%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CSR159+1 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:04:21 AM UTC 2025
% Result : Theorem 65.34s 65.51s
% Output : Proof 65.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : CSR159+1 : TPTP v9.0.0. Released v7.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 13:04:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 65.34/65.51 % SZS status Theorem
% 65.34/65.51 % SZS output start Proof
% 65.34/65.51 tff(p__d__holds3_type, type, (
% 65.34/65.51 p__d__holds3: ( $i * $i * $i ) > $o)).
% 65.34/65.51 tff(f__PredecessorFn1_type, type, (
% 65.34/65.51 f__PredecessorFn1: $i > $i)).
% 65.34/65.51 tff(f__SuccessorFn1_type, type, (
% 65.34/65.51 f__SuccessorFn1: $i > $i)).
% 65.34/65.51 tff(c__0_type, type, (
% 65.34/65.51 c__0: $i)).
% 65.34/65.51 tff(c__greaterThan_type, type, (
% 65.34/65.51 c__greaterThan: $i)).
% 65.34/65.51 tff(p__greaterThan_type, type, (
% 65.34/65.51 p__greaterThan: ( $i * $i ) > $o)).
% 65.34/65.51 tff(c__1_type, type, (
% 65.34/65.51 c__1: $i)).
% 65.34/65.51 tff(p__d__instance_type, type, (
% 65.34/65.51 p__d__instance: ( $i * $i ) > $o)).
% 65.34/65.51 tff(c__Integer_type, type, (
% 65.34/65.51 c__Integer: $i)).
% 65.34/65.51 tff(f__RemainderFn2_type, type, (
% 65.34/65.51 f__RemainderFn2: ( $i * $i ) > $i)).
% 65.34/65.51 tff(c__2_type, type, (
% 65.34/65.51 c__2: $i)).
% 65.34/65.51 tff(tptp_fun_Y_1176_type, type, (
% 65.34/65.51 tptp_fun_Y_1176: $i)).
% 65.34/65.51 tff(c__OddInteger_type, type, (
% 65.34/65.51 c__OddInteger: $i)).
% 65.34/65.51 tff(c__EvenInteger_type, type, (
% 65.34/65.51 c__EvenInteger: $i)).
% 65.34/65.51 tff(c__PositiveInteger_type, type, (
% 65.34/65.51 c__PositiveInteger: $i)).
% 65.34/65.51 tff(c__Quantity_type, type, (
% 65.34/65.51 c__Quantity: $i)).
% 65.34/65.51 tff(c__IrreflexiveRelation_type, type, (
% 65.34/65.51 c__IrreflexiveRelation: $i)).
% 65.34/65.51 tff(tptp_fun_INST_48_type, type, (
% 65.34/65.51 tptp_fun_INST_48: $i > $i)).
% 65.34/65.51 tff(c__BinaryRelation_type, type, (
% 65.34/65.51 c__BinaryRelation: $i)).
% 65.34/65.51 tff(c__lessThan_type, type, (
% 65.34/65.51 c__lessThan: $i)).
% 65.34/65.51 tff(p__inverse_type, type, (
% 65.34/65.51 p__inverse: ( $i * $i ) > $o)).
% 65.34/65.51 tff(1,plain,
% 65.34/65.51 (^[INT: $i] : refl(((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT)))) <=> ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT)))))),
% 65.34/65.51 inference(bind,[status(th)],[])).
% 65.34/65.51 tff(2,plain,
% 65.34/65.51 (![INT: $i] : ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT)))) <=> ![INT: $i] : ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT))))),
% 65.34/65.51 inference(quant_intro,[status(thm)],[1])).
% 65.34/65.51 tff(3,plain,
% 65.34/65.51 (![INT: $i] : ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT)))) <=> ![INT: $i] : ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT))))),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(4,plain,
% 65.34/65.51 (^[INT: $i] : rewrite((p__d__instance(INT, c__Integer) => (INT = f__PredecessorFn1(f__SuccessorFn1(INT)))) <=> ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT)))))),
% 65.34/65.51 inference(bind,[status(th)],[])).
% 65.34/65.51 tff(5,plain,
% 65.34/65.51 (![INT: $i] : (p__d__instance(INT, c__Integer) => (INT = f__PredecessorFn1(f__SuccessorFn1(INT)))) <=> ![INT: $i] : ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT))))),
% 65.34/65.51 inference(quant_intro,[status(thm)],[4])).
% 65.34/65.51 tff(6,axiom,(![INT: $i] : (p__d__instance(INT, c__Integer) => (INT = f__PredecessorFn1(f__SuccessorFn1(INT))))), file('/export/starexec/sandbox/benchmark/Axioms/CSR006+0.ax','mergeA1330')).
% 65.34/65.51 tff(7,plain,
% 65.34/65.51 (![INT: $i] : ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT))))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[6, 5])).
% 65.34/65.51 tff(8,plain,
% 65.34/65.51 (![INT: $i] : ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT))))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[7, 3])).
% 65.34/65.51 tff(9,plain,(
% 65.34/65.51 ![INT: $i] : ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT))))),
% 65.34/65.51 inference(skolemize,[status(sab)],[8])).
% 65.34/65.51 tff(10,plain,
% 65.34/65.51 (![INT: $i] : ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT))))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[9, 2])).
% 65.34/65.51 tff(11,plain,
% 65.34/65.51 (p__d__instance(c__0, c__Integer) <=> p__d__instance(c__0, c__Integer)),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(12,axiom,(p__d__instance(c__0, c__Integer)), file('/export/starexec/sandbox/benchmark/Axioms/CSR006+0.ax','mergeA401')).
% 65.34/65.51 tff(13,plain,
% 65.34/65.51 (p__d__instance(c__0, c__Integer)),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[12, 11])).
% 65.34/65.51 tff(14,plain,
% 65.34/65.51 (((~![INT: $i] : ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT))))) | ((~p__d__instance(c__0, c__Integer)) | (c__0 = f__PredecessorFn1(f__SuccessorFn1(c__0))))) <=> ((~![INT: $i] : ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT))))) | (~p__d__instance(c__0, c__Integer)) | (c__0 = f__PredecessorFn1(f__SuccessorFn1(c__0))))),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(15,plain,
% 65.34/65.51 ((~![INT: $i] : ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT))))) | ((~p__d__instance(c__0, c__Integer)) | (c__0 = f__PredecessorFn1(f__SuccessorFn1(c__0))))),
% 65.34/65.51 inference(quant_inst,[status(thm)],[])).
% 65.34/65.51 tff(16,plain,
% 65.34/65.51 ((~![INT: $i] : ((~p__d__instance(INT, c__Integer)) | (INT = f__PredecessorFn1(f__SuccessorFn1(INT))))) | (~p__d__instance(c__0, c__Integer)) | (c__0 = f__PredecessorFn1(f__SuccessorFn1(c__0)))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[15, 14])).
% 65.34/65.51 tff(17,plain,
% 65.34/65.51 (c__0 = f__PredecessorFn1(f__SuccessorFn1(c__0))),
% 65.34/65.51 inference(unit_resolution,[status(thm)],[16, 13, 10])).
% 65.34/65.51 tff(18,plain,
% 65.34/65.51 (f__PredecessorFn1(f__SuccessorFn1(c__0)) = c__0),
% 65.34/65.51 inference(symmetry,[status(thm)],[17])).
% 65.34/65.51 tff(19,plain,
% 65.34/65.51 ((~![Y: $i] : ((~p__d__instance(Y, c__EvenInteger)) | (~p__d__instance(Y, c__OddInteger)))) <=> (~![Y: $i] : ((~p__d__instance(Y, c__EvenInteger)) | (~p__d__instance(Y, c__OddInteger))))),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(20,plain,
% 65.34/65.51 ((~![X: $i, Y: $i] : ((p__d__instance(X, c__EvenInteger) & p__d__instance(Y, c__OddInteger)) => (~(X = Y)))) <=> (~![Y: $i] : ((~p__d__instance(Y, c__EvenInteger)) | (~p__d__instance(Y, c__OddInteger))))),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(21,axiom,(~![X: $i, Y: $i] : ((p__d__instance(X, c__EvenInteger) & p__d__instance(Y, c__OddInteger)) => (~(X = Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','antonymPattern10035')).
% 65.34/65.51 tff(22,plain,
% 65.34/65.51 (~![Y: $i] : ((~p__d__instance(Y, c__EvenInteger)) | (~p__d__instance(Y, c__OddInteger)))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[21, 20])).
% 65.34/65.51 tff(23,plain,
% 65.34/65.51 (~![Y: $i] : ((~p__d__instance(Y, c__EvenInteger)) | (~p__d__instance(Y, c__OddInteger)))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[22, 19])).
% 65.34/65.51 tff(24,plain,
% 65.34/65.51 (~![Y: $i] : ((~p__d__instance(Y, c__EvenInteger)) | (~p__d__instance(Y, c__OddInteger)))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[23, 19])).
% 65.34/65.51 tff(25,plain,
% 65.34/65.51 (~![Y: $i] : ((~p__d__instance(Y, c__EvenInteger)) | (~p__d__instance(Y, c__OddInteger)))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[24, 19])).
% 65.34/65.51 tff(26,plain,(
% 65.34/65.51 ~((~p__d__instance(Y!1176, c__EvenInteger)) | (~p__d__instance(Y!1176, c__OddInteger)))),
% 65.34/65.51 inference(skolemize,[status(sab)],[25])).
% 65.34/65.51 tff(27,plain,
% 65.34/65.51 (p__d__instance(Y!1176, c__OddInteger)),
% 65.34/65.51 inference(or_elim,[status(thm)],[26])).
% 65.34/65.51 tff(28,plain,
% 65.34/65.51 (^[NUMBER: $i] : refl(((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1)) <=> ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1)))),
% 65.34/65.51 inference(bind,[status(th)],[])).
% 65.34/65.51 tff(29,plain,
% 65.34/65.51 (![NUMBER: $i] : ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1)) <=> ![NUMBER: $i] : ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1))),
% 65.34/65.51 inference(quant_intro,[status(thm)],[28])).
% 65.34/65.51 tff(30,plain,
% 65.34/65.51 (![NUMBER: $i] : ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1)) <=> ![NUMBER: $i] : ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1))),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(31,plain,
% 65.34/65.51 (^[NUMBER: $i] : rewrite((p__d__instance(NUMBER, c__OddInteger) => (f__RemainderFn2(NUMBER, c__2) = c__1)) <=> ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1)))),
% 65.34/65.51 inference(bind,[status(th)],[])).
% 65.34/65.51 tff(32,plain,
% 65.34/65.51 (![NUMBER: $i] : (p__d__instance(NUMBER, c__OddInteger) => (f__RemainderFn2(NUMBER, c__2) = c__1)) <=> ![NUMBER: $i] : ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1))),
% 65.34/65.51 inference(quant_intro,[status(thm)],[31])).
% 65.34/65.51 tff(33,axiom,(![NUMBER: $i] : (p__d__instance(NUMBER, c__OddInteger) => (f__RemainderFn2(NUMBER, c__2) = c__1))), file('/export/starexec/sandbox/benchmark/Axioms/CSR006+0.ax','mergeA1287')).
% 65.34/65.51 tff(34,plain,
% 65.34/65.51 (![NUMBER: $i] : ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[33, 32])).
% 65.34/65.51 tff(35,plain,
% 65.34/65.51 (![NUMBER: $i] : ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[34, 30])).
% 65.34/65.51 tff(36,plain,(
% 65.34/65.51 ![NUMBER: $i] : ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1))),
% 65.34/65.51 inference(skolemize,[status(sab)],[35])).
% 65.34/65.51 tff(37,plain,
% 65.34/65.51 (![NUMBER: $i] : ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[36, 29])).
% 65.34/65.51 tff(38,plain,
% 65.34/65.51 (((~![NUMBER: $i] : ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1))) | ((~p__d__instance(Y!1176, c__OddInteger)) | (f__RemainderFn2(Y!1176, c__2) = c__1))) <=> ((~![NUMBER: $i] : ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1))) | (~p__d__instance(Y!1176, c__OddInteger)) | (f__RemainderFn2(Y!1176, c__2) = c__1))),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(39,plain,
% 65.34/65.51 ((~![NUMBER: $i] : ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1))) | ((~p__d__instance(Y!1176, c__OddInteger)) | (f__RemainderFn2(Y!1176, c__2) = c__1))),
% 65.34/65.51 inference(quant_inst,[status(thm)],[])).
% 65.34/65.51 tff(40,plain,
% 65.34/65.51 ((~![NUMBER: $i] : ((~p__d__instance(NUMBER, c__OddInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__1))) | (~p__d__instance(Y!1176, c__OddInteger)) | (f__RemainderFn2(Y!1176, c__2) = c__1)),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[39, 38])).
% 65.34/65.51 tff(41,plain,
% 65.34/65.51 (f__RemainderFn2(Y!1176, c__2) = c__1),
% 65.34/65.51 inference(unit_resolution,[status(thm)],[40, 37, 27])).
% 65.34/65.51 tff(42,plain,
% 65.34/65.51 (p__d__instance(Y!1176, c__EvenInteger)),
% 65.34/65.51 inference(or_elim,[status(thm)],[26])).
% 65.34/65.51 tff(43,plain,
% 65.34/65.51 (^[NUMBER: $i] : refl(((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0)) <=> ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0)))),
% 65.34/65.51 inference(bind,[status(th)],[])).
% 65.34/65.51 tff(44,plain,
% 65.34/65.51 (![NUMBER: $i] : ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0)) <=> ![NUMBER: $i] : ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0))),
% 65.34/65.51 inference(quant_intro,[status(thm)],[43])).
% 65.34/65.51 tff(45,plain,
% 65.34/65.51 (![NUMBER: $i] : ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0)) <=> ![NUMBER: $i] : ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0))),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(46,plain,
% 65.34/65.51 (^[NUMBER: $i] : rewrite((p__d__instance(NUMBER, c__EvenInteger) => (f__RemainderFn2(NUMBER, c__2) = c__0)) <=> ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0)))),
% 65.34/65.51 inference(bind,[status(th)],[])).
% 65.34/65.51 tff(47,plain,
% 65.34/65.51 (![NUMBER: $i] : (p__d__instance(NUMBER, c__EvenInteger) => (f__RemainderFn2(NUMBER, c__2) = c__0)) <=> ![NUMBER: $i] : ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0))),
% 65.34/65.51 inference(quant_intro,[status(thm)],[46])).
% 65.34/65.51 tff(48,axiom,(![NUMBER: $i] : (p__d__instance(NUMBER, c__EvenInteger) => (f__RemainderFn2(NUMBER, c__2) = c__0))), file('/export/starexec/sandbox/benchmark/Axioms/CSR006+0.ax','mergeA1286')).
% 65.34/65.51 tff(49,plain,
% 65.34/65.51 (![NUMBER: $i] : ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[48, 47])).
% 65.34/65.51 tff(50,plain,
% 65.34/65.51 (![NUMBER: $i] : ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[49, 45])).
% 65.34/65.51 tff(51,plain,(
% 65.34/65.51 ![NUMBER: $i] : ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0))),
% 65.34/65.51 inference(skolemize,[status(sab)],[50])).
% 65.34/65.51 tff(52,plain,
% 65.34/65.51 (![NUMBER: $i] : ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[51, 44])).
% 65.34/65.51 tff(53,plain,
% 65.34/65.51 (((~![NUMBER: $i] : ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0))) | ((~p__d__instance(Y!1176, c__EvenInteger)) | (f__RemainderFn2(Y!1176, c__2) = c__0))) <=> ((~![NUMBER: $i] : ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0))) | (~p__d__instance(Y!1176, c__EvenInteger)) | (f__RemainderFn2(Y!1176, c__2) = c__0))),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(54,plain,
% 65.34/65.51 ((~![NUMBER: $i] : ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0))) | ((~p__d__instance(Y!1176, c__EvenInteger)) | (f__RemainderFn2(Y!1176, c__2) = c__0))),
% 65.34/65.51 inference(quant_inst,[status(thm)],[])).
% 65.34/65.51 tff(55,plain,
% 65.34/65.51 ((~![NUMBER: $i] : ((~p__d__instance(NUMBER, c__EvenInteger)) | (f__RemainderFn2(NUMBER, c__2) = c__0))) | (~p__d__instance(Y!1176, c__EvenInteger)) | (f__RemainderFn2(Y!1176, c__2) = c__0)),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[54, 53])).
% 65.34/65.51 tff(56,plain,
% 65.34/65.51 (f__RemainderFn2(Y!1176, c__2) = c__0),
% 65.34/65.51 inference(unit_resolution,[status(thm)],[55, 52, 42])).
% 65.34/65.51 tff(57,plain,
% 65.34/65.51 (c__0 = f__RemainderFn2(Y!1176, c__2)),
% 65.34/65.51 inference(symmetry,[status(thm)],[56])).
% 65.34/65.51 tff(58,plain,
% 65.34/65.51 (f__PredecessorFn1(f__SuccessorFn1(c__0)) = c__1),
% 65.34/65.51 inference(transitivity,[status(thm)],[18, 57, 41])).
% 65.34/65.51 tff(59,plain,
% 65.34/65.51 (p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(c__1, c__0)),
% 65.34/65.51 inference(monotonicity,[status(thm)],[58, 18])).
% 65.34/65.51 tff(60,plain,
% 65.34/65.51 (p__greaterThan(c__1, c__0) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))),
% 65.34/65.51 inference(symmetry,[status(thm)],[59])).
% 65.34/65.51 tff(61,plain,
% 65.34/65.51 (^[X: $i] : refl(((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0)) <=> ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0)))),
% 65.34/65.51 inference(bind,[status(th)],[])).
% 65.34/65.51 tff(62,plain,
% 65.34/65.51 (![X: $i] : ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0)) <=> ![X: $i] : ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0))),
% 65.34/65.51 inference(quant_intro,[status(thm)],[61])).
% 65.34/65.51 tff(63,plain,
% 65.34/65.51 (![X: $i] : ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0)) <=> ![X: $i] : ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0))),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(64,plain,
% 65.34/65.51 (^[X: $i] : rewrite((p__d__instance(X, c__PositiveInteger) => p__greaterThan(X, c__0)) <=> ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0)))),
% 65.34/65.51 inference(bind,[status(th)],[])).
% 65.34/65.51 tff(65,plain,
% 65.34/65.51 (![X: $i] : (p__d__instance(X, c__PositiveInteger) => p__greaterThan(X, c__0)) <=> ![X: $i] : ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0))),
% 65.34/65.51 inference(quant_intro,[status(thm)],[64])).
% 65.34/65.51 tff(66,axiom,(![X: $i] : (p__d__instance(X, c__PositiveInteger) => p__greaterThan(X, c__0))), file('/export/starexec/sandbox/benchmark/Axioms/CSR006+0.ax','mergeA557')).
% 65.34/65.51 tff(67,plain,
% 65.34/65.51 (![X: $i] : ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[66, 65])).
% 65.34/65.51 tff(68,plain,
% 65.34/65.51 (![X: $i] : ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[67, 63])).
% 65.34/65.51 tff(69,plain,(
% 65.34/65.51 ![X: $i] : ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0))),
% 65.34/65.51 inference(skolemize,[status(sab)],[68])).
% 65.34/65.51 tff(70,plain,
% 65.34/65.51 (![X: $i] : ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[69, 62])).
% 65.34/65.51 tff(71,plain,
% 65.34/65.51 (p__d__instance(c__1, c__PositiveInteger) <=> p__d__instance(c__1, c__PositiveInteger)),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(72,axiom,(p__d__instance(c__1, c__PositiveInteger)), file('/export/starexec/sandbox/benchmark/Axioms/CSR006+0.ax','mergeA412')).
% 65.34/65.51 tff(73,plain,
% 65.34/65.51 (p__d__instance(c__1, c__PositiveInteger)),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[72, 71])).
% 65.34/65.51 tff(74,plain,
% 65.34/65.51 (((~![X: $i] : ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0))) | ((~p__d__instance(c__1, c__PositiveInteger)) | p__greaterThan(c__1, c__0))) <=> ((~![X: $i] : ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0))) | (~p__d__instance(c__1, c__PositiveInteger)) | p__greaterThan(c__1, c__0))),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(75,plain,
% 65.34/65.51 ((~![X: $i] : ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0))) | ((~p__d__instance(c__1, c__PositiveInteger)) | p__greaterThan(c__1, c__0))),
% 65.34/65.51 inference(quant_inst,[status(thm)],[])).
% 65.34/65.51 tff(76,plain,
% 65.34/65.51 ((~![X: $i] : ((~p__d__instance(X, c__PositiveInteger)) | p__greaterThan(X, c__0))) | (~p__d__instance(c__1, c__PositiveInteger)) | p__greaterThan(c__1, c__0)),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[75, 74])).
% 65.34/65.51 tff(77,plain,
% 65.34/65.51 (p__greaterThan(c__1, c__0)),
% 65.34/65.51 inference(unit_resolution,[status(thm)],[76, 73, 70])).
% 65.34/65.51 tff(78,plain,
% 65.34/65.51 (p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[77, 60])).
% 65.34/65.51 tff(79,plain,
% 65.34/65.51 (^[X1: $i, X2: $i] : refl(((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity))))) <=> ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity))))))),
% 65.34/65.51 inference(bind,[status(th)],[])).
% 65.34/65.51 tff(80,plain,
% 65.34/65.51 (![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity))))) <=> ![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity)))))),
% 65.34/65.51 inference(quant_intro,[status(thm)],[79])).
% 65.34/65.51 tff(81,plain,
% 65.34/65.51 (^[X1: $i, X2: $i] : rewrite(((~p__greaterThan(X1, X2)) | (p__d__instance(X2, c__Quantity) & p__d__instance(X1, c__Quantity))) <=> ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity))))))),
% 65.34/65.51 inference(bind,[status(th)],[])).
% 65.34/65.51 tff(82,plain,
% 65.34/65.51 (![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (p__d__instance(X2, c__Quantity) & p__d__instance(X1, c__Quantity))) <=> ![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity)))))),
% 65.34/65.51 inference(quant_intro,[status(thm)],[81])).
% 65.34/65.51 tff(83,plain,
% 65.34/65.51 (![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (p__d__instance(X2, c__Quantity) & p__d__instance(X1, c__Quantity))) <=> ![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (p__d__instance(X2, c__Quantity) & p__d__instance(X1, c__Quantity)))),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(84,plain,
% 65.34/65.51 (^[X1: $i, X2: $i] : rewrite((p__greaterThan(X1, X2) => (p__d__instance(X2, c__Quantity) & p__d__instance(X1, c__Quantity))) <=> ((~p__greaterThan(X1, X2)) | (p__d__instance(X2, c__Quantity) & p__d__instance(X1, c__Quantity))))),
% 65.34/65.51 inference(bind,[status(th)],[])).
% 65.34/65.51 tff(85,plain,
% 65.34/65.51 (![X1: $i, X2: $i] : (p__greaterThan(X1, X2) => (p__d__instance(X2, c__Quantity) & p__d__instance(X1, c__Quantity))) <=> ![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (p__d__instance(X2, c__Quantity) & p__d__instance(X1, c__Quantity)))),
% 65.34/65.51 inference(quant_intro,[status(thm)],[84])).
% 65.34/65.51 tff(86,axiom,(![X1: $i, X2: $i] : (p__greaterThan(X1, X2) => (p__d__instance(X2, c__Quantity) & p__d__instance(X1, c__Quantity)))), file('/export/starexec/sandbox/benchmark/Axioms/CSR006+0.ax','typeA180')).
% 65.34/65.51 tff(87,plain,
% 65.34/65.51 (![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (p__d__instance(X2, c__Quantity) & p__d__instance(X1, c__Quantity)))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[86, 85])).
% 65.34/65.51 tff(88,plain,
% 65.34/65.51 (![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (p__d__instance(X2, c__Quantity) & p__d__instance(X1, c__Quantity)))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[87, 83])).
% 65.34/65.51 tff(89,plain,(
% 65.34/65.51 ![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (p__d__instance(X2, c__Quantity) & p__d__instance(X1, c__Quantity)))),
% 65.34/65.51 inference(skolemize,[status(sab)],[88])).
% 65.34/65.51 tff(90,plain,
% 65.34/65.51 (![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity)))))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[89, 82])).
% 65.34/65.51 tff(91,plain,
% 65.34/65.51 (![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity)))))),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[90, 80])).
% 65.34/65.51 tff(92,plain,
% 65.34/65.51 (((~![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity)))))) | ((~p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity))) <=> ((~![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity)))))) | (~p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity))),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(93,plain,
% 65.34/65.51 (((~p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | (~((~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity))))) <=> ((~p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity))),
% 65.34/65.51 inference(rewrite,[status(thm)],[])).
% 65.34/65.51 tff(94,plain,
% 65.34/65.51 (((~![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity)))))) | ((~p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | (~((~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)))))) <=> ((~![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity)))))) | ((~p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)))),
% 65.34/65.51 inference(monotonicity,[status(thm)],[93])).
% 65.34/65.51 tff(95,plain,
% 65.34/65.51 (((~![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity)))))) | ((~p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | (~((~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)))))) <=> ((~![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity)))))) | (~p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity))),
% 65.34/65.51 inference(transitivity,[status(thm)],[94, 92])).
% 65.34/65.51 tff(96,plain,
% 65.34/65.51 ((~![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity)))))) | ((~p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | (~((~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)))))),
% 65.34/65.51 inference(quant_inst,[status(thm)],[])).
% 65.34/65.51 tff(97,plain,
% 65.34/65.51 ((~![X1: $i, X2: $i] : ((~p__greaterThan(X1, X2)) | (~((~p__d__instance(X2, c__Quantity)) | (~p__d__instance(X1, c__Quantity)))))) | (~p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)),
% 65.34/65.51 inference(modus_ponens,[status(thm)],[96, 95])).
% 65.34/65.51 tff(98,plain,
% 65.34/65.51 ((~p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)),
% 65.34/65.51 inference(unit_resolution,[status(thm)],[97, 91])).
% 65.34/65.52 tff(99,plain,
% 65.34/65.52 (p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)),
% 65.34/65.52 inference(unit_resolution,[status(thm)],[98, 78])).
% 65.34/65.52 tff(100,plain,
% 65.34/65.52 (^[VAR1: $i, VAR2: $i] : refl(((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity))) <=> ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity))))),
% 65.34/65.52 inference(bind,[status(th)],[])).
% 65.34/65.52 tff(101,plain,
% 65.34/65.52 (![VAR1: $i, VAR2: $i] : ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity))) <=> ![VAR1: $i, VAR2: $i] : ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))),
% 65.34/65.52 inference(quant_intro,[status(thm)],[100])).
% 65.34/65.52 tff(102,plain,
% 65.34/65.52 (^[VAR1: $i, VAR2: $i] : trans(monotonicity(trans(monotonicity(rewrite((p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity)) <=> (~((~p__d__instance(VAR2, c__Quantity)) | (~p__d__instance(VAR1, c__Quantity))))), ((~(p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity))) <=> (~(~((~p__d__instance(VAR2, c__Quantity)) | (~p__d__instance(VAR1, c__Quantity))))))), rewrite((~(~((~p__d__instance(VAR2, c__Quantity)) | (~p__d__instance(VAR1, c__Quantity))))) <=> ((~p__d__instance(VAR2, c__Quantity)) | (~p__d__instance(VAR1, c__Quantity)))), ((~(p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity))) <=> ((~p__d__instance(VAR2, c__Quantity)) | (~p__d__instance(VAR1, c__Quantity))))), (((~(p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity))) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2))) <=> (((~p__d__instance(VAR2, c__Quantity)) | (~p__d__instance(VAR1, c__Quantity))) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2))))), rewrite((((~p__d__instance(VAR2, c__Quantity)) | (~p__d__instance(VAR1, c__Quantity))) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2))) <=> ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))), (((~(p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity))) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2))) <=> ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))))),
% 65.34/65.52 inference(bind,[status(th)],[])).
% 65.34/65.52 tff(103,plain,
% 65.34/65.52 (![VAR1: $i, VAR2: $i] : ((~(p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity))) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2))) <=> ![VAR1: $i, VAR2: $i] : ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))),
% 65.34/65.52 inference(quant_intro,[status(thm)],[102])).
% 65.34/65.52 tff(104,plain,
% 65.34/65.52 (![VAR1: $i, VAR2: $i] : ((~(p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity))) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2))) <=> ![VAR1: $i, VAR2: $i] : ((~(p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity))) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)))),
% 65.34/65.52 inference(rewrite,[status(thm)],[])).
% 65.34/65.52 tff(105,plain,
% 65.34/65.52 (^[VAR1: $i, VAR2: $i] : rewrite(((p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity)) => (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2))) <=> ((~(p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity))) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2))))),
% 65.34/65.52 inference(bind,[status(th)],[])).
% 65.34/65.52 tff(106,plain,
% 65.34/65.52 (![VAR1: $i, VAR2: $i] : ((p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity)) => (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2))) <=> ![VAR1: $i, VAR2: $i] : ((~(p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity))) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)))),
% 65.34/65.52 inference(quant_intro,[status(thm)],[105])).
% 65.34/65.52 tff(107,axiom,(![VAR1: $i, VAR2: $i] : ((p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity)) => (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)))), file('/export/starexec/sandbox/benchmark/Axioms/CSR006+0.ax','schemaBinaryRelationA182')).
% 65.34/65.52 tff(108,plain,
% 65.34/65.52 (![VAR1: $i, VAR2: $i] : ((~(p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity))) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[107, 106])).
% 65.34/65.52 tff(109,plain,
% 65.34/65.52 (![VAR1: $i, VAR2: $i] : ((~(p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity))) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[108, 104])).
% 65.34/65.52 tff(110,plain,(
% 65.34/65.52 ![VAR1: $i, VAR2: $i] : ((~(p__d__instance(VAR2, c__Quantity) & p__d__instance(VAR1, c__Quantity))) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)))),
% 65.34/65.52 inference(skolemize,[status(sab)],[109])).
% 65.34/65.52 tff(111,plain,
% 65.34/65.52 (![VAR1: $i, VAR2: $i] : ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[110, 103])).
% 65.34/65.52 tff(112,plain,
% 65.34/65.52 (![VAR1: $i, VAR2: $i] : ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[111, 101])).
% 65.34/65.52 tff(113,plain,
% 65.34/65.52 (((~![VAR1: $i, VAR2: $i] : ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))) | ((~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))))) <=> ((~![VAR1: $i, VAR2: $i] : ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))) | (~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))))),
% 65.34/65.52 inference(rewrite,[status(thm)],[])).
% 65.34/65.52 tff(114,plain,
% 65.34/65.52 (((~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | (~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity))) <=> ((~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))))),
% 65.34/65.52 inference(rewrite,[status(thm)],[])).
% 65.34/65.52 tff(115,plain,
% 65.34/65.52 (((~![VAR1: $i, VAR2: $i] : ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))) | ((~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | (~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)))) <=> ((~![VAR1: $i, VAR2: $i] : ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))) | ((~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))))))),
% 65.34/65.52 inference(monotonicity,[status(thm)],[114])).
% 65.34/65.52 tff(116,plain,
% 65.34/65.52 (((~![VAR1: $i, VAR2: $i] : ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))) | ((~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | (~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)))) <=> ((~![VAR1: $i, VAR2: $i] : ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))) | (~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))))),
% 65.34/65.52 inference(transitivity,[status(thm)],[115, 113])).
% 65.34/65.52 tff(117,plain,
% 65.34/65.52 ((~![VAR1: $i, VAR2: $i] : ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))) | ((~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))) | (~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)))),
% 65.34/65.52 inference(quant_inst,[status(thm)],[])).
% 65.34/65.52 tff(118,plain,
% 65.34/65.52 ((~![VAR1: $i, VAR2: $i] : ((~p__d__instance(VAR2, c__Quantity)) | (p__d__holds3(c__greaterThan, VAR1, VAR2) <=> p__greaterThan(VAR1, VAR2)) | (~p__d__instance(VAR1, c__Quantity)))) | (~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[117, 116])).
% 65.34/65.52 tff(119,plain,
% 65.34/65.52 ((~p__d__instance(f__PredecessorFn1(f__SuccessorFn1(c__0)), c__Quantity)) | (p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))))),
% 65.34/65.52 inference(unit_resolution,[status(thm)],[118, 112])).
% 65.34/65.52 tff(120,plain,
% 65.34/65.52 (p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))),
% 65.34/65.52 inference(unit_resolution,[status(thm)],[119, 99])).
% 65.34/65.52 tff(121,plain,
% 65.34/65.52 ((~(p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) <=> p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))))) | p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))) | (~p__greaterThan(f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))))),
% 65.34/65.52 inference(tautology,[status(thm)],[])).
% 65.34/65.52 tff(122,plain,
% 65.34/65.52 (p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0)))),
% 65.34/65.52 inference(unit_resolution,[status(thm)],[121, 120, 78])).
% 65.34/65.52 tff(123,plain,
% 65.34/65.52 (^[X1: $i, X2: $i] : refl(((~p__inverse(X1, X2)) | (~((~p__d__instance(X2, c__BinaryRelation)) | (~p__d__instance(X1, c__BinaryRelation))))) <=> ((~p__inverse(X1, X2)) | (~((~p__d__instance(X2, c__BinaryRelation)) | (~p__d__instance(X1, c__BinaryRelation))))))),
% 65.34/65.52 inference(bind,[status(th)],[])).
% 65.34/65.52 tff(124,plain,
% 65.34/65.52 (![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (~((~p__d__instance(X2, c__BinaryRelation)) | (~p__d__instance(X1, c__BinaryRelation))))) <=> ![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (~((~p__d__instance(X2, c__BinaryRelation)) | (~p__d__instance(X1, c__BinaryRelation)))))),
% 65.34/65.52 inference(quant_intro,[status(thm)],[123])).
% 65.34/65.52 tff(125,plain,
% 65.34/65.52 (^[X1: $i, X2: $i] : rewrite(((~p__inverse(X1, X2)) | (p__d__instance(X2, c__BinaryRelation) & p__d__instance(X1, c__BinaryRelation))) <=> ((~p__inverse(X1, X2)) | (~((~p__d__instance(X2, c__BinaryRelation)) | (~p__d__instance(X1, c__BinaryRelation))))))),
% 65.34/65.52 inference(bind,[status(th)],[])).
% 65.34/65.52 tff(126,plain,
% 65.34/65.52 (![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (p__d__instance(X2, c__BinaryRelation) & p__d__instance(X1, c__BinaryRelation))) <=> ![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (~((~p__d__instance(X2, c__BinaryRelation)) | (~p__d__instance(X1, c__BinaryRelation)))))),
% 65.34/65.52 inference(quant_intro,[status(thm)],[125])).
% 65.34/65.52 tff(127,plain,
% 65.34/65.52 (![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (p__d__instance(X2, c__BinaryRelation) & p__d__instance(X1, c__BinaryRelation))) <=> ![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (p__d__instance(X2, c__BinaryRelation) & p__d__instance(X1, c__BinaryRelation)))),
% 65.34/65.52 inference(rewrite,[status(thm)],[])).
% 65.34/65.52 tff(128,plain,
% 65.34/65.52 (^[X1: $i, X2: $i] : rewrite((p__inverse(X1, X2) => (p__d__instance(X2, c__BinaryRelation) & p__d__instance(X1, c__BinaryRelation))) <=> ((~p__inverse(X1, X2)) | (p__d__instance(X2, c__BinaryRelation) & p__d__instance(X1, c__BinaryRelation))))),
% 65.34/65.52 inference(bind,[status(th)],[])).
% 65.34/65.52 tff(129,plain,
% 65.34/65.52 (![X1: $i, X2: $i] : (p__inverse(X1, X2) => (p__d__instance(X2, c__BinaryRelation) & p__d__instance(X1, c__BinaryRelation))) <=> ![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (p__d__instance(X2, c__BinaryRelation) & p__d__instance(X1, c__BinaryRelation)))),
% 65.34/65.52 inference(quant_intro,[status(thm)],[128])).
% 65.34/65.52 tff(130,axiom,(![X1: $i, X2: $i] : (p__inverse(X1, X2) => (p__d__instance(X2, c__BinaryRelation) & p__d__instance(X1, c__BinaryRelation)))), file('/export/starexec/sandbox/benchmark/Axioms/CSR006+0.ax','typeA176')).
% 65.34/65.52 tff(131,plain,
% 65.34/65.52 (![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (p__d__instance(X2, c__BinaryRelation) & p__d__instance(X1, c__BinaryRelation)))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[130, 129])).
% 65.34/65.52 tff(132,plain,
% 65.34/65.52 (![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (p__d__instance(X2, c__BinaryRelation) & p__d__instance(X1, c__BinaryRelation)))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[131, 127])).
% 65.34/65.52 tff(133,plain,(
% 65.34/65.52 ![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (p__d__instance(X2, c__BinaryRelation) & p__d__instance(X1, c__BinaryRelation)))),
% 65.34/65.52 inference(skolemize,[status(sab)],[132])).
% 65.34/65.52 tff(134,plain,
% 65.34/65.52 (![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (~((~p__d__instance(X2, c__BinaryRelation)) | (~p__d__instance(X1, c__BinaryRelation)))))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[133, 126])).
% 65.34/65.52 tff(135,plain,
% 65.34/65.52 (![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (~((~p__d__instance(X2, c__BinaryRelation)) | (~p__d__instance(X1, c__BinaryRelation)))))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[134, 124])).
% 65.34/65.52 tff(136,plain,
% 65.34/65.52 (p__inverse(c__greaterThan, c__lessThan) <=> p__inverse(c__greaterThan, c__lessThan)),
% 65.34/65.52 inference(rewrite,[status(thm)],[])).
% 65.34/65.52 tff(137,axiom,(p__inverse(c__greaterThan, c__lessThan)), file('/export/starexec/sandbox/benchmark/Axioms/CSR006+0.ax','mergeA370')).
% 65.34/65.52 tff(138,plain,
% 65.34/65.52 (p__inverse(c__greaterThan, c__lessThan)),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[137, 136])).
% 65.34/65.52 tff(139,plain,
% 65.34/65.52 (((~![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (~((~p__d__instance(X2, c__BinaryRelation)) | (~p__d__instance(X1, c__BinaryRelation)))))) | ((~p__inverse(c__greaterThan, c__lessThan)) | (~((~p__d__instance(c__lessThan, c__BinaryRelation)) | (~p__d__instance(c__greaterThan, c__BinaryRelation)))))) <=> ((~![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (~((~p__d__instance(X2, c__BinaryRelation)) | (~p__d__instance(X1, c__BinaryRelation)))))) | (~p__inverse(c__greaterThan, c__lessThan)) | (~((~p__d__instance(c__lessThan, c__BinaryRelation)) | (~p__d__instance(c__greaterThan, c__BinaryRelation)))))),
% 65.34/65.52 inference(rewrite,[status(thm)],[])).
% 65.34/65.52 tff(140,plain,
% 65.34/65.52 ((~![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (~((~p__d__instance(X2, c__BinaryRelation)) | (~p__d__instance(X1, c__BinaryRelation)))))) | ((~p__inverse(c__greaterThan, c__lessThan)) | (~((~p__d__instance(c__lessThan, c__BinaryRelation)) | (~p__d__instance(c__greaterThan, c__BinaryRelation)))))),
% 65.34/65.52 inference(quant_inst,[status(thm)],[])).
% 65.34/65.52 tff(141,plain,
% 65.34/65.52 ((~![X1: $i, X2: $i] : ((~p__inverse(X1, X2)) | (~((~p__d__instance(X2, c__BinaryRelation)) | (~p__d__instance(X1, c__BinaryRelation)))))) | (~p__inverse(c__greaterThan, c__lessThan)) | (~((~p__d__instance(c__lessThan, c__BinaryRelation)) | (~p__d__instance(c__greaterThan, c__BinaryRelation))))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[140, 139])).
% 65.34/65.52 tff(142,plain,
% 65.34/65.52 (~((~p__d__instance(c__lessThan, c__BinaryRelation)) | (~p__d__instance(c__greaterThan, c__BinaryRelation)))),
% 65.34/65.52 inference(unit_resolution,[status(thm)],[141, 138, 135])).
% 65.34/65.52 tff(143,plain,
% 65.34/65.52 (((~p__d__instance(c__lessThan, c__BinaryRelation)) | (~p__d__instance(c__greaterThan, c__BinaryRelation))) | p__d__instance(c__greaterThan, c__BinaryRelation)),
% 65.34/65.52 inference(tautology,[status(thm)],[])).
% 65.34/65.52 tff(144,plain,
% 65.34/65.52 (p__d__instance(c__greaterThan, c__BinaryRelation)),
% 65.34/65.52 inference(unit_resolution,[status(thm)],[143, 142])).
% 65.34/65.52 tff(145,plain,
% 65.34/65.52 (^[REL: $i] : rewrite(((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL))))))) <=> ((~p__d__instance(REL, c__BinaryRelation)) | (~((~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))) | (~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST))))))))),
% 65.34/65.52 inference(bind,[status(th)],[])).
% 65.34/65.52 tff(146,plain,
% 65.34/65.52 (![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL))))))) <=> ![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))) | (~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))))))),
% 65.34/65.52 inference(quant_intro,[status(thm)],[145])).
% 65.34/65.52 tff(147,plain,
% 65.34/65.52 (^[REL: $i] : refl(((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL))))))) <=> ((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL))))))))),
% 65.34/65.52 inference(bind,[status(th)],[])).
% 65.34/65.52 tff(148,plain,
% 65.34/65.52 (![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL))))))) <=> ![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))))))),
% 65.34/65.52 inference(quant_intro,[status(thm)],[147])).
% 65.34/65.52 tff(149,plain,
% 65.34/65.52 (^[REL: $i] : rewrite(((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL))))))) <=> ((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL))))))))),
% 65.34/65.52 inference(bind,[status(th)],[])).
% 65.34/65.52 tff(150,plain,
% 65.34/65.52 (![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL))))))) <=> ![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))))))),
% 65.34/65.52 inference(quant_intro,[status(thm)],[149])).
% 65.34/65.52 tff(151,plain,
% 65.34/65.52 (![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL))))))) <=> ![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))))))),
% 65.34/65.52 inference(transitivity,[status(thm)],[150, 148])).
% 65.34/65.52 tff(152,plain,
% 65.34/65.52 (^[REL: $i] : rewrite(((~p__d__instance(REL, c__BinaryRelation)) | (((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST))) & (p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL))))) <=> ((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL))))))))),
% 65.34/65.52 inference(bind,[status(th)],[])).
% 65.34/65.52 tff(153,plain,
% 65.34/65.52 (![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST))) & (p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL))))) <=> ![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))))))),
% 65.34/65.52 inference(quant_intro,[status(thm)],[152])).
% 65.34/65.52 tff(154,plain,
% 65.34/65.52 (![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) <=> ![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST))))),
% 65.34/65.52 inference(rewrite,[status(thm)],[])).
% 65.34/65.52 tff(155,plain,
% 65.34/65.52 (^[REL: $i] : trans(monotonicity(rewrite((p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST))) <=> (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST)))), ((p__d__instance(REL, c__BinaryRelation) => (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) <=> (p__d__instance(REL, c__BinaryRelation) => (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST)))))), rewrite((p__d__instance(REL, c__BinaryRelation) => (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) <=> ((~p__d__instance(REL, c__BinaryRelation)) | (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST))))), ((p__d__instance(REL, c__BinaryRelation) => (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) <=> ((~p__d__instance(REL, c__BinaryRelation)) | (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST))))))),
% 65.34/65.52 inference(bind,[status(th)],[])).
% 65.34/65.52 tff(156,plain,
% 65.34/65.52 (![REL: $i] : (p__d__instance(REL, c__BinaryRelation) => (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) <=> ![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST))))),
% 65.34/65.52 inference(quant_intro,[status(thm)],[155])).
% 65.34/65.52 tff(157,axiom,(![REL: $i] : (p__d__instance(REL, c__BinaryRelation) => (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST))))), file('/export/starexec/sandbox/benchmark/Axioms/CSR006+0.ax','mergeA594')).
% 65.34/65.52 tff(158,plain,
% 65.34/65.52 (![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST))))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[157, 156])).
% 65.34/65.52 tff(159,plain,
% 65.34/65.52 (![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (p__d__instance(REL, c__IrreflexiveRelation) <=> ![INST: $i] : (~p__d__holds3(REL, INST, INST))))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[158, 154])).
% 65.34/65.52 tff(160,plain,(
% 65.34/65.52 ![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST))) & (p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))))),
% 65.34/65.52 inference(skolemize,[status(sab)],[159])).
% 65.34/65.52 tff(161,plain,
% 65.34/65.52 (![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))))))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[160, 153])).
% 65.34/65.52 tff(162,plain,
% 65.34/65.52 (![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))) | (~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))))))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[161, 151])).
% 65.34/65.52 tff(163,plain,
% 65.34/65.52 (![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))) | (~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))))))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[162, 146])).
% 65.34/65.52 tff(164,plain,
% 65.34/65.52 (((~![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))) | (~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))))))) | ((~p__d__instance(c__greaterThan, c__BinaryRelation)) | (~((~(p__d__instance(c__greaterThan, c__IrreflexiveRelation) | p__d__holds3(c__greaterThan, tptp_fun_INST_48(c__greaterThan), tptp_fun_INST_48(c__greaterThan)))) | (~((~p__d__instance(c__greaterThan, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST)))))))) <=> ((~![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))) | (~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))))))) | (~p__d__instance(c__greaterThan, c__BinaryRelation)) | (~((~(p__d__instance(c__greaterThan, c__IrreflexiveRelation) | p__d__holds3(c__greaterThan, tptp_fun_INST_48(c__greaterThan), tptp_fun_INST_48(c__greaterThan)))) | (~((~p__d__instance(c__greaterThan, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST)))))))),
% 65.34/65.52 inference(rewrite,[status(thm)],[])).
% 65.34/65.52 tff(165,plain,
% 65.34/65.52 ((~![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))) | (~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))))))) | ((~p__d__instance(c__greaterThan, c__BinaryRelation)) | (~((~(p__d__instance(c__greaterThan, c__IrreflexiveRelation) | p__d__holds3(c__greaterThan, tptp_fun_INST_48(c__greaterThan), tptp_fun_INST_48(c__greaterThan)))) | (~((~p__d__instance(c__greaterThan, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST)))))))),
% 65.34/65.52 inference(quant_inst,[status(thm)],[])).
% 65.34/65.52 tff(166,plain,
% 65.34/65.52 ((~![REL: $i] : ((~p__d__instance(REL, c__BinaryRelation)) | (~((~(p__d__instance(REL, c__IrreflexiveRelation) | p__d__holds3(REL, tptp_fun_INST_48(REL), tptp_fun_INST_48(REL)))) | (~((~p__d__instance(REL, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(REL, INST, INST)))))))) | (~p__d__instance(c__greaterThan, c__BinaryRelation)) | (~((~(p__d__instance(c__greaterThan, c__IrreflexiveRelation) | p__d__holds3(c__greaterThan, tptp_fun_INST_48(c__greaterThan), tptp_fun_INST_48(c__greaterThan)))) | (~((~p__d__instance(c__greaterThan, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST))))))),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[165, 164])).
% 65.34/65.52 tff(167,plain,
% 65.34/65.52 ((~p__d__instance(c__greaterThan, c__BinaryRelation)) | (~((~(p__d__instance(c__greaterThan, c__IrreflexiveRelation) | p__d__holds3(c__greaterThan, tptp_fun_INST_48(c__greaterThan), tptp_fun_INST_48(c__greaterThan)))) | (~((~p__d__instance(c__greaterThan, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST))))))),
% 65.34/65.52 inference(unit_resolution,[status(thm)],[166, 163])).
% 65.34/65.52 tff(168,plain,
% 65.34/65.52 (~((~(p__d__instance(c__greaterThan, c__IrreflexiveRelation) | p__d__holds3(c__greaterThan, tptp_fun_INST_48(c__greaterThan), tptp_fun_INST_48(c__greaterThan)))) | (~((~p__d__instance(c__greaterThan, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST)))))),
% 65.34/65.52 inference(unit_resolution,[status(thm)],[167, 144])).
% 65.34/65.52 tff(169,plain,
% 65.34/65.52 (((~(p__d__instance(c__greaterThan, c__IrreflexiveRelation) | p__d__holds3(c__greaterThan, tptp_fun_INST_48(c__greaterThan), tptp_fun_INST_48(c__greaterThan)))) | (~((~p__d__instance(c__greaterThan, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST))))) | ((~p__d__instance(c__greaterThan, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST)))),
% 65.34/65.52 inference(tautology,[status(thm)],[])).
% 65.34/65.52 tff(170,plain,
% 65.34/65.52 ((~p__d__instance(c__greaterThan, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST))),
% 65.34/65.52 inference(unit_resolution,[status(thm)],[169, 168])).
% 65.34/65.52 tff(171,plain,
% 65.34/65.52 (p__d__instance(c__greaterThan, c__IrreflexiveRelation) <=> p__d__instance(c__greaterThan, c__IrreflexiveRelation)),
% 65.34/65.52 inference(rewrite,[status(thm)],[])).
% 65.34/65.52 tff(172,axiom,(p__d__instance(c__greaterThan, c__IrreflexiveRelation)), file('/export/starexec/sandbox/benchmark/Axioms/CSR006+0.ax','mergeA365')).
% 65.34/65.52 tff(173,plain,
% 65.34/65.52 (p__d__instance(c__greaterThan, c__IrreflexiveRelation)),
% 65.34/65.52 inference(modus_ponens,[status(thm)],[172, 171])).
% 65.75/65.96 tff(174,plain,
% 65.75/65.96 ((~((~p__d__instance(c__greaterThan, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST)))) | (~p__d__instance(c__greaterThan, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST))),
% 65.75/65.96 inference(tautology,[status(thm)],[])).
% 65.75/65.96 tff(175,plain,
% 65.75/65.96 ((~((~p__d__instance(c__greaterThan, c__IrreflexiveRelation)) | ![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST)))) | ![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST))),
% 65.75/65.96 inference(unit_resolution,[status(thm)],[174, 173])).
% 65.75/65.96 tff(176,plain,
% 65.75/65.96 (![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST))),
% 65.75/65.96 inference(unit_resolution,[status(thm)],[175, 170])).
% 65.75/65.96 tff(177,plain,
% 65.75/65.96 ((~![INST: $i] : (~p__d__holds3(c__greaterThan, INST, INST))) | (~p__d__holds3(c__greaterThan, f__PredecessorFn1(f__SuccessorFn1(c__0)), f__PredecessorFn1(f__SuccessorFn1(c__0))))),
% 65.75/65.96 inference(quant_inst,[status(thm)],[])).
% 65.75/65.96 tff(178,plain,
% 65.75/65.96 ($false),
% 65.75/65.96 inference(unit_resolution,[status(thm)],[177, 176, 122])).
% 65.75/65.96 % SZS output end Proof
% 65.75/65.97 % E exiting
%------------------------------------------------------------------------------