TSTP Solution File: COM007+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM007+2 : TPTP v8.1.0. Released v3.2.0.
% 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 : Tue Sep 6 18:05:44 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM007+2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 13:36:42 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(reflexive_rewrite_type, type, (
% 0.20/0.41 reflexive_rewrite: ( $i * $i ) > $o)).
% 0.20/0.41 tff(c_type, type, (
% 0.20/0.41 c: $i)).
% 0.20/0.41 tff(b_type, type, (
% 0.20/0.41 b: $i)).
% 0.20/0.41 tff(a_type, type, (
% 0.20/0.41 a: $i)).
% 0.20/0.41 tff(rewrite_type, type, (
% 0.20/0.41 rewrite: ( $i * $i ) > $o)).
% 0.20/0.41 tff(goal_type, type, (
% 0.20/0.41 goal: $o)).
% 0.20/0.41 tff(tptp_fun_D_0_type, type, (
% 0.20/0.41 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.20/0.41 tff(1,assumption,(a = c), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (reflexive_rewrite(a, b) <=> reflexive_rewrite(c, b)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (reflexive_rewrite(c, b) <=> reflexive_rewrite(a, b)),
% 0.20/0.41 inference(symmetry,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 ((~reflexive_rewrite(c, b)) <=> (~reflexive_rewrite(a, b))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[3])).
% 0.20/0.41 tff(5,assumption,(~reflexive_rewrite(b, b)), introduced(assumption)).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (^[A: $i, B: $i] : refl(((~(A = B)) | reflexive_rewrite(A, B)) <=> ((~(A = B)) | reflexive_rewrite(A, B)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B)) <=> ![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B)) <=> ![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (^[A: $i, B: $i] : rewrite(((A = B) => reflexive_rewrite(A, B)) <=> ((~(A = B)) | reflexive_rewrite(A, B)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((A = B) => reflexive_rewrite(A, B)) <=> ![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.41 tff(11,axiom,(![A: $i, B: $i] : ((A = B) => reflexive_rewrite(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_in_reflexive_rewrite')).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.41 tff(14,plain,(
% 0.20/0.41 ![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(skolemize,[status(sab)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | reflexive_rewrite(b, b)) <=> ((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | reflexive_rewrite(b, b))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (($false | reflexive_rewrite(b, b)) <=> reflexive_rewrite(b, b)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 ((~$true) <=> $false),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 ((b = b) <=> $true),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 ((~(b = b)) <=> (~$true)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 ((~(b = b)) <=> $false),
% 0.20/0.41 inference(transitivity,[status(thm)],[20, 18])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (((~(b = b)) | reflexive_rewrite(b, b)) <=> ($false | reflexive_rewrite(b, b))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (((~(b = b)) | reflexive_rewrite(b, b)) <=> reflexive_rewrite(b, b)),
% 0.20/0.41 inference(transitivity,[status(thm)],[22, 17])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | ((~(b = b)) | reflexive_rewrite(b, b))) <=> ((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | reflexive_rewrite(b, b))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | ((~(b = b)) | reflexive_rewrite(b, b))) <=> ((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | reflexive_rewrite(b, b))),
% 0.20/0.41 inference(transitivity,[status(thm)],[24, 16])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | ((~(b = b)) | reflexive_rewrite(b, b))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | reflexive_rewrite(b, b)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[27, 15, 5])).
% 0.20/0.41 tff(29,plain,(reflexive_rewrite(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (^[A: $i] : refl(((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A))) <=> ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A))) <=> ![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(rewrite((reflexive_rewrite(b, A) & reflexive_rewrite(c, A)) <=> (~((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A))))), ((~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A))) <=> (~(~((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A))))))), rewrite((~(~((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A))))) <=> ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))), ((~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A))) <=> ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![A: $i] : (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A))) <=> ![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (![A: $i] : (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A))) <=> ![A: $i] : (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(iff_false(asserted(~goal), (goal <=> $false)), ((goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))) <=> ($false | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))))), rewrite(($false | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))) <=> (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))), ((goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))) <=> (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (![A: $i] : (goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))) <=> ![A: $i] : (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (^[A: $i] : rewrite(((reflexive_rewrite(b, A) & reflexive_rewrite(c, A)) => goal) <=> (goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (![A: $i] : ((reflexive_rewrite(b, A) & reflexive_rewrite(c, A)) => goal) <=> ![A: $i] : (goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.41 tff(39,axiom,(![A: $i] : ((reflexive_rewrite(b, A) & reflexive_rewrite(c, A)) => goal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goal_ax')).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![A: $i] : (goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (![A: $i] : (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (![A: $i] : (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.20/0.41 tff(43,plain,(
% 0.20/0.41 ![A: $i] : (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[42])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[44, 31])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (((~![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | ((~reflexive_rewrite(b, b)) | (~reflexive_rewrite(c, b)))) <=> ((~![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | (~reflexive_rewrite(b, b)) | (~reflexive_rewrite(c, b)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 ((~![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | ((~reflexive_rewrite(b, b)) | (~reflexive_rewrite(c, b)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 ((~![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | (~reflexive_rewrite(b, b)) | (~reflexive_rewrite(c, b))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (~reflexive_rewrite(c, b)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[48, 45, 29])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (~reflexive_rewrite(a, b)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[49, 4])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (reflexive_rewrite(a, b) <=> reflexive_rewrite(a, b)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(52,axiom,(reflexive_rewrite(a, b) & reflexive_rewrite(a, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','assumption')).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (reflexive_rewrite(a, b)),
% 0.20/0.41 inference(and_elim,[status(thm)],[52])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (reflexive_rewrite(a, b)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[53, 51])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[54, 50])).
% 0.20/0.41 tff(56,plain,(~(a = c)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (^[A: $i, B: $i] : refl(((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B))) <=> ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B))) <=> ![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B))) <=> ![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (^[A: $i, B: $i] : rewrite((reflexive_rewrite(A, B) => ((A = B) | rewrite(A, B))) <=> ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (![A: $i, B: $i] : (reflexive_rewrite(A, B) => ((A = B) | rewrite(A, B))) <=> ![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.41 tff(62,axiom,(![A: $i, B: $i] : (reflexive_rewrite(A, B) => ((A = B) | rewrite(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_or_rewrite')).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.41 tff(65,plain,(
% 0.20/0.41 ![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[64])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (reflexive_rewrite(a, c) <=> reflexive_rewrite(a, c)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (reflexive_rewrite(a, c)),
% 0.20/0.41 inference(and_elim,[status(thm)],[52])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (reflexive_rewrite(a, c)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (((~![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | ((a = c) | rewrite(a, c) | (~reflexive_rewrite(a, c)))) <=> ((~![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | (a = c) | rewrite(a, c) | (~reflexive_rewrite(a, c)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | ((a = c) | rewrite(a, c) | (~reflexive_rewrite(a, c)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | (a = c) | rewrite(a, c) | (~reflexive_rewrite(a, c))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 ((a = c) | rewrite(a, c)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[72, 69, 66])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (rewrite(a, c)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[73, 56])).
% 0.20/0.41 tff(75,assumption,(~((~rewrite(b, tptp_fun_D_0(c, b))) | (~rewrite(c, tptp_fun_D_0(c, b))))), introduced(assumption)).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (((~rewrite(b, tptp_fun_D_0(c, b))) | (~rewrite(c, tptp_fun_D_0(c, b)))) | rewrite(b, tptp_fun_D_0(c, b))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (rewrite(b, tptp_fun_D_0(c, b))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (^[A: $i, B: $i] : refl(((~rewrite(A, B)) | reflexive_rewrite(A, B)) <=> ((~rewrite(A, B)) | reflexive_rewrite(A, B)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B)) <=> ![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B)) <=> ![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (^[A: $i, B: $i] : rewrite((rewrite(A, B) => reflexive_rewrite(A, B)) <=> ((~rewrite(A, B)) | reflexive_rewrite(A, B)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (![A: $i, B: $i] : (rewrite(A, B) => reflexive_rewrite(A, B)) <=> ![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.41 tff(83,axiom,(![A: $i, B: $i] : (rewrite(A, B) => reflexive_rewrite(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rewrite_in_reflexive_rewrite')).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.41 tff(86,plain,(
% 0.20/0.41 ![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(skolemize,[status(sab)],[85])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (((~![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))) | ((~rewrite(b, tptp_fun_D_0(c, b))) | reflexive_rewrite(b, tptp_fun_D_0(c, b)))) <=> ((~![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))) | (~rewrite(b, tptp_fun_D_0(c, b))) | reflexive_rewrite(b, tptp_fun_D_0(c, b)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))) | ((~rewrite(b, tptp_fun_D_0(c, b))) | reflexive_rewrite(b, tptp_fun_D_0(c, b)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))) | (~rewrite(b, tptp_fun_D_0(c, b))) | reflexive_rewrite(b, tptp_fun_D_0(c, b))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (reflexive_rewrite(b, tptp_fun_D_0(c, b))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[90, 87, 77])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (((~rewrite(b, tptp_fun_D_0(c, b))) | (~rewrite(c, tptp_fun_D_0(c, b)))) | rewrite(c, tptp_fun_D_0(c, b))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (rewrite(c, tptp_fun_D_0(c, b))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[92, 75])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (((~![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))) | ((~rewrite(c, tptp_fun_D_0(c, b))) | reflexive_rewrite(c, tptp_fun_D_0(c, b)))) <=> ((~![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))) | (~rewrite(c, tptp_fun_D_0(c, b))) | reflexive_rewrite(c, tptp_fun_D_0(c, b)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))) | ((~rewrite(c, tptp_fun_D_0(c, b))) | reflexive_rewrite(c, tptp_fun_D_0(c, b)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))) | (~rewrite(c, tptp_fun_D_0(c, b))) | reflexive_rewrite(c, tptp_fun_D_0(c, b))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (reflexive_rewrite(c, tptp_fun_D_0(c, b))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[96, 87, 93])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (((~![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | ((~reflexive_rewrite(b, tptp_fun_D_0(c, b))) | (~reflexive_rewrite(c, tptp_fun_D_0(c, b))))) <=> ((~![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | (~reflexive_rewrite(b, tptp_fun_D_0(c, b))) | (~reflexive_rewrite(c, tptp_fun_D_0(c, b))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 ((~![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | ((~reflexive_rewrite(b, tptp_fun_D_0(c, b))) | (~reflexive_rewrite(c, tptp_fun_D_0(c, b))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 ((~![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | (~reflexive_rewrite(b, tptp_fun_D_0(c, b))) | (~reflexive_rewrite(c, tptp_fun_D_0(c, b)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[100, 45, 97, 91])).
% 0.20/0.42 tff(102,plain,((~rewrite(b, tptp_fun_D_0(c, b))) | (~rewrite(c, tptp_fun_D_0(c, b)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(103,assumption,(rewrite(a, c)), introduced(assumption)).
% 0.20/0.42 tff(104,assumption,(rewrite(a, b)), introduced(assumption)).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : refl(((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B)))))) <=> ((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B)))))) <=> ![A: $i, B: $i, C: $i] : ((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((rewrite(A, B) & rewrite(A, C)) <=> (~((~rewrite(A, B)) | (~rewrite(A, C))))), ((~(rewrite(A, B) & rewrite(A, C))) <=> (~(~((~rewrite(A, B)) | (~rewrite(A, C))))))), rewrite((~(~((~rewrite(A, B)) | (~rewrite(A, C))))) <=> ((~rewrite(A, B)) | (~rewrite(A, C)))), ((~(rewrite(A, B) & rewrite(A, C))) <=> ((~rewrite(A, B)) | (~rewrite(A, C))))), rewrite((rewrite(B, tptp_fun_D_0(C, B)) & rewrite(C, tptp_fun_D_0(C, B))) <=> (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B)))))), (((~(rewrite(A, B) & rewrite(A, C))) | (rewrite(B, tptp_fun_D_0(C, B)) & rewrite(C, tptp_fun_D_0(C, B)))) <=> (((~rewrite(A, B)) | (~rewrite(A, C))) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B)))))))), rewrite((((~rewrite(A, B)) | (~rewrite(A, C))) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B)))))) <=> ((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B))))))), (((~(rewrite(A, B) & rewrite(A, C))) | (rewrite(B, tptp_fun_D_0(C, B)) & rewrite(C, tptp_fun_D_0(C, B)))) <=> ((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~(rewrite(A, B) & rewrite(A, C))) | (rewrite(B, tptp_fun_D_0(C, B)) & rewrite(C, tptp_fun_D_0(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~(rewrite(A, B) & rewrite(A, C))) | ?[D: $i] : (rewrite(B, D) & rewrite(C, D))) <=> ![A: $i, B: $i, C: $i] : ((~(rewrite(A, B) & rewrite(A, C))) | ?[D: $i] : (rewrite(B, D) & rewrite(C, D)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : rewrite(((rewrite(A, B) & rewrite(A, C)) => ?[D: $i] : (rewrite(B, D) & rewrite(C, D))) <=> ((~(rewrite(A, B) & rewrite(A, C))) | ?[D: $i] : (rewrite(B, D) & rewrite(C, D))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((rewrite(A, B) & rewrite(A, C)) => ?[D: $i] : (rewrite(B, D) & rewrite(C, D))) <=> ![A: $i, B: $i, C: $i] : ((~(rewrite(A, B) & rewrite(A, C))) | ?[D: $i] : (rewrite(B, D) & rewrite(C, D)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.42 tff(112,axiom,(![A: $i, B: $i, C: $i] : ((rewrite(A, B) & rewrite(A, C)) => ?[D: $i] : (rewrite(B, D) & rewrite(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rewrite_diamond')).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~(rewrite(A, B) & rewrite(A, C))) | ?[D: $i] : (rewrite(B, D) & rewrite(C, D)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~(rewrite(A, B) & rewrite(A, C))) | ?[D: $i] : (rewrite(B, D) & rewrite(C, D)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.20/0.42 tff(115,plain,(
% 0.20/0.42 ![A: $i, B: $i, C: $i] : ((~(rewrite(A, B) & rewrite(A, C))) | (rewrite(B, tptp_fun_D_0(C, B)) & rewrite(C, tptp_fun_D_0(C, B))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[114])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i] : ((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B))))))) | ((~rewrite(a, b)) | (~rewrite(a, c)) | (~((~rewrite(b, tptp_fun_D_0(c, b))) | (~rewrite(c, tptp_fun_D_0(c, b))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B))))))) | (~rewrite(a, b)) | (~rewrite(a, c)) | (~((~rewrite(b, tptp_fun_D_0(c, b))) | (~rewrite(c, tptp_fun_D_0(c, b))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : ((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B))))))) | ((~rewrite(a, b)) | (~rewrite(a, c)) | (~((~rewrite(b, tptp_fun_D_0(c, b))) | (~rewrite(c, tptp_fun_D_0(c, b))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : ((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B))))))) | (~rewrite(a, b)) | (~rewrite(a, c)) | (~((~rewrite(b, tptp_fun_D_0(c, b))) | (~rewrite(c, tptp_fun_D_0(c, b)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[120, 117, 104, 103, 102])).
% 0.20/0.42 tff(122,plain,((~rewrite(a, c)) | (~rewrite(a, b))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (~rewrite(a, b)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[122, 74])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 (((~![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | ((a = b) | rewrite(a, b) | (~reflexive_rewrite(a, b)))) <=> ((~![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | (a = b) | rewrite(a, b) | (~reflexive_rewrite(a, b)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | ((a = b) | rewrite(a, b) | (~reflexive_rewrite(a, b)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : ((A = B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | (a = b) | rewrite(a, b) | (~reflexive_rewrite(a, b))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 ((a = b) | rewrite(a, b)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[126, 54, 66])).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 (a = b),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[127, 123])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 (b = a),
% 0.20/0.42 inference(symmetry,[status(thm)],[128])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 (reflexive_rewrite(b, c) <=> reflexive_rewrite(a, c)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[129])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 (reflexive_rewrite(a, c) <=> reflexive_rewrite(b, c)),
% 0.20/0.42 inference(symmetry,[status(thm)],[130])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (reflexive_rewrite(b, c)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[69, 131])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (((~![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | ((~reflexive_rewrite(b, c)) | (~reflexive_rewrite(c, c)))) <=> ((~![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | (~reflexive_rewrite(b, c)) | (~reflexive_rewrite(c, c)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 ((~![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | ((~reflexive_rewrite(b, c)) | (~reflexive_rewrite(c, c)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 ((~![A: $i] : ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | (~reflexive_rewrite(b, c)) | (~reflexive_rewrite(c, c))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 ((~reflexive_rewrite(b, c)) | (~reflexive_rewrite(c, c))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[135, 45])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 (~reflexive_rewrite(c, c)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[136, 132])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 (((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | reflexive_rewrite(c, c)) <=> ((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | reflexive_rewrite(c, c))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 (($false | reflexive_rewrite(c, c)) <=> reflexive_rewrite(c, c)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 ((c = c) <=> $true),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(141,plain,
% 0.20/0.42 ((~(c = c)) <=> (~$true)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[140])).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 ((~(c = c)) <=> $false),
% 0.20/0.42 inference(transitivity,[status(thm)],[141, 18])).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 (((~(c = c)) | reflexive_rewrite(c, c)) <=> ($false | reflexive_rewrite(c, c))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.42 tff(144,plain,
% 0.20/0.42 (((~(c = c)) | reflexive_rewrite(c, c)) <=> reflexive_rewrite(c, c)),
% 0.20/0.42 inference(transitivity,[status(thm)],[143, 139])).
% 0.20/0.42 tff(145,plain,
% 0.20/0.42 (((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | ((~(c = c)) | reflexive_rewrite(c, c))) <=> ((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | reflexive_rewrite(c, c))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[144])).
% 0.20/0.42 tff(146,plain,
% 0.20/0.42 (((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | ((~(c = c)) | reflexive_rewrite(c, c))) <=> ((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | reflexive_rewrite(c, c))),
% 0.20/0.42 inference(transitivity,[status(thm)],[145, 138])).
% 0.20/0.42 tff(147,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | ((~(c = c)) | reflexive_rewrite(c, c))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(148,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : ((~(A = B)) | reflexive_rewrite(A, B))) | reflexive_rewrite(c, c)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.42 tff(149,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[148, 15, 137])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------