TSTP Solution File: MSC012+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MSC012+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 05:34:04 EDT 2022
% Result : Theorem 0.19s 0.39s
% 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 v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 03:22:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(less_type, type, (
% 0.19/0.39 less: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_B_0_type, type, (
% 0.19/0.39 tptp_fun_B_0: $i > $i)).
% 0.19/0.39 tff(tptp_fun_B_1_type, type, (
% 0.19/0.39 tptp_fun_B_1: $i > $i)).
% 0.19/0.39 tff(elem_2_type, type, (
% 0.19/0.39 elem_2: $i)).
% 0.19/0.39 tff(p_type, type, (
% 0.19/0.39 p: $i > $o)).
% 0.19/0.39 tff(goal_type, type, (
% 0.19/0.39 goal: $o)).
% 0.19/0.39 tff(1,assumption,(p(tptp_fun_B_0(elem!2))), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![A: $i] : ?[B: $i] : less(A, B) <=> ![A: $i] : ?[B: $i] : less(A, B)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(3,axiom,(![A: $i] : ?[B: $i] : less(A, B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','serial_less')).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![A: $i] : ?[B: $i] : less(A, B)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.39 tff(5,plain,(
% 0.19/0.39 ![A: $i] : less(A, tptp_fun_B_1(A))),
% 0.19/0.39 inference(skolemize,[status(sab)],[4])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 ((~![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)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (less(tptp_fun_B_0(elem!2), tptp_fun_B_1(tptp_fun_B_0(elem!2)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[6, 5])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (^[A: $i, B: $i] : refl(((~p(A)) | (~less(A, B)) | (~p(B))) <=> ((~p(A)) | (~less(A, B)) | (~p(B))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B))) <=> ![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (^[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))) <=> (~(~((~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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~(p(A) & less(A, B) & p(B))) <=> ![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~(p(A) & less(A, B) & p(B))) <=> ![A: $i, B: $i] : (~(p(A) & less(A, B) & p(B)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (^[A: $i, B: $i] : trans(monotonicity(iff_false(asserted(~goal), (goal <=> $false)), ((goal | (~(p(A) & less(A, B) & p(B)))) <=> ($false | (~(p(A) & less(A, B) & p(B)))))), rewrite(($false | (~(p(A) & less(A, B) & p(B)))) <=> (~(p(A) & less(A, B) & p(B)))), ((goal | (~(p(A) & less(A, B) & p(B)))) <=> (~(p(A) & less(A, B) & p(B)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![A: $i, B: $i] : (goal | (~(p(A) & less(A, B) & p(B)))) <=> ![A: $i, B: $i] : (~(p(A) & less(A, B) & p(B)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (^[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))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![A: $i, B: $i] : (((p(A) & less(A, B)) & p(B)) => goal) <=> ![A: $i, B: $i] : (goal | (~(p(A) & less(A, B) & p(B))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.39 tff(17,axiom,(![A: $i, B: $i] : (((p(A) & less(A, B)) & p(B)) => goal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','left_to_right')).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (![A: $i, B: $i] : (goal | (~(p(A) & less(A, B) & p(B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~(p(A) & less(A, B) & p(B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~(p(A) & less(A, B) & p(B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.39 tff(21,plain,(
% 0.19/0.39 ![A: $i, B: $i] : (~(p(A) & less(A, B) & p(B)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 9])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~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] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | (~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)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (((~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))))) <=> ((~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)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~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] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~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))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[25])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~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] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | (~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)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[26, 24])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~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)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | (~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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 ((~p(tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[29, 23, 7])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (~p(tptp_fun_B_1(tptp_fun_B_0(elem!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[30, 1])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (^[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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (^[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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (![A: $i] : (p(A) | ?[B: $i] : (less(A, B) & p(B))) <=> ![A: $i] : (p(A) | ?[B: $i] : (less(A, B) & p(B)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(37,axiom,(![A: $i] : (p(A) | ?[B: $i] : (less(A, B) & p(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','right_to_left')).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (![A: $i] : (p(A) | ?[B: $i] : (less(A, B) & p(B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.40 tff(39,plain,(
% 0.19/0.40 ![A: $i] : (p(A) | (less(A, tptp_fun_B_0(A)) & p(tptp_fun_B_0(A))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[38])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.19/0.40 tff(42,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(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))))))))) <=> ((~![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))) | (~((~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))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 ((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)))))))) <=> (p(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))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(44,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(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))) | (~((~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)))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.40 tff(45,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(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))) | (~((~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))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[44, 42])).
% 0.19/0.40 tff(46,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(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))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(47,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(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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (~((~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))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[47, 41, 31])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (((~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)))))) | 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))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (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))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (^[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)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.40 tff(57,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')).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~(less(A, B) & less(B, C))) | less(A, C))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~(less(A, B) & less(B, C))) | less(A, C))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.40 tff(60,plain,(
% 0.19/0.40 ![A: $i, B: $i, C: $i] : ((~(less(A, B) & less(B, C))) | less(A, C))),
% 0.19/0.40 inference(skolemize,[status(sab)],[59])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.19/0.40 tff(63,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(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_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)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(64,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(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)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(65,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(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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[65, 62, 7, 50])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (((~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)))))) | p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[67, 48])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~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] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | (~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))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~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))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | (~p(tptp_fun_B_0(elem!2))) | (~less(tptp_fun_B_0(elem!2), tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2))))) | (~p(tptp_fun_B_0(tptp_fun_B_1(tptp_fun_B_0(elem!2)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[71, 23, 1, 68, 66])).
% 0.19/0.40 tff(73,plain,(~p(tptp_fun_B_0(elem!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (((~p(tptp_fun_B_0(elem!2))) | (~less(elem!2, tptp_fun_B_0(elem!2)))) | p(tptp_fun_B_0(elem!2))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~p(tptp_fun_B_0(elem!2))) | (~less(elem!2, tptp_fun_B_0(elem!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | (p(elem!2) | (~((~p(tptp_fun_B_0(elem!2))) | (~less(elem!2, tptp_fun_B_0(elem!2))))))) <=> ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | p(elem!2) | (~((~p(tptp_fun_B_0(elem!2))) | (~less(elem!2, tptp_fun_B_0(elem!2))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ((p(elem!2) | (~((~less(elem!2, tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_0(elem!2)))))) <=> (p(elem!2) | (~((~p(tptp_fun_B_0(elem!2))) | (~less(elem!2, tptp_fun_B_0(elem!2))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | (p(elem!2) | (~((~less(elem!2, tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_0(elem!2))))))) <=> ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | (p(elem!2) | (~((~p(tptp_fun_B_0(elem!2))) | (~less(elem!2, tptp_fun_B_0(elem!2)))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[77])).
% 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(elem!2) | (~((~less(elem!2, tptp_fun_B_0(elem!2))) | (~p(tptp_fun_B_0(elem!2))))))) <=> ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | p(elem!2) | (~((~p(tptp_fun_B_0(elem!2))) | (~less(elem!2, tptp_fun_B_0(elem!2))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[78, 76])).
% 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(elem!2) | (~((~less(elem!2, tptp_fun_B_0(elem!2))) | (~p(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(elem!2) | (~((~p(tptp_fun_B_0(elem!2))) | (~less(elem!2, 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 (p(elem!2) | (~((~p(tptp_fun_B_0(elem!2))) | (~less(elem!2, tptp_fun_B_0(elem!2)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[81, 41])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (p(elem!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[82, 75])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 ((~![A: $i] : less(A, tptp_fun_B_1(A))) | less(elem!2, tptp_fun_B_1(elem!2))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (less(elem!2, tptp_fun_B_1(elem!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[84, 5])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~p(elem!2)) | (~less(elem!2, tptp_fun_B_1(elem!2))) | (~p(tptp_fun_B_1(elem!2))))) <=> ((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | (~p(elem!2)) | (~less(elem!2, tptp_fun_B_1(elem!2))) | (~p(tptp_fun_B_1(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] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~p(elem!2)) | (~less(elem!2, tptp_fun_B_1(elem!2))) | (~p(tptp_fun_B_1(elem!2))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | (~p(elem!2)) | (~less(elem!2, tptp_fun_B_1(elem!2))) | (~p(tptp_fun_B_1(elem!2)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 ((~p(elem!2)) | (~p(tptp_fun_B_1(elem!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[88, 23, 85])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (~p(tptp_fun_B_1(elem!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[89, 83])).
% 0.19/0.40 tff(91,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(elem!2)) | (~((~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))))))) <=> ((~![A: $i] : (p(A) | (~((~less(A, tptp_fun_B_0(A))) | (~p(tptp_fun_B_0(A))))))) | p(tptp_fun_B_1(elem!2)) | (~((~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 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(elem!2)) | (~((~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(93,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(elem!2)) | (~((~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (p(tptp_fun_B_1(elem!2)) | (~((~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[93, 41])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (~((~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[94, 90])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (((~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2))))) | less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | ((~less(elem!2, tptp_fun_B_1(elem!2))) | (~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2))))) <=> ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (~less(elem!2, tptp_fun_B_1(elem!2))) | (~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 ((less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2))) | (~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~less(elem!2, tptp_fun_B_1(elem!2)))) <=> ((~less(elem!2, tptp_fun_B_1(elem!2))) | (~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2))) | (~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~less(elem!2, tptp_fun_B_1(elem!2))))) <=> ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | ((~less(elem!2, tptp_fun_B_1(elem!2))) | (~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2))) | (~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~less(elem!2, tptp_fun_B_1(elem!2))))) <=> ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (~less(elem!2, tptp_fun_B_1(elem!2))) | (~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[100, 98])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2))) | (~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~less(elem!2, tptp_fun_B_1(elem!2))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (less(A, C) | (~less(B, C)) | (~less(A, B)))) | (~less(elem!2, tptp_fun_B_1(elem!2))) | (~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[103, 62, 85, 97])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (((~less(tptp_fun_B_1(elem!2), tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2))))) | p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[105, 95])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~p(elem!2)) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2)))))) <=> ((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | (~p(elem!2)) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (((~p(elem!2)) | (~less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2))))) <=> ((~p(elem!2)) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~p(elem!2)) | (~less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))))) <=> ((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~p(elem!2)) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~p(elem!2)) | (~less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))))) <=> ((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | (~p(elem!2)) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[109, 107])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | ((~p(elem!2)) | (~less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~p(A)) | (~less(A, B)) | (~p(B)))) | (~p(elem!2)) | (~p(tptp_fun_B_0(tptp_fun_B_1(elem!2)))) | (~less(elem!2, tptp_fun_B_0(tptp_fun_B_1(elem!2))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[112, 23, 83, 106, 104])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------