TSTP Solution File: KLE029+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE029+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:23:55 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
% 0.03/0.11 % Problem : KLE029+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 07:41:02 EDT 2022
% 0.13/0.33 % 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(leq_type, type, (
% 0.19/0.39 leq: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_X0_4_type, type, (
% 0.19/0.39 tptp_fun_X0_4: $i)).
% 0.19/0.39 tff(tptp_fun_X3_0_type, type, (
% 0.19/0.39 tptp_fun_X3_0: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_X1_3_type, type, (
% 0.19/0.39 tptp_fun_X1_3: $i)).
% 0.19/0.39 tff(tptp_fun_X2_2_type, type, (
% 0.19/0.39 tptp_fun_X2_2: $i)).
% 0.19/0.39 tff(ismeetu_type, type, (
% 0.19/0.39 ismeetu: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(addition_type, type, (
% 0.19/0.39 addition: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_X3_1_type, type, (
% 0.19/0.39 tptp_fun_X3_1: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(ismeet_type, type, (
% 0.19/0.39 ismeet: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','order')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!4, X2!2) <=> (addition(X0!4, X2!2) = X2!2))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (leq(X0!4, X2!2) <=> (addition(X0!4, X2!2) = X2!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,assumption,(~ismeetu(X0!4, X1!3, X2!2)), introduced(assumption)).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ((~(ismeet(X0!4, X1!3, X2!2) <=> ismeetu(X0!4, X1!3, X2!2))) <=> ((~ismeet(X0!4, X1!3, X2!2)) <=> ismeetu(X0!4, X1!3, X2!2))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 ((~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))) <=> (~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(13,axiom,(~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (~![X0: $i, X1: $i, X2: $i] : (ismeet(X0, X1, X2) <=> ismeetu(X0, X1, X2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.39 tff(21,plain,(
% 0.19/0.39 ~(ismeet(X0!4, X1!3, X2!2) <=> ismeetu(X0!4, X1!3, X2!2))),
% 0.19/0.39 inference(skolemize,[status(sab)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 ((~ismeet(X0!4, X1!3, X2!2)) <=> ismeetu(X0!4, X1!3, X2!2)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (ismeet(X0!4, X1!3, X2!2) | ismeetu(X0!4, X1!3, X2!2) | (~((~ismeet(X0!4, X1!3, X2!2)) <=> ismeetu(X0!4, X1!3, X2!2)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (ismeet(X0!4, X1!3, X2!2) | ismeetu(X0!4, X1!3, X2!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (ismeet(X0!4, X1!3, X2!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[24, 10])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[X0: $i, X1: $i, X2: $i] : rewrite((~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (^[X0: $i, X1: $i, X2: $i] : refl((~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (^[X0: $i, X1: $i, X2: $i] : rewrite((~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[31, 29])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (^[X0: $i, X1: $i, X2: $i] : trans(monotonicity(rewrite(((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) <=> ((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))), trans(monotonicity(rewrite((~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2))) <=> (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))), ((ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2)))) <=> (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))), rewrite((ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))) <=> (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))), ((ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2)))) <=> (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))), ((((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2))))) <=> (((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))))), rewrite((((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) <=> (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))), ((((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2))))) <=> (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![X0: $i, X1: $i, X2: $i] : (((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (^[X0: $i, X1: $i, X2: $i] : rewrite((((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | ((~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2)))))) <=> (((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![X0: $i, X1: $i, X2: $i] : (((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | ((~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2)))))) <=> ![X0: $i, X1: $i, X2: $i] : (((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) <=> ![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (^[X0: $i, X1: $i, X2: $i] : rewrite((ismeet(X2, X0, X1) <=> ((leq(X2, X0) & leq(X2, X1)) & ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) => leq(X3, X2)))) <=> (ismeet(X2, X0, X1) <=> (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> ((leq(X2, X0) & leq(X2, X1)) & ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) => leq(X3, X2)))) <=> ![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.39 tff(40,axiom,(![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> ((leq(X2, X0) & leq(X2, X1)) & ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) => leq(X3, X2))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+3.ax','ismeet')).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (ismeet(X2, X0, X1) <=> (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.40 tff(43,plain,(
% 0.19/0.40 ![X0: $i, X1: $i, X2: $i] : (((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | ((~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[42])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (((~ismeet(X2, X0, X1)) | (leq(X2, X0) & leq(X2, X1) & ![X3: $i] : ((~(leq(X3, X0) & leq(X3, X1))) | leq(X3, X2)))) & (ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~((~(leq(tptp_fun_X3_0(X2, X1, X0), X0) & leq(tptp_fun_X3_0(X2, X1, X0), X1))) | leq(tptp_fun_X3_0(X2, X1, X0), X2)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0)))))))) | (~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[45, 32])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[46, 27])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 ((~![X0: $i, X1: $i, X2: $i] : (~((~(ismeet(X2, X0, X1) | (~leq(X2, X0)) | (~leq(X2, X1)) | (~(leq(tptp_fun_X3_0(X2, X1, X0), X2) | (~leq(tptp_fun_X3_0(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_0(X2, X1, X0), X1)))))) | (~((~ismeet(X2, X0, X1)) | (~((~leq(X2, X0)) | (~leq(X2, X1)) | (~![X3: $i] : (leq(X3, X2) | (~leq(X3, X1)) | (~leq(X3, X0))))))))))) | (~((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (~((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))))) | ((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 ((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 ((~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))))))) | (~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 ((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[53, 25])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))) | leq(X0!4, X2!2)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (leq(X0!4, X2!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 ((~(leq(X0!4, X2!2) <=> (addition(X0!4, X2!2) = X2!2))) | (~leq(X0!4, X2!2)) | (addition(X0!4, X2!2) = X2!2)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 ((~(leq(X0!4, X2!2) <=> (addition(X0!4, X2!2) = X2!2))) | (addition(X0!4, X2!2) = X2!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (addition(X0!4, X2!2) = X2!2),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[58, 9])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = X0!4))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = X0!4)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[60, 7])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (^[X0: $i, X1: $i, X2: $i] : rewrite((~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> (~((~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) | (~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) | (~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (^[X0: $i, X1: $i, X2: $i] : refl((~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (^[X0: $i, X1: $i, X2: $i] : rewrite((~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (^[X0: $i, X1: $i, X2: $i] : trans(monotonicity(rewrite(((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) <=> ((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))), trans(monotonicity(rewrite(((~(leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)) <=> (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))), ((ismeetu(X2, X0, X1) | ((~(leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))) <=> (ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))), rewrite((ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))) <=> (ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))), ((ismeetu(X2, X0, X1) | ((~(leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))) <=> (ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))), ((((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | ((~(leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) <=> (((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))), rewrite((((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) <=> (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))), ((((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | ((~(leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) <=> (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | ((~(leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) <=> ![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (^[X0: $i, X1: $i, X2: $i] : rewrite((((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | (~((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))) <=> (((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | ((~(leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | (~((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))) <=> ![X0: $i, X1: $i, X2: $i] : (((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | ((~(leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (ismeetu(X2, X0, X1) <=> ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) <=> ![X0: $i, X1: $i, X2: $i] : (ismeetu(X2, X0, X1) <=> ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(74,axiom,(![X0: $i, X1: $i, X2: $i] : (ismeetu(X2, X0, X1) <=> ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+3.ax','ismeetu')).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (![X0: $i, X1: $i, X2: $i] : (ismeetu(X2, X0, X1) <=> ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.40 tff(76,plain,(
% 0.19/0.41 ![X0: $i, X1: $i, X2: $i] : (((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | (~((leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1)) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[75])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![X0: $i, X1: $i, X2: $i] : (((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((leq(X3, X0) & leq(X3, X1)) <=> leq(X3, X2))) & (ismeetu(X2, X0, X1) | ((~(leq(tptp_fun_X3_1(X2, X1, X0), X0) & leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![X0: $i, X1: $i, X2: $i] : (~((~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2)))) | (~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (![X0: $i, X1: $i, X2: $i] : (~((~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) | (~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[79, 63])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 ((~![X0: $i, X1: $i, X2: $i] : (~((~(ismeetu(X2, X0, X1) | (((~leq(tptp_fun_X3_1(X2, X1, X0), X0)) | (~leq(tptp_fun_X3_1(X2, X1, X0), X1))) <=> leq(tptp_fun_X3_1(X2, X1, X0), X2)))) | (~((~ismeetu(X2, X0, X1)) | ![X3: $i] : ((~((~leq(X3, X1)) | (~leq(X3, X0)))) <=> leq(X3, X2))))))) | (~((~(ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))) | (~((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (~((~(ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))) | (~((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (((~(ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))) | (~((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))))) | (ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 ((~(ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))) | ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[86, 10])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))) | ![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[88, 54])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!4, X1!3) <=> (addition(X0!4, X1!3) = X1!3))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (leq(X0!4, X1!3) <=> (addition(X0!4, X1!3) = X1!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[90, 7])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))) | leq(X0!4, X1!3)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (leq(X0!4, X1!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[92, 54])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 ((~(leq(X0!4, X1!3) <=> (addition(X0!4, X1!3) = X1!3))) | (~leq(X0!4, X1!3)) | (addition(X0!4, X1!3) = X1!3)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 ((~(leq(X0!4, X1!3) <=> (addition(X0!4, X1!3) = X1!3))) | (addition(X0!4, X1!3) = X1!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (addition(X0!4, X1!3) = X1!3),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[95, 91])).
% 0.19/0.41 tff(97,assumption,(addition(X0!4, X1!3) = X1!3), introduced(assumption)).
% 0.19/0.41 tff(98,assumption,(((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)), introduced(assumption)).
% 0.19/0.41 tff(99,assumption,(~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)), introduced(assumption)).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 ((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 ((~(((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))) | (~((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)))) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[102, 101, 98])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 ((~(leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = X0!4))) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)) | (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = X0!4)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = X0!4),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[104, 103, 61])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(109,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.41 tff(111,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.19/0.41 inference(skolemize,[status(sab)],[110])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)) = addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.41 inference(symmetry,[status(thm)],[114])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)) = X0!4),
% 0.19/0.41 inference(transitivity,[status(thm)],[115, 105])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))) = addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[116])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))) = X0!4),
% 0.19/0.41 inference(transitivity,[status(thm)],[117, 105])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (addition(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))), X1!3) = addition(X0!4, X1!3)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[118])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (^[C: $i, B: $i, A: $i] : refl((addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> (addition(A, addition(B, C)) = addition(addition(A, B), C)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[120])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(123,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.41 tff(125,plain,(
% 0.19/0.41 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.41 inference(skolemize,[status(sab)],[124])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X1!3)) = addition(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))), X1!3))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X1!3)) = addition(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))), X1!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X1!3) = addition(X0!4, X1!3)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[116])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (addition(X0!4, X1!3) = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X1!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[129])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 (X1!3 = addition(X0!4, X1!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[97])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (X1!3 = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X1!3)),
% 0.19/0.42 inference(transitivity,[status(thm)],[131, 130])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X1!3))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[132])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3),
% 0.19/0.42 inference(transitivity,[status(thm)],[133, 128, 119, 97])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[135, 7])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 ((~(leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3))) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) | (~(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 ((~(leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3))) | (~(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[137, 99])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (~(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) = X1!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[138, 136])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[139, 134])).
% 0.19/0.42 tff(141,plain,(leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3) | (~(addition(X0!4, X1!3) = X1!3)) | (~(((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[141, 96, 87])).
% 0.19/0.42 tff(143,assumption,(leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)), introduced(assumption)).
% 0.19/0.42 tff(144,assumption,(~((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)))), introduced(assumption)).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 ((~(((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))) | ((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[147, 144, 98])).
% 0.19/0.42 tff(149,assumption,(![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))), introduced(assumption)).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (((~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))) | ((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))) <=> ((~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 ((leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3))) <=> ((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 (((~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))) | (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)))) <=> ((~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))) | ((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[151])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 (((~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))) | (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)))) <=> ((~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4))),
% 0.19/0.42 inference(transitivity,[status(thm)],[152, 150])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 ((~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))) | (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 ((~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 ((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[155, 149])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[156, 148, 146, 143])).
% 0.19/0.42 tff(158,plain,(((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3)))) | (~(((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 ((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[158, 142, 89, 87])).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[102, 159, 87])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4) = X0!4),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[104, 160, 61])).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.19/0.42 inference(quant_intro,[status(thm)],[162])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(165,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 (![A: $i] : (addition(A, A) = A)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.19/0.42 tff(167,plain,(
% 0.19/0.42 ![A: $i] : (addition(A, A) = A)),
% 0.19/0.42 inference(skolemize,[status(sab)],[166])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 (![A: $i] : (addition(A, A) = A)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.19/0.42 tff(169,plain,
% 0.19/0.42 ((~![A: $i] : (addition(A, A) = A)) | (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), tptp_fun_X3_1(X0!4, X2!2, X1!3)) = tptp_fun_X3_1(X0!4, X2!2, X1!3))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(170,plain,
% 0.19/0.42 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), tptp_fun_X3_1(X0!4, X2!2, X1!3)) = tptp_fun_X3_1(X0!4, X2!2, X1!3)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.19/0.42 tff(171,plain,
% 0.19/0.42 (addition(X0!4, addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), tptp_fun_X3_1(X0!4, X2!2, X1!3))) = addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[170])).
% 0.19/0.43 tff(172,plain,
% 0.19/0.43 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!4, addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), tptp_fun_X3_1(X0!4, X2!2, X1!3))) = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), tptp_fun_X3_1(X0!4, X2!2, X1!3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(173,plain,
% 0.19/0.43 (addition(X0!4, addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), tptp_fun_X3_1(X0!4, X2!2, X1!3))) = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), tptp_fun_X3_1(X0!4, X2!2, X1!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[172, 126])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 (addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), tptp_fun_X3_1(X0!4, X2!2, X1!3)) = addition(X0!4, addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), tptp_fun_X3_1(X0!4, X2!2, X1!3)))),
% 0.19/0.43 inference(symmetry,[status(thm)],[173])).
% 0.19/0.43 tff(175,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), tptp_fun_X3_1(X0!4, X2!2, X1!3)) = addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 (addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), tptp_fun_X3_1(X0!4, X2!2, X1!3)) = addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[175, 112])).
% 0.19/0.43 tff(177,plain,
% 0.19/0.43 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))) = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), tptp_fun_X3_1(X0!4, X2!2, X1!3))),
% 0.19/0.43 inference(symmetry,[status(thm)],[176])).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))) = X0!4),
% 0.19/0.43 inference(transitivity,[status(thm)],[177, 174, 171, 115, 161])).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 (addition(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))), X2!2) = addition(X0!4, X2!2)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[178])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X2!2)) = addition(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))), X2!2))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X2!2)) = addition(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3))), X2!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[180, 126])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 (addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)) = X0!4),
% 0.19/0.43 inference(transitivity,[status(thm)],[115, 161])).
% 0.19/0.43 tff(183,plain,
% 0.19/0.43 (addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X2!2) = addition(X0!4, X2!2)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[182])).
% 0.19/0.43 tff(184,plain,
% 0.19/0.43 (addition(X0!4, X2!2) = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X2!2)),
% 0.19/0.43 inference(symmetry,[status(thm)],[183])).
% 0.19/0.43 tff(185,plain,
% 0.19/0.43 (X2!2 = addition(X0!4, X2!2)),
% 0.19/0.43 inference(symmetry,[status(thm)],[59])).
% 0.19/0.43 tff(186,plain,
% 0.19/0.43 (X2!2 = addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X2!2)),
% 0.19/0.43 inference(transitivity,[status(thm)],[185, 184])).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), addition(addition(X0!4, tptp_fun_X3_1(X0!4, X2!2, X1!3)), X2!2))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[186])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2),
% 0.19/0.43 inference(transitivity,[status(thm)],[187, 181, 179, 59])).
% 0.19/0.43 tff(189,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 (leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[189, 7])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 ((~((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)))) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(192,plain,
% 0.19/0.43 (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[191, 159, 142])).
% 0.19/0.43 tff(193,plain,
% 0.19/0.43 ((~(leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2))) | leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) | (~(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 ((~(leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) <=> (addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2))) | (~(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 (~(addition(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2) = X2!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[194, 190])).
% 0.19/0.43 tff(196,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[195, 188])).
% 0.19/0.43 tff(197,plain,(ismeetu(X0!4, X1!3, X2!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(198,plain,
% 0.19/0.43 (((~(ismeetu(X0!4, X1!3, X2!2) | (((~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X2!2))) <=> leq(tptp_fun_X3_1(X0!4, X2!2, X1!3), X0!4)))) | (~((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))))) | ((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(199,plain,
% 0.19/0.43 ((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[198, 82])).
% 0.19/0.43 tff(200,plain,
% 0.19/0.43 ((~((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4)))) | (~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(201,plain,
% 0.19/0.43 ((~ismeetu(X0!4, X1!3, X2!2)) | ![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.19/0.43 tff(202,plain,
% 0.19/0.43 (![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[201, 197])).
% 0.19/0.43 tff(203,plain,
% 0.19/0.43 (((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)))) <=> leq(X0!4, X0!4))) <=> ((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)))) <=> leq(X0!4, X0!4)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(204,plain,
% 0.19/0.43 (((~((~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)))) <=> leq(X0!4, X0!4)) <=> ((~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)))) <=> leq(X0!4, X0!4))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(205,plain,
% 0.19/0.43 (((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)))) <=> leq(X0!4, X0!4))) <=> ((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)))) <=> leq(X0!4, X0!4)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[204])).
% 0.19/0.43 tff(206,plain,
% 0.19/0.43 (((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)))) <=> leq(X0!4, X0!4))) <=> ((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)))) <=> leq(X0!4, X0!4)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[205, 203])).
% 0.19/0.43 tff(207,plain,
% 0.19/0.43 ((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(X0!4, X2!2)) | (~leq(X0!4, X1!3)))) <=> leq(X0!4, X0!4))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(208,plain,
% 0.19/0.43 ((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)))) <=> leq(X0!4, X0!4))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.43 tff(209,plain,
% 0.19/0.43 ((~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)))) <=> leq(X0!4, X0!4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[208, 202])).
% 0.19/0.43 tff(210,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!4, X0!4) <=> (addition(X0!4, X0!4) = X0!4))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(211,plain,
% 0.19/0.43 (leq(X0!4, X0!4) <=> (addition(X0!4, X0!4) = X0!4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[210, 7])).
% 0.19/0.43 tff(212,assumption,(~(addition(X0!4, X0!4) = X0!4)), introduced(assumption)).
% 0.19/0.43 tff(213,plain,
% 0.19/0.43 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!4, X0!4) = X0!4)),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(214,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[213, 168, 212])).
% 0.19/0.43 tff(215,plain,(addition(X0!4, X0!4) = X0!4), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(216,plain,
% 0.19/0.43 ((~(leq(X0!4, X0!4) <=> (addition(X0!4, X0!4) = X0!4))) | leq(X0!4, X0!4) | (~(addition(X0!4, X0!4) = X0!4))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(217,plain,
% 0.19/0.43 ((~(leq(X0!4, X0!4) <=> (addition(X0!4, X0!4) = X0!4))) | leq(X0!4, X0!4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.19/0.43 tff(218,plain,
% 0.19/0.43 (leq(X0!4, X0!4)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[217, 211])).
% 0.19/0.43 tff(219,plain,
% 0.19/0.43 ((~((~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)))) <=> leq(X0!4, X0!4))) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)))) | (~leq(X0!4, X0!4))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(220,plain,
% 0.19/0.43 ((~((~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)))) <=> leq(X0!4, X0!4))) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.19/0.43 tff(221,plain,
% 0.19/0.43 (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[220, 209])).
% 0.19/0.43 tff(222,plain,
% 0.19/0.43 (((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2))) | leq(X0!4, X1!3)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(223,plain,
% 0.19/0.43 (leq(X0!4, X1!3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.19/0.43 tff(224,plain,
% 0.19/0.43 ((~ismeet(X0!4, X1!3, X2!2)) | (~ismeetu(X0!4, X1!3, X2!2)) | (~((~ismeet(X0!4, X1!3, X2!2)) <=> ismeetu(X0!4, X1!3, X2!2)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(225,plain,
% 0.19/0.43 ((~ismeet(X0!4, X1!3, X2!2)) | (~ismeetu(X0!4, X1!3, X2!2))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[224, 22])).
% 0.19/0.43 tff(226,plain,
% 0.19/0.43 (~ismeet(X0!4, X1!3, X2!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[225, 197])).
% 0.19/0.43 tff(227,plain,
% 0.19/0.43 (((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2))) | leq(X0!4, X2!2)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(228,plain,
% 0.19/0.43 (leq(X0!4, X2!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[227, 221])).
% 0.19/0.43 tff(229,plain,
% 0.19/0.43 (((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))))) | (~((~ismeet(X0!4, X1!3, X2!2)) | (~((~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~![X3: $i] : (leq(X3, X0!4) | (~leq(X3, X2!2)) | (~leq(X3, X1!3))))))))) | (ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(230,plain,
% 0.19/0.43 (ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[229, 49])).
% 0.19/0.43 tff(231,plain,
% 0.19/0.43 ((~(ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))))) | ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(232,plain,
% 0.19/0.44 (ismeet(X0!4, X1!3, X2!2) | (~leq(X0!4, X1!3)) | (~leq(X0!4, X2!2)) | (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[231, 230])).
% 0.19/0.44 tff(233,plain,
% 0.19/0.44 (~(leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[232, 228, 226, 223])).
% 0.19/0.44 tff(234,plain,
% 0.19/0.44 ((leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2))) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(235,plain,
% 0.19/0.44 (leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.19/0.44 tff(236,plain,
% 0.19/0.44 ((leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2))) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(237,plain,
% 0.19/0.44 (leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[236, 233])).
% 0.19/0.44 tff(238,plain,
% 0.19/0.44 ((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(239,plain,
% 0.19/0.44 (~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[238, 237, 235])).
% 0.19/0.44 tff(240,plain,
% 0.19/0.44 ((leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2))) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(241,plain,
% 0.19/0.44 (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[240, 233])).
% 0.19/0.44 tff(242,plain,
% 0.19/0.44 ((~((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))) | ((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2))) | leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(243,plain,
% 0.19/0.44 (~((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[242, 241, 239])).
% 0.19/0.44 tff(244,plain,
% 0.19/0.44 (((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))) <=> ((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(245,plain,
% 0.19/0.44 (((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)) <=> ((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(246,plain,
% 0.19/0.44 (((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))) <=> ((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[245])).
% 0.19/0.44 tff(247,plain,
% 0.19/0.44 (((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))) <=> ((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[246, 244])).
% 0.19/0.44 tff(248,plain,
% 0.19/0.44 ((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(249,plain,
% 0.19/0.44 ((~![X3: $i] : ((~((~leq(X3, X2!2)) | (~leq(X3, X1!3)))) <=> leq(X3, X0!4))) | ((~((~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X1!3)) | (~leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X2!2)))) <=> leq(tptp_fun_X3_0(X0!4, X2!2, X1!3), X0!4))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.19/0.44 tff(250,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[249, 202, 243])).
% 0.19/0.44 % SZS output end Proof
%------------------------------------------------------------------------------