%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM007+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:00:57 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM007+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 12:21:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(equalish_type, type, (
% 0.18/0.37 equalish: ( $i * $i ) > $o)).
% 0.18/0.37 tff(c_type, type, (
% 0.18/0.37 c: $i)).
% 0.18/0.37 tff(reflexive_rewrite_type, type, (
% 0.18/0.37 reflexive_rewrite: ( $i * $i ) > $o)).
% 0.18/0.37 tff(b_type, type, (
% 0.18/0.37 b: $i)).
% 0.18/0.37 tff(a_type, type, (
% 0.18/0.37 a: $i)).
% 0.18/0.37 tff(rewrite_type, type, (
% 0.18/0.37 rewrite: ( $i * $i ) > $o)).
% 0.18/0.37 tff(goal_type, type, (
% 0.18/0.37 goal: $o)).
% 0.18/0.37 tff(tptp_fun_D_0_type, type, (
% 0.18/0.37 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.18/0.37 tff(1,assumption,(~equalish(c, c)), introduced(assumption)).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (^[A: $i] : refl(equalish(A, A) <=> equalish(A, A))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (![A: $i] : equalish(A, A) <=> ![A: $i] : equalish(A, A)),
% 0.18/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (![A: $i] : equalish(A, A) <=> ![A: $i] : equalish(A, A)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(5,axiom,(![A: $i] : equalish(A, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (![A: $i] : equalish(A, A)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.37 tff(7,plain,(
% 0.18/0.37 ![A: $i] : equalish(A, A)),
% 0.18/0.37 inference(skolemize,[status(sab)],[6])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (![A: $i] : equalish(A, A)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 ((~![A: $i] : equalish(A, A)) | equalish(c, c)),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.37 tff(11,plain,(equalish(c, c)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(12,assumption,(~equalish(b, b)), introduced(assumption)).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 ((~![A: $i] : equalish(A, A)) | equalish(b, b)),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[13, 8, 12])).
% 0.18/0.37 tff(15,plain,(equalish(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (^[A: $i, B: $i] : refl(((~equalish(A, B)) | reflexive_rewrite(A, B)) <=> ((~equalish(A, B)) | reflexive_rewrite(A, B)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B)) <=> ![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B)) <=> ![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (^[A: $i, B: $i] : rewrite((equalish(A, B) => reflexive_rewrite(A, B)) <=> ((~equalish(A, B)) | reflexive_rewrite(A, B)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (![A: $i, B: $i] : (equalish(A, B) => reflexive_rewrite(A, B)) <=> ![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.37 tff(21,axiom,(![A: $i, B: $i] : (equalish(A, B) => reflexive_rewrite(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equalish_in_reflexive_rewrite')).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.18/0.37 tff(24,plain,(
% 0.18/0.37 ![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.37 inference(skolemize,[status(sab)],[23])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 (((~![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))) | ((~equalish(b, b)) | reflexive_rewrite(b, b))) <=> ((~![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))) | (~equalish(b, b)) | reflexive_rewrite(b, b))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 ((~![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))) | ((~equalish(b, b)) | reflexive_rewrite(b, b))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 ((~![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))) | (~equalish(b, b)) | reflexive_rewrite(b, b)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (reflexive_rewrite(b, b)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[28, 25, 15])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 ((~goal) <=> (~goal)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(31,axiom,(~goal), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goal_to_be_proved')).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (~goal),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (^[A: $i] : refl((goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A))) <=> (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A))) <=> ![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 (^[A: $i] : trans(monotonicity(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))))), ((goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))) <=> (goal | ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))))), rewrite((goal | ((~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) <=> (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))), ((goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))) <=> (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 (![A: $i] : (goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))) <=> ![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 (![A: $i] : (goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))) <=> ![A: $i] : (goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 (^[A: $i] : rewrite(((reflexive_rewrite(b, A) & reflexive_rewrite(c, A)) => goal) <=> (goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 (![A: $i] : ((reflexive_rewrite(b, A) & reflexive_rewrite(c, A)) => goal) <=> ![A: $i] : (goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.18/0.38 tff(40,axiom,(![A: $i] : ((reflexive_rewrite(b, A) & reflexive_rewrite(c, A)) => goal)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goal_ax')).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (![A: $i] : (goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (![A: $i] : (goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.18/0.38 tff(43,plain,(
% 0.18/0.38 ![A: $i] : (goal | (~(reflexive_rewrite(b, A) & reflexive_rewrite(c, A))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[42])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (((~![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | (goal | (~reflexive_rewrite(b, b)) | (~reflexive_rewrite(c, b)))) <=> ((~![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | goal | (~reflexive_rewrite(b, b)) | (~reflexive_rewrite(c, b)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 ((~![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | (goal | (~reflexive_rewrite(b, b)) | (~reflexive_rewrite(c, b)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 ((~![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | goal | (~reflexive_rewrite(b, b)) | (~reflexive_rewrite(c, b))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 (~reflexive_rewrite(c, b)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[48, 45, 32, 29])).
% 0.18/0.38 tff(50,assumption,(equalish(c, a)), introduced(assumption)).
% 0.18/0.38 tff(51,assumption,(~reflexive_rewrite(c, b)), introduced(assumption)).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 (^[A: $i, B: $i, C: $i] : refl((reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B))) <=> (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B))) <=> ![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[52])).
% 0.18/0.38 tff(54,plain,
% 0.18/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((equalish(A, B) & reflexive_rewrite(B, C)) <=> (~((~equalish(A, B)) | (~reflexive_rewrite(B, C))))), ((~(equalish(A, B) & reflexive_rewrite(B, C))) <=> (~(~((~equalish(A, B)) | (~reflexive_rewrite(B, C))))))), rewrite((~(~((~equalish(A, B)) | (~reflexive_rewrite(B, C))))) <=> ((~equalish(A, B)) | (~reflexive_rewrite(B, C)))), ((~(equalish(A, B) & reflexive_rewrite(B, C))) <=> ((~equalish(A, B)) | (~reflexive_rewrite(B, C))))), (((~(equalish(A, B) & reflexive_rewrite(B, C))) | reflexive_rewrite(A, C)) <=> (((~equalish(A, B)) | (~reflexive_rewrite(B, C))) | reflexive_rewrite(A, C)))), rewrite((((~equalish(A, B)) | (~reflexive_rewrite(B, C))) | reflexive_rewrite(A, C)) <=> (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))), (((~(equalish(A, B) & reflexive_rewrite(B, C))) | reflexive_rewrite(A, C)) <=> (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(55,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : ((~(equalish(A, B) & reflexive_rewrite(B, C))) | reflexive_rewrite(A, C)) <=> ![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[54])).
% 0.18/0.38 tff(56,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : ((~(equalish(A, B) & reflexive_rewrite(B, C))) | reflexive_rewrite(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(equalish(A, B) & reflexive_rewrite(B, C))) | reflexive_rewrite(A, C))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(57,plain,
% 0.18/0.38 (^[A: $i, B: $i, C: $i] : rewrite(((equalish(A, B) & reflexive_rewrite(B, C)) => reflexive_rewrite(A, C)) <=> ((~(equalish(A, B) & reflexive_rewrite(B, C))) | reflexive_rewrite(A, C)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(58,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : ((equalish(A, B) & reflexive_rewrite(B, C)) => reflexive_rewrite(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(equalish(A, B) & reflexive_rewrite(B, C))) | reflexive_rewrite(A, C))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[57])).
% 0.18/0.38 tff(59,axiom,(![A: $i, B: $i, C: $i] : ((equalish(A, B) & reflexive_rewrite(B, C)) => reflexive_rewrite(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','substitution')).
% 0.18/0.38 tff(60,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : ((~(equalish(A, B) & reflexive_rewrite(B, C))) | reflexive_rewrite(A, C))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.18/0.38 tff(61,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : ((~(equalish(A, B) & reflexive_rewrite(B, C))) | reflexive_rewrite(A, C))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.18/0.38 tff(62,plain,(
% 0.18/0.38 ![A: $i, B: $i, C: $i] : ((~(equalish(A, B) & reflexive_rewrite(B, C))) | reflexive_rewrite(A, C))),
% 0.18/0.38 inference(skolemize,[status(sab)],[61])).
% 0.18/0.38 tff(63,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.18/0.38 tff(64,plain,
% 0.18/0.38 (![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.18/0.38 tff(65,plain,
% 0.18/0.38 (reflexive_rewrite(a, b) <=> reflexive_rewrite(a, b)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(66,axiom,(reflexive_rewrite(a, b) & reflexive_rewrite(a, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','assumption')).
% 0.18/0.38 tff(67,plain,
% 0.18/0.38 (reflexive_rewrite(a, b)),
% 0.18/0.38 inference(and_elim,[status(thm)],[66])).
% 0.18/0.38 tff(68,plain,
% 0.18/0.38 (reflexive_rewrite(a, b)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[67, 65])).
% 0.18/0.38 tff(69,plain,
% 0.18/0.38 (((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | ((~reflexive_rewrite(a, b)) | reflexive_rewrite(c, b) | (~equalish(c, a)))) <=> ((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | (~reflexive_rewrite(a, b)) | reflexive_rewrite(c, b) | (~equalish(c, a)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(70,plain,
% 0.18/0.38 ((reflexive_rewrite(c, b) | (~reflexive_rewrite(a, b)) | (~equalish(c, a))) <=> ((~reflexive_rewrite(a, b)) | reflexive_rewrite(c, b) | (~equalish(c, a)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(71,plain,
% 0.18/0.38 (((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | (reflexive_rewrite(c, b) | (~reflexive_rewrite(a, b)) | (~equalish(c, a)))) <=> ((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | ((~reflexive_rewrite(a, b)) | reflexive_rewrite(c, b) | (~equalish(c, a))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[70])).
% 0.18/0.38 tff(72,plain,
% 0.18/0.38 (((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | (reflexive_rewrite(c, b) | (~reflexive_rewrite(a, b)) | (~equalish(c, a)))) <=> ((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | (~reflexive_rewrite(a, b)) | reflexive_rewrite(c, b) | (~equalish(c, a)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[71, 69])).
% 0.18/0.38 tff(73,plain,
% 0.18/0.38 ((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | (reflexive_rewrite(c, b) | (~reflexive_rewrite(a, b)) | (~equalish(c, a)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(74,plain,
% 0.18/0.38 ((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | (~reflexive_rewrite(a, b)) | reflexive_rewrite(c, b) | (~equalish(c, a))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.38 tff(75,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[74, 68, 64, 51, 50])).
% 0.18/0.38 tff(76,plain,(reflexive_rewrite(c, b) | (~equalish(c, a))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(77,plain,
% 0.18/0.38 (~equalish(c, a)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[76, 49])).
% 0.18/0.38 tff(78,plain,
% 0.18/0.38 (^[A: $i, B: $i] : refl(((~equalish(A, B)) | equalish(B, A)) <=> ((~equalish(A, B)) | equalish(B, A)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(79,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A)) <=> ![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[78])).
% 0.18/0.38 tff(80,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A)) <=> ![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(81,plain,
% 0.18/0.38 (^[A: $i, B: $i] : rewrite((equalish(A, B) => equalish(B, A)) <=> ((~equalish(A, B)) | equalish(B, A)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(82,plain,
% 0.18/0.38 (![A: $i, B: $i] : (equalish(A, B) => equalish(B, A)) <=> ![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[81])).
% 0.18/0.38 tff(83,axiom,(![A: $i, B: $i] : (equalish(A, B) => equalish(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmtery')).
% 0.18/0.38 tff(84,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.18/0.38 tff(85,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.18/0.38 tff(86,plain,(
% 0.18/0.38 ![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))),
% 0.18/0.38 inference(skolemize,[status(sab)],[85])).
% 0.18/0.38 tff(87,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.18/0.38 tff(88,plain,
% 0.18/0.38 (((~![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))) | ((~equalish(a, c)) | equalish(c, a))) <=> ((~![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))) | (~equalish(a, c)) | equalish(c, a))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(89,plain,
% 0.18/0.38 ((~![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))) | ((~equalish(a, c)) | equalish(c, a))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(90,plain,
% 0.18/0.38 ((~![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))) | (~equalish(a, c)) | equalish(c, a)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.18/0.38 tff(91,plain,
% 0.18/0.38 (~equalish(a, c)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[90, 87, 77])).
% 0.18/0.38 tff(92,plain,
% 0.18/0.38 (^[A: $i, B: $i] : refl((equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B))) <=> (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(93,plain,
% 0.18/0.38 (![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B))) <=> ![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[92])).
% 0.18/0.38 tff(94,plain,
% 0.18/0.38 (![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B))) <=> ![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(95,plain,
% 0.18/0.38 (^[A: $i, B: $i] : rewrite((reflexive_rewrite(A, B) => (equalish(A, B) | rewrite(A, B))) <=> (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(96,plain,
% 0.18/0.38 (![A: $i, B: $i] : (reflexive_rewrite(A, B) => (equalish(A, B) | rewrite(A, B))) <=> ![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[95])).
% 0.18/0.38 tff(97,axiom,(![A: $i, B: $i] : (reflexive_rewrite(A, B) => (equalish(A, B) | rewrite(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equalish_or_rewrite')).
% 0.18/0.38 tff(98,plain,
% 0.18/0.38 (![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.18/0.38 tff(99,plain,
% 0.18/0.38 (![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.18/0.38 tff(100,plain,(
% 0.18/0.38 ![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[99])).
% 0.18/0.38 tff(101,plain,
% 0.18/0.38 (![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.18/0.38 tff(102,plain,
% 0.18/0.38 (reflexive_rewrite(a, c) <=> reflexive_rewrite(a, c)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(103,plain,
% 0.18/0.38 (reflexive_rewrite(a, c)),
% 0.18/0.38 inference(and_elim,[status(thm)],[66])).
% 0.18/0.38 tff(104,plain,
% 0.18/0.38 (reflexive_rewrite(a, c)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.18/0.38 tff(105,plain,
% 0.18/0.38 (((~![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | (equalish(a, c) | rewrite(a, c) | (~reflexive_rewrite(a, c)))) <=> ((~![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | equalish(a, c) | rewrite(a, c) | (~reflexive_rewrite(a, c)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(106,plain,
% 0.18/0.38 ((~![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | (equalish(a, c) | rewrite(a, c) | (~reflexive_rewrite(a, c)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(107,plain,
% 0.18/0.38 ((~![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | equalish(a, c) | rewrite(a, c) | (~reflexive_rewrite(a, c))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.18/0.38 tff(108,plain,
% 0.18/0.38 (equalish(a, c) | rewrite(a, c)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[107, 104, 101])).
% 0.18/0.38 tff(109,plain,
% 0.18/0.38 (rewrite(a, c)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[108, 91])).
% 0.18/0.38 tff(110,assumption,(~((~rewrite(b, tptp_fun_D_0(c, b))) | (~rewrite(c, tptp_fun_D_0(c, b))))), introduced(assumption)).
% 0.18/0.38 tff(111,plain,
% 0.18/0.38 (((~rewrite(b, tptp_fun_D_0(c, b))) | (~rewrite(c, tptp_fun_D_0(c, b)))) | rewrite(b, tptp_fun_D_0(c, b))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(112,plain,
% 0.18/0.38 (rewrite(b, tptp_fun_D_0(c, b))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.18/0.38 tff(113,plain,
% 0.18/0.38 (^[A: $i, B: $i] : refl(((~rewrite(A, B)) | reflexive_rewrite(A, B)) <=> ((~rewrite(A, B)) | reflexive_rewrite(A, B)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(114,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B)) <=> ![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[113])).
% 0.18/0.38 tff(115,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B)) <=> ![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(116,plain,
% 0.18/0.38 (^[A: $i, B: $i] : rewrite((rewrite(A, B) => reflexive_rewrite(A, B)) <=> ((~rewrite(A, B)) | reflexive_rewrite(A, B)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(117,plain,
% 0.18/0.38 (![A: $i, B: $i] : (rewrite(A, B) => reflexive_rewrite(A, B)) <=> ![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[116])).
% 0.18/0.38 tff(118,axiom,(![A: $i, B: $i] : (rewrite(A, B) => reflexive_rewrite(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rewrite_in_reflexive_rewrite')).
% 0.18/0.38 tff(119,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.18/0.38 tff(120,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.18/0.38 tff(121,plain,(
% 0.18/0.38 ![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.38 inference(skolemize,[status(sab)],[120])).
% 0.18/0.38 tff(122,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~rewrite(A, B)) | reflexive_rewrite(A, B))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.18/0.38 tff(123,plain,
% 0.18/0.38 (((~![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)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(124,plain,
% 0.18/0.38 ((~![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)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(125,plain,
% 0.18/0.38 ((~![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))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.18/0.38 tff(126,plain,
% 0.18/0.38 (reflexive_rewrite(b, tptp_fun_D_0(c, b))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[125, 122, 112])).
% 0.18/0.38 tff(127,plain,
% 0.18/0.38 (((~rewrite(b, tptp_fun_D_0(c, b))) | (~rewrite(c, tptp_fun_D_0(c, b)))) | rewrite(c, tptp_fun_D_0(c, b))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(128,plain,
% 0.18/0.38 (rewrite(c, tptp_fun_D_0(c, b))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[127, 110])).
% 0.18/0.38 tff(129,plain,
% 0.18/0.38 (((~![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)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(130,plain,
% 0.18/0.38 ((~![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)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(131,plain,
% 0.18/0.38 ((~![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))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.18/0.39 tff(132,plain,
% 0.18/0.39 (reflexive_rewrite(c, tptp_fun_D_0(c, b))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[131, 122, 128])).
% 0.18/0.39 tff(133,plain,
% 0.18/0.39 (((~![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | (goal | (~reflexive_rewrite(b, tptp_fun_D_0(c, b))) | (~reflexive_rewrite(c, tptp_fun_D_0(c, b))))) <=> ((~![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | goal | (~reflexive_rewrite(b, tptp_fun_D_0(c, b))) | (~reflexive_rewrite(c, tptp_fun_D_0(c, b))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(134,plain,
% 0.18/0.39 ((~![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | (goal | (~reflexive_rewrite(b, tptp_fun_D_0(c, b))) | (~reflexive_rewrite(c, tptp_fun_D_0(c, b))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(135,plain,
% 0.18/0.39 ((~![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | goal | (~reflexive_rewrite(b, tptp_fun_D_0(c, b))) | (~reflexive_rewrite(c, tptp_fun_D_0(c, b)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.18/0.39 tff(136,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[135, 45, 32, 132, 126])).
% 0.18/0.39 tff(137,plain,((~rewrite(b, tptp_fun_D_0(c, b))) | (~rewrite(c, tptp_fun_D_0(c, b)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(138,assumption,(rewrite(a, c)), introduced(assumption)).
% 0.18/0.39 tff(139,assumption,(rewrite(a, b)), introduced(assumption)).
% 0.18/0.39 tff(140,plain,
% 0.18/0.39 (^[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)))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(141,plain,
% 0.18/0.39 (![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))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[140])).
% 0.18/0.39 tff(142,plain,
% 0.18/0.39 (^[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))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(143,plain,
% 0.18/0.39 (![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))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[142])).
% 0.18/0.39 tff(144,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(145,plain,
% 0.18/0.39 (^[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))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(146,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[145])).
% 0.18/0.39 tff(147,axiom,(![A: $i, B: $i, C: $i] : ((rewrite(A, B) & rewrite(A, C)) => ?[D: $i] : (rewrite(B, D) & rewrite(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rewrite_diamond')).
% 0.18/0.39 tff(148,plain,
% 0.18/0.39 (![A: $i, B: $i, C: $i] : ((~(rewrite(A, B) & rewrite(A, C))) | ?[D: $i] : (rewrite(B, D) & rewrite(C, D)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.18/0.39 tff(149,plain,
% 0.18/0.39 (![A: $i, B: $i, C: $i] : ((~(rewrite(A, B) & rewrite(A, C))) | ?[D: $i] : (rewrite(B, D) & rewrite(C, D)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.18/0.39 tff(150,plain,(
% 0.18/0.39 ![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))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[149])).
% 0.18/0.39 tff(151,plain,
% 0.18/0.39 (![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))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.18/0.39 tff(152,plain,
% 0.18/0.39 (![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))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[151, 141])).
% 0.18/0.39 tff(153,plain,
% 0.18/0.39 (((~![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))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(154,plain,
% 0.18/0.39 ((~![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))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(155,plain,
% 0.18/0.39 ((~![A: $i, B: $i, C: $i] : ((~rewrite(A, B)) | (~rewrite(A, C)) | (~((~rewrite(B, tptp_fun_D_0(C, B))) | (~rewrite(C, tptp_fun_D_0(C, B))))))) | (~rewrite(a, b)) | (~rewrite(a, c)) | (~((~rewrite(b, tptp_fun_D_0(c, b))) | (~rewrite(c, tptp_fun_D_0(c, b)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.18/0.39 tff(156,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[155, 152, 139, 138, 137])).
% 0.18/0.39 tff(157,plain,((~rewrite(a, c)) | (~rewrite(a, b))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(158,plain,
% 0.18/0.39 (~rewrite(a, b)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[157, 109])).
% 0.18/0.39 tff(159,plain,
% 0.18/0.39 (((~![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | (equalish(a, b) | rewrite(a, b) | (~reflexive_rewrite(a, b)))) <=> ((~![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | equalish(a, b) | rewrite(a, b) | (~reflexive_rewrite(a, b)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(160,plain,
% 0.18/0.39 ((~![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | (equalish(a, b) | rewrite(a, b) | (~reflexive_rewrite(a, b)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(161,plain,
% 0.18/0.39 ((~![A: $i, B: $i] : (equalish(A, B) | rewrite(A, B) | (~reflexive_rewrite(A, B)))) | equalish(a, b) | rewrite(a, b) | (~reflexive_rewrite(a, b))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.18/0.39 tff(162,plain,
% 0.18/0.39 (equalish(a, b) | rewrite(a, b)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[161, 68, 101])).
% 0.18/0.39 tff(163,plain,
% 0.18/0.39 (equalish(a, b)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[162, 158])).
% 0.18/0.39 tff(164,plain,
% 0.18/0.39 (((~![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))) | ((~equalish(a, b)) | equalish(b, a))) <=> ((~![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))) | (~equalish(a, b)) | equalish(b, a))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(165,plain,
% 0.18/0.39 ((~![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))) | ((~equalish(a, b)) | equalish(b, a))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(166,plain,
% 0.18/0.39 ((~![A: $i, B: $i] : ((~equalish(A, B)) | equalish(B, A))) | (~equalish(a, b)) | equalish(b, a)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.18/0.39 tff(167,plain,
% 0.18/0.39 (equalish(b, a)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[166, 87, 163])).
% 0.18/0.39 tff(168,assumption,(~reflexive_rewrite(b, c)), introduced(assumption)).
% 0.18/0.39 tff(169,plain,
% 0.18/0.39 (((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | ((~reflexive_rewrite(a, c)) | reflexive_rewrite(b, c) | (~equalish(b, a)))) <=> ((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | (~reflexive_rewrite(a, c)) | reflexive_rewrite(b, c) | (~equalish(b, a)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(170,plain,
% 0.18/0.39 ((reflexive_rewrite(b, c) | (~reflexive_rewrite(a, c)) | (~equalish(b, a))) <=> ((~reflexive_rewrite(a, c)) | reflexive_rewrite(b, c) | (~equalish(b, a)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(171,plain,
% 0.18/0.39 (((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | (reflexive_rewrite(b, c) | (~reflexive_rewrite(a, c)) | (~equalish(b, a)))) <=> ((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | ((~reflexive_rewrite(a, c)) | reflexive_rewrite(b, c) | (~equalish(b, a))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[170])).
% 0.18/0.39 tff(172,plain,
% 0.18/0.39 (((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | (reflexive_rewrite(b, c) | (~reflexive_rewrite(a, c)) | (~equalish(b, a)))) <=> ((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | (~reflexive_rewrite(a, c)) | reflexive_rewrite(b, c) | (~equalish(b, a)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[171, 169])).
% 0.18/0.39 tff(173,plain,
% 0.18/0.39 ((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | (reflexive_rewrite(b, c) | (~reflexive_rewrite(a, c)) | (~equalish(b, a)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(174,plain,
% 0.18/0.39 ((~![A: $i, B: $i, C: $i] : (reflexive_rewrite(A, C) | (~reflexive_rewrite(B, C)) | (~equalish(A, B)))) | (~reflexive_rewrite(a, c)) | reflexive_rewrite(b, c) | (~equalish(b, a))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.18/0.39 tff(175,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[174, 104, 64, 168, 167])).
% 0.18/0.39 tff(176,plain,(reflexive_rewrite(b, c)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(177,plain,
% 0.18/0.39 (((~![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | (goal | (~reflexive_rewrite(b, c)) | (~reflexive_rewrite(c, c)))) <=> ((~![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | goal | (~reflexive_rewrite(b, c)) | (~reflexive_rewrite(c, c)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(178,plain,
% 0.18/0.39 ((~![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | (goal | (~reflexive_rewrite(b, c)) | (~reflexive_rewrite(c, c)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(179,plain,
% 0.18/0.39 ((~![A: $i] : (goal | (~reflexive_rewrite(b, A)) | (~reflexive_rewrite(c, A)))) | goal | (~reflexive_rewrite(b, c)) | (~reflexive_rewrite(c, c))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.18/0.40 tff(180,plain,
% 0.18/0.40 (~reflexive_rewrite(c, c)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[179, 45, 32, 176])).
% 0.18/0.40 tff(181,plain,
% 0.18/0.40 (((~![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))) | ((~equalish(c, c)) | reflexive_rewrite(c, c))) <=> ((~![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))) | (~equalish(c, c)) | reflexive_rewrite(c, c))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(182,plain,
% 0.18/0.40 ((~![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))) | ((~equalish(c, c)) | reflexive_rewrite(c, c))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(183,plain,
% 0.18/0.40 ((~![A: $i, B: $i] : ((~equalish(A, B)) | reflexive_rewrite(A, B))) | (~equalish(c, c)) | reflexive_rewrite(c, c)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.18/0.40 tff(184,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[183, 25, 180, 11])).
% 0.18/0.40 % SZS output end Proof
% 0.18/0.40 % E exiting
%------------------------------------------------------------------------------