TSTP Solution File: PLA002-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PLA002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 13:39:51 EDT 2022
% Result : Unsatisfiable 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : PLA002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n029.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Sep 2 17:14:59 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.18/0.39 % SZS status Unsatisfiable
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(at_type, type, (
% 0.18/0.39 at: ( $i * $i ) > $o)).
% 0.18/0.39 tff(walk_type, type, (
% 0.18/0.39 walk: ( $i * $i ) > $i)).
% 0.18/0.39 tff(skate_type, type, (
% 0.18/0.39 skate: ( $i * $i ) > $i)).
% 0.18/0.39 tff(go_type, type, (
% 0.18/0.39 go: ( $i * $i ) > $i)).
% 0.18/0.39 tff(s0_type, type, (
% 0.18/0.39 s0: $i)).
% 0.18/0.39 tff(d_type, type, (
% 0.18/0.39 d: $i)).
% 0.18/0.39 tff(f_type, type, (
% 0.18/0.39 f: $i)).
% 0.18/0.39 tff(c_type, type, (
% 0.18/0.39 c: $i)).
% 0.18/0.39 tff(b_type, type, (
% 0.18/0.39 b: $i)).
% 0.18/0.39 tff(a_type, type, (
% 0.18/0.39 a: $i)).
% 0.18/0.39 tff(cold_type, type, (
% 0.18/0.39 cold: $i > $o)).
% 0.18/0.39 tff(warm_type, type, (
% 0.18/0.39 warm: $i > $o)).
% 0.18/0.39 tff(e_type, type, (
% 0.18/0.39 e: $i)).
% 0.18/0.39 tff(climb_type, type, (
% 0.18/0.39 climb: ( $i * $i ) > $i)).
% 0.18/0.39 tff(1,assumption,(at(a, walk(a, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))))), introduced(assumption)).
% 0.18/0.39 tff(2,plain,
% 0.18/0.39 (^[S: $i] : refl((~at(a, S)) <=> (~at(a, S)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(3,plain,
% 0.18/0.39 (![S: $i] : (~at(a, S)) <=> ![S: $i] : (~at(a, S))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.39 tff(4,plain,
% 0.18/0.39 (![S: $i] : (~at(a, S)) <=> ![S: $i] : (~at(a, S))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(5,axiom,(![S: $i] : (~at(a, S))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_you_can_get_to_a')).
% 0.18/0.39 tff(6,plain,
% 0.18/0.39 (![S: $i] : (~at(a, S))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.39 tff(7,plain,(
% 0.18/0.39 ![S: $i] : (~at(a, S))),
% 0.18/0.39 inference(skolemize,[status(sab)],[6])).
% 0.18/0.39 tff(8,plain,
% 0.18/0.39 (![S: $i] : (~at(a, S))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 ((~![S: $i] : (~at(a, S))) | (~at(a, walk(a, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.39 tff(11,plain,(~at(a, walk(a, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(12,plain,
% 0.18/0.39 (^[Situation: $i] : refl(((~at(b, Situation)) | at(a, walk(a, Situation))) <=> ((~at(b, Situation)) | at(a, walk(a, Situation))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation))) <=> ![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation))) <=> ![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(15,axiom,(![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','walk_b_to_a')).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 (![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.39 tff(17,plain,(
% 0.18/0.39 ![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[16])).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 (![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (((~![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))) | ((~at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))) | at(a, walk(a, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))))) <=> ((~![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))) | (~at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))) | at(a, walk(a, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 ((~![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))) | ((~at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))) | at(a, walk(a, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 ((~![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))) | (~at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))) | at(a, walk(a, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 (~at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (at(f, s0) <=> at(f, s0)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(24,axiom,(at(f, s0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','initial')).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (at(f, s0)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (^[Situation: $i] : refl(((~at(f, Situation)) | at(d, go(d, Situation))) <=> ((~at(f, Situation)) | at(d, go(d, Situation))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 (![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation))) <=> ![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation))) <=> ![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(29,axiom,(![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','go_f_to_d')).
% 0.18/0.40 tff(30,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.18/0.40 tff(31,plain,(
% 0.18/0.40 ![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[30])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 (((~![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))) | ((~at(f, s0)) | at(d, go(d, s0)))) <=> ((~![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))) | (~at(f, s0)) | at(d, go(d, s0)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 ((~![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))) | ((~at(f, s0)) | at(d, go(d, s0)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 ((~![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))) | (~at(f, s0)) | at(d, go(d, s0))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 (at(d, go(d, s0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[35, 32, 25])).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (^[Situation: $i] : refl(((~at(d, Situation)) | at(c, go(c, Situation))) <=> ((~at(d, Situation)) | at(c, go(c, Situation))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(38,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation))) <=> ![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.18/0.40 tff(39,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation))) <=> ![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(40,axiom,(![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','go_d_to_c')).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.40 tff(42,plain,(
% 0.18/0.40 ![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[41])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | ((~at(d, go(d, s0))) | at(c, go(c, go(d, s0))))) <=> ((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | (~at(d, go(d, s0))) | at(c, go(c, go(d, s0))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 ((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | ((~at(d, go(d, s0))) | at(c, go(c, go(d, s0))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 ((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | (~at(d, go(d, s0))) | at(c, go(c, go(d, s0)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 (at(c, go(c, go(d, s0)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[46, 43, 36])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 (^[Situation: $i] : refl(((~at(c, Situation)) | at(d, go(d, Situation))) <=> ((~at(c, Situation)) | at(d, go(d, Situation))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation))) <=> ![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.18/0.40 tff(50,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation))) <=> ![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(51,axiom,(![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','go_c_to_d')).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.18/0.40 tff(53,plain,(
% 0.18/0.40 ![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[52])).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 (((~![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))) | ((~at(c, go(c, go(d, s0)))) | at(d, go(d, go(c, go(d, s0)))))) <=> ((~![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))) | (~at(c, go(c, go(d, s0)))) | at(d, go(d, go(c, go(d, s0)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 ((~![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))) | ((~at(c, go(c, go(d, s0)))) | at(d, go(d, go(c, go(d, s0)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 ((~![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))) | (~at(c, go(c, go(d, s0)))) | at(d, go(d, go(c, go(d, s0))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 (at(d, go(d, go(c, go(d, s0))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[57, 54, 47])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 (((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | ((~at(d, go(d, go(c, go(d, s0))))) | at(c, go(c, go(d, go(c, go(d, s0))))))) <=> ((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | (~at(d, go(d, go(c, go(d, s0))))) | at(c, go(c, go(d, go(c, go(d, s0))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 ((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | ((~at(d, go(d, go(c, go(d, s0))))) | at(c, go(c, go(d, go(c, go(d, s0))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 ((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | (~at(d, go(d, go(c, go(d, s0))))) | at(c, go(c, go(d, go(c, go(d, s0)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (at(c, go(c, go(d, go(c, go(d, s0)))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[61, 43, 58])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (^[Situation: $i] : refl(((~at(c, Situation)) | at(e, go(e, Situation))) <=> ((~at(c, Situation)) | at(e, go(e, Situation))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(c, Situation)) | at(e, go(e, Situation))) <=> ![Situation: $i] : ((~at(c, Situation)) | at(e, go(e, Situation)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[63])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(c, Situation)) | at(e, go(e, Situation))) <=> ![Situation: $i] : ((~at(c, Situation)) | at(e, go(e, Situation)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(66,axiom,(![Situation: $i] : ((~at(c, Situation)) | at(e, go(e, Situation)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','go_c_to_e')).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(c, Situation)) | at(e, go(e, Situation)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.18/0.40 tff(68,plain,(
% 0.18/0.40 ![Situation: $i] : ((~at(c, Situation)) | at(e, go(e, Situation)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[67])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(c, Situation)) | at(e, go(e, Situation)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (((~![Situation: $i] : ((~at(c, Situation)) | at(e, go(e, Situation)))) | ((~at(c, go(c, go(d, go(c, go(d, s0)))))) | at(e, go(e, go(c, go(d, go(c, go(d, s0)))))))) <=> ((~![Situation: $i] : ((~at(c, Situation)) | at(e, go(e, Situation)))) | (~at(c, go(c, go(d, go(c, go(d, s0)))))) | at(e, go(e, go(c, go(d, go(c, go(d, s0)))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 ((~![Situation: $i] : ((~at(c, Situation)) | at(e, go(e, Situation)))) | ((~at(c, go(c, go(d, go(c, go(d, s0)))))) | at(e, go(e, go(c, go(d, go(c, go(d, s0)))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 ((~![Situation: $i] : ((~at(c, Situation)) | at(e, go(e, Situation)))) | (~at(c, go(c, go(d, go(c, go(d, s0)))))) | at(e, go(e, go(c, go(d, go(c, go(d, s0))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (at(e, go(e, go(c, go(d, go(c, go(d, s0))))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[72, 69, 62])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (^[Situation: $i] : refl(((~at(e, Situation)) | at(c, go(c, Situation))) <=> ((~at(e, Situation)) | at(c, go(c, Situation))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(e, Situation)) | at(c, go(c, Situation))) <=> ![Situation: $i] : ((~at(e, Situation)) | at(c, go(c, Situation)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(e, Situation)) | at(c, go(c, Situation))) <=> ![Situation: $i] : ((~at(e, Situation)) | at(c, go(c, Situation)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(77,axiom,(![Situation: $i] : ((~at(e, Situation)) | at(c, go(c, Situation)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','go_e_to_c')).
% 0.18/0.40 tff(78,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(e, Situation)) | at(c, go(c, Situation)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.18/0.40 tff(79,plain,(
% 0.18/0.40 ![Situation: $i] : ((~at(e, Situation)) | at(c, go(c, Situation)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[78])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 (![Situation: $i] : ((~at(e, Situation)) | at(c, go(c, Situation)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.18/0.40 tff(81,plain,
% 0.18/0.40 (((~![Situation: $i] : ((~at(e, Situation)) | at(c, go(c, Situation)))) | ((~at(e, go(e, go(c, go(d, go(c, go(d, s0))))))) | at(c, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) <=> ((~![Situation: $i] : ((~at(e, Situation)) | at(c, go(c, Situation)))) | (~at(e, go(e, go(c, go(d, go(c, go(d, s0))))))) | at(c, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 ((~![Situation: $i] : ((~at(e, Situation)) | at(c, go(c, Situation)))) | ((~at(e, go(e, go(c, go(d, go(c, go(d, s0))))))) | at(c, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 ((~![Situation: $i] : ((~at(e, Situation)) | at(c, go(c, Situation)))) | (~at(e, go(e, go(c, go(d, go(c, go(d, s0))))))) | at(c, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.18/0.40 tff(84,plain,
% 0.18/0.40 (at(c, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[83, 80, 73])).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 (((~![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))) | ((~at(c, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))) | at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))) <=> ((~![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))) | (~at(c, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))) | at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 ((~![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))) | ((~at(c, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))) | at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(87,plain,
% 0.18/0.41 ((~![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))) | (~at(c, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))) | at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 (at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[87, 54, 84])).
% 0.18/0.41 tff(89,plain,
% 0.18/0.41 (^[Situation: $i] : refl(((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation))) <=> ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(90,plain,
% 0.18/0.41 (![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation))) <=> ![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[89])).
% 0.18/0.41 tff(91,plain,
% 0.18/0.41 (![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation))) <=> ![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(92,plain,
% 0.18/0.41 (^[Situation: $i] : rewrite((((~warm(Situation)) | (~at(d, Situation))) | at(b, climb(b, Situation))) <=> ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(93,plain,
% 0.18/0.41 (![Situation: $i] : (((~warm(Situation)) | (~at(d, Situation))) | at(b, climb(b, Situation))) <=> ![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.18/0.41 tff(94,axiom,(![Situation: $i] : (((~warm(Situation)) | (~at(d, Situation))) | at(b, climb(b, Situation)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','climb_mountain_d_to_b')).
% 0.18/0.41 tff(95,plain,
% 0.18/0.41 (![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.41 tff(96,plain,
% 0.18/0.41 (![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.18/0.41 tff(97,plain,(
% 0.18/0.41 ![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[96])).
% 0.18/0.41 tff(98,plain,
% 0.18/0.41 (![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.18/0.41 tff(99,plain,
% 0.18/0.41 (((~![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | ((~at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | (~warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))))) <=> ((~![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | (~at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | (~warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(100,plain,
% 0.18/0.41 (((~warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | (~at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))) <=> ((~at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | (~warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(101,plain,
% 0.18/0.41 (((~![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | ((~warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | (~at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))))) <=> ((~![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | ((~at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | (~warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[100])).
% 0.18/0.41 tff(102,plain,
% 0.18/0.41 (((~![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | ((~warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | (~at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))))) <=> ((~![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | (~at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | (~warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[101, 99])).
% 0.18/0.41 tff(103,plain,
% 0.18/0.41 ((~![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | ((~warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | (~at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(104,plain,
% 0.18/0.41 ((~![Situation: $i] : ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | (~at(d, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | (~warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 ((~warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) | at(b, climb(b, go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[104, 98, 88])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 (~warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[105, 22])).
% 0.18/0.41 tff(107,assumption,(~cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))), introduced(assumption)).
% 0.18/0.41 tff(108,assumption,(~warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))), introduced(assumption)).
% 0.18/0.41 tff(109,plain,
% 0.18/0.41 (^[Situation1: $i, Situation2: $i] : refl((cold(Situation2) | warm(Situation1)) <=> (cold(Situation2) | warm(Situation1)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(110,plain,
% 0.18/0.41 (![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1)) <=> ![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[109])).
% 0.18/0.41 tff(111,plain,
% 0.18/0.41 (![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1)) <=> ![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(112,plain,
% 0.18/0.41 (^[Situation1: $i, Situation2: $i] : rewrite((warm(Situation1) | cold(Situation2)) <=> (cold(Situation2) | warm(Situation1)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(113,plain,
% 0.18/0.41 (![Situation1: $i, Situation2: $i] : (warm(Situation1) | cold(Situation2)) <=> ![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[112])).
% 0.18/0.41 tff(114,axiom,(![Situation1: $i, Situation2: $i] : (warm(Situation1) | cold(Situation2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','warm_or_cold')).
% 0.18/0.41 tff(115,plain,
% 0.18/0.41 (![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.18/0.41 tff(116,plain,
% 0.18/0.41 (![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.18/0.41 tff(117,plain,(
% 0.18/0.41 ![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))),
% 0.18/0.41 inference(skolemize,[status(sab)],[116])).
% 0.18/0.41 tff(118,plain,
% 0.18/0.41 (![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.18/0.41 tff(119,plain,
% 0.18/0.41 (((~![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))) | (warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))) | cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))) <=> ((~![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))) | warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))) | cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(120,plain,
% 0.18/0.42 ((cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))) | warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0))))))))) <=> (warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))) | cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(121,plain,
% 0.18/0.42 (((~![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))) | (cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))) | warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))) <=> ((~![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))) | (warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))) | cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[120])).
% 0.18/0.42 tff(122,plain,
% 0.18/0.42 (((~![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))) | (cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))) | warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))) <=> ((~![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))) | warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))) | cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[121, 119])).
% 0.18/0.42 tff(123,plain,
% 0.18/0.42 ((~![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))) | (cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))) | warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(124,plain,
% 0.18/0.42 ((~![Situation1: $i, Situation2: $i] : (cold(Situation2) | warm(Situation1))) | warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))) | cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.18/0.42 tff(125,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[124, 118, 108, 107])).
% 0.18/0.42 tff(126,plain,(warm(go(d, go(c, go(e, go(c, go(d, go(c, go(d, s0)))))))) | cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(127,plain,
% 0.18/0.42 (cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[126, 106])).
% 0.18/0.42 tff(128,plain,
% 0.18/0.42 (^[Situation: $i] : refl(((~at(d, Situation)) | at(f, go(f, Situation))) <=> ((~at(d, Situation)) | at(f, go(f, Situation))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(129,plain,
% 0.18/0.42 (![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation))) <=> ![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[128])).
% 0.18/0.42 tff(130,plain,
% 0.18/0.42 (![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation))) <=> ![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(131,axiom,(![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','go_d_to_f')).
% 0.18/0.42 tff(132,plain,
% 0.18/0.42 (![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.18/0.42 tff(133,plain,(
% 0.18/0.42 ![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[132])).
% 0.18/0.42 tff(134,plain,
% 0.18/0.42 (![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.18/0.42 tff(135,plain,
% 0.18/0.42 (((~![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))) | ((~at(d, go(d, s0))) | at(f, go(f, go(d, s0))))) <=> ((~![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))) | (~at(d, go(d, s0))) | at(f, go(f, go(d, s0))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(136,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))) | ((~at(d, go(d, s0))) | at(f, go(f, go(d, s0))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(137,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))) | (~at(d, go(d, s0))) | at(f, go(f, go(d, s0)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.18/0.43 tff(138,plain,
% 0.18/0.43 (at(f, go(f, go(d, s0)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[137, 134, 36])).
% 0.18/0.43 tff(139,plain,
% 0.18/0.43 (((~![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))) | ((~at(f, go(f, go(d, s0)))) | at(d, go(d, go(f, go(d, s0)))))) <=> ((~![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))) | (~at(f, go(f, go(d, s0)))) | at(d, go(d, go(f, go(d, s0)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(140,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))) | ((~at(f, go(f, go(d, s0)))) | at(d, go(d, go(f, go(d, s0)))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(141,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))) | (~at(f, go(f, go(d, s0)))) | at(d, go(d, go(f, go(d, s0))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.18/0.43 tff(142,plain,
% 0.18/0.43 (at(d, go(d, go(f, go(d, s0))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[141, 32, 138])).
% 0.18/0.43 tff(143,plain,
% 0.18/0.43 (((~![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))) | ((~at(d, go(d, go(f, go(d, s0))))) | at(f, go(f, go(d, go(f, go(d, s0))))))) <=> ((~![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))) | (~at(d, go(d, go(f, go(d, s0))))) | at(f, go(f, go(d, go(f, go(d, s0))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(144,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))) | ((~at(d, go(d, go(f, go(d, s0))))) | at(f, go(f, go(d, go(f, go(d, s0))))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(145,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(d, Situation)) | at(f, go(f, Situation)))) | (~at(d, go(d, go(f, go(d, s0))))) | at(f, go(f, go(d, go(f, go(d, s0)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.18/0.43 tff(146,plain,
% 0.18/0.43 (at(f, go(f, go(d, go(f, go(d, s0)))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[145, 134, 142])).
% 0.18/0.43 tff(147,plain,
% 0.18/0.43 (((~![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))) | ((~at(f, go(f, go(d, go(f, go(d, s0)))))) | at(d, go(d, go(f, go(d, go(f, go(d, s0)))))))) <=> ((~![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))) | (~at(f, go(f, go(d, go(f, go(d, s0)))))) | at(d, go(d, go(f, go(d, go(f, go(d, s0)))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(148,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))) | ((~at(f, go(f, go(d, go(f, go(d, s0)))))) | at(d, go(d, go(f, go(d, go(f, go(d, s0)))))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(149,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(f, Situation)) | at(d, go(d, Situation)))) | (~at(f, go(f, go(d, go(f, go(d, s0)))))) | at(d, go(d, go(f, go(d, go(f, go(d, s0))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.18/0.43 tff(150,plain,
% 0.18/0.43 (at(d, go(d, go(f, go(d, go(f, go(d, s0))))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[149, 32, 146])).
% 0.18/0.43 tff(151,plain,
% 0.18/0.43 (((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | ((~at(d, go(d, go(f, go(d, go(f, go(d, s0))))))) | at(c, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))) <=> ((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | (~at(d, go(d, go(f, go(d, go(f, go(d, s0))))))) | at(c, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(152,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | ((~at(d, go(d, go(f, go(d, go(f, go(d, s0))))))) | at(c, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(153,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | (~at(d, go(d, go(f, go(d, go(f, go(d, s0))))))) | at(c, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.18/0.43 tff(154,plain,
% 0.18/0.43 (at(c, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[153, 43, 150])).
% 0.18/0.43 tff(155,plain,
% 0.18/0.43 (((~![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))) | ((~at(c, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))) | at(d, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) <=> ((~![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))) | (~at(c, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))) | at(d, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(156,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))) | ((~at(c, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))) | at(d, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(157,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(c, Situation)) | at(d, go(d, Situation)))) | (~at(c, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))) | at(d, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.18/0.43 tff(158,plain,
% 0.18/0.43 (at(d, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[157, 54, 154])).
% 0.18/0.43 tff(159,plain,
% 0.18/0.43 (((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | ((~at(d, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))) | at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))) <=> ((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | (~at(d, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))) | at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(160,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | ((~at(d, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))) | at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(161,plain,
% 0.18/0.43 ((~![Situation: $i] : ((~at(d, Situation)) | at(c, go(c, Situation)))) | (~at(d, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))) | at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.18/0.43 tff(162,plain,
% 0.18/0.43 (at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[161, 43, 158])).
% 0.18/0.43 tff(163,plain,
% 0.18/0.43 (^[Situation: $i] : refl(((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation))) <=> ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(164,plain,
% 0.18/0.43 (![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation))) <=> ![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[163])).
% 0.18/0.43 tff(165,plain,
% 0.18/0.43 (![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation))) <=> ![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(166,plain,
% 0.18/0.43 (^[Situation: $i] : rewrite((((~cold(Situation)) | (~at(c, Situation))) | at(b, skate(b, Situation))) <=> ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(167,plain,
% 0.18/0.43 (![Situation: $i] : (((~cold(Situation)) | (~at(c, Situation))) | at(b, skate(b, Situation))) <=> ![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[166])).
% 0.18/0.43 tff(168,axiom,(![Situation: $i] : (((~cold(Situation)) | (~at(c, Situation))) | at(b, skate(b, Situation)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cross_river_c_to_b')).
% 0.18/0.43 tff(169,plain,
% 0.18/0.43 (![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.18/0.44 tff(170,plain,
% 0.18/0.44 (![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.18/0.44 tff(171,plain,(
% 0.18/0.44 ![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[170])).
% 0.18/0.44 tff(172,plain,
% 0.18/0.44 (![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.18/0.44 tff(173,plain,
% 0.18/0.44 (((~![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | ((~at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | (~cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))))) <=> ((~![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | (~at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | (~cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(174,plain,
% 0.18/0.44 (((~cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | (~at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))) <=> ((~at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | (~cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(175,plain,
% 0.18/0.44 (((~![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | ((~cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | (~at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))))) <=> ((~![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | ((~at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | (~cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[174])).
% 0.18/0.44 tff(176,plain,
% 0.18/0.44 (((~![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | ((~cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | (~at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))))) <=> ((~![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | (~at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | (~cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[175, 173])).
% 0.18/0.44 tff(177,plain,
% 0.18/0.44 ((~![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | ((~cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | (~at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(178,plain,
% 0.18/0.44 ((~![Situation: $i] : ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | (~at(c, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | (~cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.18/0.44 tff(179,plain,
% 0.18/0.44 ((~cold(go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))) | at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[178, 172, 162])).
% 0.18/0.44 tff(180,plain,
% 0.18/0.44 (at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[179, 127])).
% 0.18/0.44 tff(181,plain,
% 0.18/0.44 (((~![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))) | ((~at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))) | at(a, walk(a, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))))) <=> ((~![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))) | (~at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))) | at(a, walk(a, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(182,plain,
% 0.18/0.44 ((~![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))) | ((~at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))) | at(a, walk(a, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(183,plain,
% 0.18/0.44 ((~![Situation: $i] : ((~at(b, Situation)) | at(a, walk(a, Situation)))) | (~at(b, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))) | at(a, walk(a, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.18/0.44 tff(184,plain,
% 0.18/0.44 (at(a, walk(a, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0)))))))))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[183, 18, 180])).
% 0.18/0.44 tff(185,plain,
% 0.18/0.44 ((~![S: $i] : (~at(a, S))) | (~at(a, walk(a, skate(b, go(c, go(d, go(c, go(d, go(f, go(d, go(f, go(d, s0))))))))))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(186,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[185, 8, 184])).
% 0.18/0.44 % SZS output end Proof
%------------------------------------------------------------------------------