%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MSC012+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:17:32 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MSC012+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 23:33:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(less_type, type, (
% 0.12/0.38 less: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_B_0_type, type, (
% 0.12/0.38 tptp_fun_B_0: $i > $i)).
% 0.12/0.38 tff(tptp_fun_B_1_type, type, (
% 0.12/0.38 tptp_fun_B_1: $i > $i)).
% 0.12/0.38 tff(elem_2_type, type, (
% 0.12/0.38 elem_2: $i)).
% 0.12/0.38 tff(p_type, type, (
% 0.12/0.38 p: $i > $o)).
% 0.12/0.38 tff(goal_type, type, (
% 0.12/0.38 goal: $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (![A: $i] : ?[B: $i] : less(A, B) <=> ![A: $i] : ?[B: $i] : less(A, B)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,axiom,(![A: $i] : ?[B: $i] : less(A, B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','serial_less')).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![A: $i] : ?[B: $i] : less(A, B)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.12/0.38 tff(4,plain,(
% 0.12/0.38 ![A: $i] : less(A, tptp_fun_B_1(A))),
% 0.12/0.38 inference(skolemize,[status(sab)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 ((~![A: $i] : less(A, tptp_fun_B_1(A))) | less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.12/0.38 tff(7,assumption,(p(tptp_fun_B_0(elem!2))), introduced(assumption)).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![A: $i] : less(A, tptp_fun_B_1(A))) | less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 4])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 ((~goal) <=> (~goal)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(11,axiom,(~goal), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goal_to_be_proved')).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (~goal),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((goal | (~p(A)) | (~less(A, B)) | (~p(B))) <=> (goal | (~p(A)) | (~less(A, B)) | (~p(B))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B))) <=> ![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((p(A) & less(A, B) & p(B)) <=> (~((~p(A)) | (~less(A, B)) | (~p(B))))), ((~(p(A) & less(A, B) & p(B))) <=> (~(~((~p(A)) | (~less(A, B)) | (~p(B))))))), rewrite((~(~((~p(A)) | (~less(A, B)) | (~p(B))))) <=> ((~p(A)) | (~less(A, B)) | (~p(B)))), ((~(p(A) & less(A, B) & p(B))) <=> ((~p(A)) | (~less(A, B)) | (~p(B))))), ((goal | (~(p(A) & less(A, B) & p(B)))) <=> (goal | ((~p(A)) | (~less(A, B)) | (~p(B)))))), rewrite((goal | ((~p(A)) | (~less(A, B)) | (~p(B)))) <=> (goal | (~p(A)) | (~less(A, B)) | (~p(B)))), ((goal | (~(p(A) & less(A, B) & p(B)))) <=> (goal | (~p(A)) | (~less(A, B)) | (~p(B)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![A: $i, B: $i] : (goal | (~(p(A) & less(A, B) & p(B)))) <=> ![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![A: $i, B: $i] : (goal | (~(p(A) & less(A, B) & p(B)))) <=> ![A: $i, B: $i] : (goal | (~(p(A) & less(A, B) & p(B))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((p(A) & less(A, B)) & p(B)) <=> (p(A) & less(A, B) & p(B))), ((((p(A) & less(A, B)) & p(B)) => goal) <=> ((p(A) & less(A, B) & p(B)) => goal))), rewrite(((p(A) & less(A, B) & p(B)) => goal) <=> (goal | (~(p(A) & less(A, B) & p(B))))), ((((p(A) & less(A, B)) & p(B)) => goal) <=> (goal | (~(p(A) & less(A, B) & p(B))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![A: $i, B: $i] : (((p(A) & less(A, B)) & p(B)) => goal) <=> ![A: $i, B: $i] : (goal | (~(p(A) & less(A, B) & p(B))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.38 tff(20,axiom,(![A: $i, B: $i] : (((p(A) & less(A, B)) & p(B)) => goal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','left_to_right')).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![A: $i, B: $i] : (goal | (~(p(A) & less(A, B) & p(B))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![A: $i, B: $i] : (goal | (~(p(A) & less(A, B) & p(B))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.12/0.39 tff(23,plain,(
% 0.12/0.39 ![A: $i, B: $i] : (goal | (~(p(A) & less(A, B) & p(B))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[22])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))))) <=> ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | goal | (~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 ((goal | (~p(tptp_fun_B_0(elem!2))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) <=> (goal | (~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(elem!2))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))) <=> ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[27])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(elem!2))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))) <=> ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | goal | (~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[28, 26])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(elem!2))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | goal | (~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 ((~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[31, 25, 12, 9])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[32, 7])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (^[A: $i] : refl((p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A)))))) <=> (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A)))))) <=> ![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (^[A: $i] : rewrite((p(A) | (less(A, tptp_fun_B_0(A)) & p(tptp_fun_B_0(A)))) <=> (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (![A: $i] : (p(A) | (less(A, tptp_fun_B_0(A)) & p(tptp_fun_B_0(A)))) <=> ![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![A: $i] : (p(A) | ?[B: $i] : (less(A, B) & p(B))) <=> ![A: $i] : (p(A) | ?[B: $i] : (less(A, B) & p(B)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(39,axiom,(![A: $i] : (p(A) | ?[B: $i] : (less(A, B) & p(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','right_to_left')).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (![A: $i] : (p(A) | ?[B: $i] : (less(A, B) & p(B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.39 tff(41,plain,(
% 0.12/0.39 ![A: $i] : (p(A) | (less(A, tptp_fun_B_0(A)) & p(tptp_fun_B_0(A))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[40])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | (p(tptp_fun_B_1(tptp_fun_B_0(elem!2))) | (~((~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))))))) <=> ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | p(tptp_fun_B_1(tptp_fun_B_0(elem!2))) | (~((~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | (p(tptp_fun_B_1(tptp_fun_B_0(elem!2))) | (~((~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | p(tptp_fun_B_1(tptp_fun_B_0(elem!2))) | (~((~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (~((~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[46, 43, 33])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (((~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))) | less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B))) <=> ![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((less(A, B) & less(B, C)) <=> (~((~less(B, C)) | (~less(A, B))))), ((~(less(A, B) & less(B, C))) <=> (~(~((~less(B, C)) | (~less(A, B))))))), rewrite((~(~((~less(B, C)) | (~less(A, B))))) <=> ((~less(B, C)) | (~less(A, B)))), ((~(less(A, B) & less(B, C))) <=> ((~less(B, C)) | (~less(A, B))))), (((~(less(A, B) & less(B, C))) | less(A, C)) <=> (((~less(B, C)) | (~less(A, B))) | less(A, C)))), rewrite((((~less(B, C)) | (~less(A, B))) | less(A, C)) <=> (less(A, C) | (~less(B, C)) | (~less(A, B)))), (((~(less(A, B) & less(B, C))) | less(A, C)) <=> (less(A, C) | (~less(B, C)) | (~less(A, B)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((~(less(A, B) & less(B, C))) | less(A, C)) <=> ![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : ((~(less(A, B) & less(B, C))) | less(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(less(A, B) & less(B, C))) | less(A, C))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i] : rewrite(((less(A, B) & less(B, C)) => less(A, C)) <=> ((~(less(A, B) & less(B, C))) | less(A, C)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : ((less(A, B) & less(B, C)) => less(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(less(A, B) & less(B, C))) | less(A, C))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.39 tff(56,axiom,(![A: $i, B: $i, C: $i] : ((less(A, B) & less(B, C)) => less(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitive_less')).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : ((~(less(A, B) & less(B, C))) | less(A, C))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : ((~(less(A, B) & less(B, C))) | less(A, C))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.39 tff(59,plain,(
% 0.19/0.39 ![A: $i, B: $i, C: $i] : ((~(less(A, B) & less(B, C))) | less(A, C))),
% 0.19/0.39 inference(skolemize,[status(sab)],[58])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | ((~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))) <=> ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2))))) <=> ((~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))))) <=> ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | ((~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[63])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))))) <=> ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[64, 62])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[67, 61, 9, 49])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (((~less(tptp_fun_B_1(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))) | p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[69, 47])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))))) <=> ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | goal | (~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 ((goal | (~p(tptp_fun_B_0(elem!2))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))) <=> (goal | (~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(elem!2))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))))) <=> ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[72])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(elem!2))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))))) <=> ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | goal | (~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(elem!2))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | goal | (~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 25, 12, 7, 70, 68])).
% 0.19/0.40 tff(78,plain,(~p(tptp_fun_B_0(elem!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | (p(tptp_fun_B_0(elem!2)) | (~((~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))) <=> ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | p(tptp_fun_B_0(elem!2)) | (~((~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | (p(tptp_fun_B_0(elem!2)) | (~((~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | p(tptp_fun_B_0(elem!2)) | (~((~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (~((~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[81, 43, 78])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (((~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))) <=> ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 ((goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) <=> (goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))) <=> ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[86])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))) <=> ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[87, 85])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (~p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[90, 25, 12, 84, 6])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | (p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~((~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))))) <=> ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~((~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 ((p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~((~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))))) <=> (p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~((~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | (p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~((~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))))) <=> ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | (p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~((~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[93])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | (p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~((~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))))) <=> ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~((~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[94, 92])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | (p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~((~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | p(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~((~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (~((~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[97, 43, 91])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (((~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))) | less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | ((~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))) <=> ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 ((less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) <=> ((~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))) <=> ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | ((~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[102])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))) <=> ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[103, 101])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[106, 61, 6, 100])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (((~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))) | p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[108, 98])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))) <=> ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 ((goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))) <=> (goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))) <=> ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))) <=> ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[112, 110])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | (goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (goal | (~p(A)) | (~less(A, B)) | (~p(B)))) | goal | (~p(tptp_fun_B_0(tptp_fun_B_0(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2)))))) | (~less(tptp_fun_B_0(tptp_fun_B_0(elem!2)), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(tptp_fun_B_0(elem!2))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[115, 25, 12, 84, 109, 107])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------