,
% 0.57/0.70 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.57/0.70 inference(quant_intro,[status(thm)],[120])).
% 0.57/0.70 tff(122,plain,
% 0.57/0.70 (^[B: $i, C: $i] : rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))),
% 0.57/0.70 inference(bind,[status(th)],[])).
% 0.57/0.70 tff(123,plain,
% 0.57/0.70 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))),
% 0.57/0.70 inference(quant_intro,[status(thm)],[122])).
% 0.57/0.70 tff(124,plain,
% 0.57/0.70 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.57/0.70 inference(rewrite,[status(thm)],[])).
% 0.57/0.70 tff(125,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_member_defn')).
% 0.57/0.70 tff(126,plain,
% 0.57/0.70 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.57/0.70 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.57/0.70 tff(127,plain,(
% 0.57/0.70 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))),
% 0.57/0.71 inference(skolemize,[status(sab)],[126])).
% 0.57/0.71 tff(128,plain,
% 0.57/0.71 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))),
% 0.57/0.71 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.57/0.71 tff(129,plain,
% 0.57/0.71 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.57/0.71 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.57/0.71 tff(130,plain,
% 0.57/0.71 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.57/0.71 inference(modus_ponens,[status(thm)],[129, 119])).
% 0.57/0.71 tff(131,plain,
% 0.57/0.71 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))) | (~((~((~(difference(B!4, C!3) = B!4)) | (member(tptp_fun_D_0(tptp_fun_D_0(C!3, B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(tptp_fun_D_0(C!3, B!4), difference(B!4, C!3)), B!4)))) | (~((difference(B!4, C!3) = B!4) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4))))))),
% 0.57/0.71 inference(quant_inst,[status(thm)],[])).
% 0.57/0.71 tff(132,plain,
% 0.57/0.71 (~((~((~(difference(B!4, C!3) = B!4)) | (member(tptp_fun_D_0(tptp_fun_D_0(C!3, B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(tptp_fun_D_0(C!3, B!4), difference(B!4, C!3)), B!4)))) | (~((difference(B!4, C!3) = B!4) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)))))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.57/0.71 tff(133,plain,
% 0.57/0.71 (((~((~(difference(B!4, C!3) = B!4)) | (member(tptp_fun_D_0(tptp_fun_D_0(C!3, B!4), difference(B!4, C!3)), difference(B!4, C!3)) <=> member(tptp_fun_D_0(tptp_fun_D_0(C!3, B!4), difference(B!4, C!3)), B!4)))) | (~((difference(B!4, C!3) = B!4) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4))))) | ((difference(B!4, C!3) = B!4) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)))),
% 0.57/0.71 inference(tautology,[status(thm)],[])).
% 0.57/0.71 tff(134,plain,
% 0.57/0.71 ((difference(B!4, C!3) = B!4) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.57/0.71 tff(135,plain,
% 0.57/0.71 ((~(intersection(B!4, C!3) = empty_set)) | (~(difference(B!4, C!3) = B!4)) | (~((~(intersection(B!4, C!3) = empty_set)) <=> (difference(B!4, C!3) = B!4)))),
% 0.57/0.71 inference(tautology,[status(thm)],[])).
% 0.57/0.71 tff(136,plain,
% 0.57/0.71 ((~(intersection(B!4, C!3) = empty_set)) | (~(difference(B!4, C!3) = B!4))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[135, 34])).
% 0.57/0.71 tff(137,plain,
% 0.57/0.71 (~(difference(B!4, C!3) = B!4)),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[136, 98])).
% 0.57/0.71 tff(138,plain,
% 0.57/0.71 ((~((difference(B!4, C!3) = B!4) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)))) | (difference(B!4, C!3) = B!4) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4))),
% 0.57/0.71 inference(tautology,[status(thm)],[])).
% 0.57/0.71 tff(139,plain,
% 0.57/0.71 ((~((difference(B!4, C!3) = B!4) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)))) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.57/0.71 tff(140,plain,
% 0.57/0.71 ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[139, 134])).
% 0.57/0.71 tff(141,assumption,(~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)), introduced(assumption)).
% 0.57/0.71 tff(142,plain,
% 0.57/0.71 ((~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4))) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)),
% 0.57/0.71 inference(tautology,[status(thm)],[])).
% 0.57/0.71 tff(143,plain,
% 0.57/0.71 (member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[142, 141, 140])).
% 0.57/0.71 tff(144,plain,
% 0.57/0.71 (((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)),
% 0.57/0.71 inference(tautology,[status(thm)],[])).
% 0.57/0.71 tff(145,plain,
% 0.57/0.71 ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3)),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[144, 141])).
% 0.57/0.71 tff(146,plain,
% 0.57/0.71 ((~(member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3))))) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3)))),
% 0.57/0.71 inference(tautology,[status(thm)],[])).
% 0.57/0.71 tff(147,plain,
% 0.57/0.71 ($false),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[146, 145, 143, 109])).
% 0.57/0.71 tff(148,plain,(member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.71 tff(149,plain,
% 0.57/0.71 ((~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3)))) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3))),
% 0.57/0.71 inference(tautology,[status(thm)],[])).
% 0.57/0.71 tff(150,plain,
% 0.57/0.71 ((~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3)))) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.57/0.71 tff(151,plain,
% 0.57/0.71 (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3)),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[150, 107])).
% 0.57/0.71 tff(152,plain,
% 0.57/0.71 ((~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3))) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3)),
% 0.57/0.71 inference(tautology,[status(thm)],[])).
% 0.57/0.71 tff(153,plain,
% 0.57/0.71 (~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[152, 148, 151])).
% 0.57/0.71 tff(154,plain,
% 0.57/0.71 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))) | (~((~((~(difference(B!4, C!3) = B!4)) | (member(tptp_fun_D_0(intersection(C!3, B!4), B!4), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(C!3, B!4), B!4), B!4)))) | (~((difference(B!4, C!3) = B!4) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4))))))),
% 0.57/0.71 inference(quant_inst,[status(thm)],[])).
% 0.57/0.71 tff(155,plain,
% 0.57/0.71 (~((~((~(difference(B!4, C!3) = B!4)) | (member(tptp_fun_D_0(intersection(C!3, B!4), B!4), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(C!3, B!4), B!4), B!4)))) | (~((difference(B!4, C!3) = B!4) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)))))),
% 0.57/0.71 inference(unit_resolution,[status(thm)],[154, 130])).
% 0.57/0.71 tff(156,plain,
% 0.57/0.71 (((~((~(difference(B!4, C!3) = B!4)) | (member(tptp_fun_D_0(intersection(C!3, B!4), B!4), difference(B!4, C!3)) <=> member(tptp_fun_D_0(intersection(C!3, B!4), B!4), B!4)))) | (~((difference(B!4, C!3) = B!4) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4))))) | ((difference(B!4, C!3) = B!4) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)))),
% 0.57/0.72 inference(tautology,[status(thm)],[])).
% 0.57/0.72 tff(157,plain,
% 0.57/0.72 ((difference(B!4, C!3) = B!4) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4))),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.57/0.72 tff(158,plain,
% 0.57/0.72 ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[139, 157])).
% 0.57/0.72 tff(159,plain,
% 0.57/0.72 ((~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4))) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4))),
% 0.57/0.72 inference(tautology,[status(thm)],[])).
% 0.57/0.72 tff(160,plain,
% 0.57/0.72 ((~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))) <=> member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4))) | (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3)))),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[159, 148])).
% 0.57/0.72 tff(161,plain,
% 0.57/0.72 (~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3))),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[160, 158])).
% 0.57/0.72 tff(162,plain,
% 0.57/0.72 ((~(member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3))))) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3)) | ((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3))),
% 0.57/0.72 inference(tautology,[status(thm)],[])).
% 0.57/0.72 tff(163,plain,
% 0.57/0.72 (~(member(tptp_fun_D_0(B!4, difference(B!4, C!3)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(B!4, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(B!4, difference(B!4, C!3)), C!3))))),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[162, 161, 153])).
% 0.57/0.72 tff(164,plain,
% 0.57/0.72 ($false),
% 0.57/0.72 inference(unit_resolution,[status(thm)],[108, 87, 163])).
% 0.57/0.72 % SZS output end Proof
%------------------------------------------------------------------------------