TSTP Solution File: KLE021+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE021+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 17:23:51 EDT 2022
% Result : Theorem 0.15s 0.36s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : KLE021+4 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.30 % Computer : n014.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Thu Sep 1 07:51:02 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.15/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.31 Usage: tptp [options] [-file:]file
% 0.15/0.31 -h, -? prints this message.
% 0.15/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.31 -m, -model generate model.
% 0.15/0.31 -p, -proof generate proof.
% 0.15/0.31 -c, -core generate unsat core of named formulas.
% 0.15/0.31 -st, -statistics display statistics.
% 0.15/0.31 -t:timeout set timeout (in second).
% 0.15/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.31 -<param>:<value> configuration parameter and value.
% 0.15/0.31 -o:<output-file> file to place output in.
% 0.15/0.36 % SZS status Theorem
% 0.15/0.36 % SZS output start Proof
% 0.15/0.36 tff(addition_type, type, (
% 0.15/0.36 addition: ( $i * $i ) > $i)).
% 0.15/0.36 tff(multiplication_type, type, (
% 0.15/0.36 multiplication: ( $i * $i ) > $i)).
% 0.15/0.36 tff(tptp_fun_X0_2_type, type, (
% 0.15/0.36 tptp_fun_X0_2: $i)).
% 0.15/0.36 tff(c_type, type, (
% 0.15/0.36 c: $i > $i)).
% 0.15/0.36 tff(tptp_fun_X1_1_type, type, (
% 0.15/0.36 tptp_fun_X1_1: $i)).
% 0.15/0.36 tff(tptp_fun_X1_0_type, type, (
% 0.15/0.36 tptp_fun_X1_0: $i > $i)).
% 0.15/0.36 tff(complement_type, type, (
% 0.15/0.36 complement: ( $i * $i ) > $o)).
% 0.15/0.36 tff(test_type, type, (
% 0.15/0.36 test: $i > $o)).
% 0.15/0.36 tff(leq_type, type, (
% 0.15/0.36 leq: ( $i * $i ) > $o)).
% 0.15/0.36 tff(one_type, type, (
% 0.15/0.36 one: $i)).
% 0.15/0.36 tff(zero_type, type, (
% 0.15/0.36 zero: $i)).
% 0.15/0.36 tff(1,plain,
% 0.15/0.36 ((~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))) <=> (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(2,plain,
% 0.15/0.36 ((~![X0: $i, X1: $i] : (test(X1) => (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))) <=> (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(3,axiom,(~![X0: $i, X1: $i] : (test(X1) => (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.15/0.36 tff(4,plain,
% 0.15/0.36 (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.15/0.36 tff(5,plain,
% 0.15/0.36 (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.15/0.36 tff(6,plain,
% 0.15/0.36 (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.15/0.36 tff(7,plain,
% 0.15/0.36 (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.15/0.36 tff(8,plain,
% 0.15/0.36 (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.15/0.36 tff(9,plain,
% 0.15/0.36 (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.15/0.36 tff(10,plain,
% 0.15/0.36 (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.15/0.36 tff(11,plain,(
% 0.15/0.36 ~((~test(X1!1)) | (leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) & leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)))),
% 0.15/0.36 inference(skolemize,[status(sab)],[10])).
% 0.15/0.36 tff(12,plain,
% 0.15/0.36 (test(X1!1)),
% 0.15/0.36 inference(or_elim,[status(thm)],[11])).
% 0.15/0.36 tff(13,plain,
% 0.15/0.36 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(14,plain,
% 0.15/0.36 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.15/0.37 tff(15,plain,
% 0.15/0.37 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(16,plain,
% 0.15/0.37 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(17,plain,
% 0.15/0.37 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.15/0.37 tff(18,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_3')).
% 0.15/0.37 tff(19,plain,
% 0.15/0.37 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.15/0.37 tff(20,plain,
% 0.15/0.37 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.15/0.37 tff(21,plain,(
% 0.15/0.37 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.15/0.37 inference(skolemize,[status(sab)],[20])).
% 0.15/0.37 tff(22,plain,
% 0.15/0.37 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.15/0.37 tff(23,plain,
% 0.15/0.37 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(24,plain,
% 0.15/0.37 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(25,plain,
% 0.15/0.37 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.15/0.37 tff(26,plain,
% 0.15/0.37 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.15/0.37 tff(27,plain,
% 0.15/0.37 (^[X0: $i, X1: $i] : refl((complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))) <=> (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(28,plain,
% 0.15/0.37 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[27])).
% 0.15/0.37 tff(29,plain,
% 0.15/0.37 (^[X0: $i, X1: $i] : rewrite((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(30,plain,
% 0.15/0.37 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[29])).
% 0.15/0.37 tff(31,plain,
% 0.15/0.37 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(32,plain,
% 0.15/0.37 (^[X0: $i, X1: $i] : rewrite((complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one))) <=> (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(33,plain,
% 0.15/0.37 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[32])).
% 0.15/0.37 tff(34,axiom,(![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_2')).
% 0.15/0.37 tff(35,plain,
% 0.15/0.37 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.15/0.37 tff(36,plain,
% 0.15/0.37 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.15/0.37 tff(37,plain,(
% 0.15/0.37 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.15/0.37 inference(skolemize,[status(sab)],[36])).
% 0.15/0.37 tff(38,plain,
% 0.15/0.37 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.15/0.37 tff(39,plain,
% 0.15/0.37 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.15/0.37 tff(40,plain,
% 0.15/0.37 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(41,plain,
% 0.15/0.37 ((complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))) <=> (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(42,plain,
% 0.15/0.37 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))))),
% 0.15/0.37 inference(monotonicity,[status(thm)],[41])).
% 0.15/0.37 tff(43,plain,
% 0.15/0.37 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))))),
% 0.15/0.37 inference(transitivity,[status(thm)],[42, 40])).
% 0.15/0.37 tff(44,plain,
% 0.15/0.37 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(45,plain,
% 0.15/0.37 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.15/0.37 tff(46,plain,
% 0.15/0.37 (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[45, 39])).
% 0.15/0.37 tff(47,plain,
% 0.15/0.37 ((addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1))) <=> (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1))),
% 0.15/0.37 inference(commutativity,[status(thm)],[])).
% 0.15/0.37 tff(48,plain,
% 0.15/0.37 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(tptp_fun_X1_0(X1!1), X1!1) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(49,plain,
% 0.15/0.37 (complement(tptp_fun_X1_0(X1!1), X1!1) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[48, 39])).
% 0.15/0.37 tff(50,plain,
% 0.15/0.37 (^[X0: $i] : refl((~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(51,plain,
% 0.15/0.37 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[50])).
% 0.15/0.37 tff(52,plain,
% 0.15/0.37 (^[X0: $i] : rewrite((~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(53,plain,
% 0.15/0.37 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[52])).
% 0.15/0.37 tff(54,plain,
% 0.15/0.37 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.15/0.37 inference(transitivity,[status(thm)],[53, 51])).
% 0.15/0.37 tff(55,plain,
% 0.15/0.37 (^[X0: $i] : trans(monotonicity(rewrite((test(X0) | ![X1: $i] : (~complement(X1, X0))) <=> (test(X0) | ![X1: $i] : (~complement(X1, X0)))), ((((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))))), rewrite((((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))), ((((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(56,plain,
% 0.15/0.37 (![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[55])).
% 0.15/0.37 tff(57,plain,
% 0.15/0.37 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(58,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 0.15/0.37 tff(59,plain,
% 0.15/0.37 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.15/0.37 tff(60,plain,(
% 0.15/0.37 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 0.15/0.37 inference(skolemize,[status(sab)],[59])).
% 0.15/0.37 tff(61,plain,
% 0.15/0.37 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.15/0.37 tff(62,plain,
% 0.15/0.37 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.15/0.37 tff(63,plain,
% 0.15/0.37 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1))))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(64,plain,
% 0.15/0.37 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.15/0.37 tff(65,plain,
% 0.15/0.37 (((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1))))) | ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))),
% 0.15/0.37 inference(tautology,[status(thm)],[])).
% 0.15/0.37 tff(66,plain,
% 0.15/0.37 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.15/0.37 tff(67,plain,
% 0.15/0.37 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.15/0.37 inference(tautology,[status(thm)],[])).
% 0.15/0.37 tff(68,plain,
% 0.15/0.37 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[67, 12])).
% 0.15/0.37 tff(69,plain,
% 0.15/0.37 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[68, 66])).
% 0.15/0.38 tff(70,plain,
% 0.15/0.38 ((~(complement(tptp_fun_X1_0(X1!1), X1!1) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))))) | (~complement(tptp_fun_X1_0(X1!1), X1!1)) | (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))))),
% 0.15/0.38 inference(tautology,[status(thm)],[])).
% 0.15/0.38 tff(71,plain,
% 0.15/0.38 ((~(complement(tptp_fun_X1_0(X1!1), X1!1) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))))) | (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.15/0.38 tff(72,plain,
% 0.15/0.38 (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[71, 49])).
% 0.15/0.38 tff(73,plain,
% 0.15/0.38 (((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) | (addition(X1!1, tptp_fun_X1_0(X1!1)) = one)),
% 0.15/0.38 inference(tautology,[status(thm)],[])).
% 0.15/0.38 tff(74,plain,
% 0.15/0.38 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.15/0.38 tff(75,plain,
% 0.15/0.38 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 0.15/0.38 inference(symmetry,[status(thm)],[74])).
% 0.15/0.38 tff(76,plain,
% 0.15/0.38 ((addition(tptp_fun_X1_0(X1!1), X1!1) = one) <=> (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 0.15/0.38 inference(monotonicity,[status(thm)],[75])).
% 0.15/0.38 tff(77,plain,
% 0.15/0.38 ((addition(tptp_fun_X1_0(X1!1), X1!1) = one) <=> (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1))),
% 0.15/0.38 inference(transitivity,[status(thm)],[76, 47])).
% 0.15/0.38 tff(78,plain,
% 0.15/0.38 ((addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)) <=> (addition(tptp_fun_X1_0(X1!1), X1!1) = one)),
% 0.15/0.38 inference(symmetry,[status(thm)],[77])).
% 0.15/0.38 tff(79,plain,
% 0.15/0.38 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.15/0.38 inference(bind,[status(th)],[])).
% 0.15/0.38 tff(80,plain,
% 0.15/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.15/0.38 inference(quant_intro,[status(thm)],[79])).
% 0.15/0.38 tff(81,plain,
% 0.15/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(82,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.15/0.38 tff(83,plain,
% 0.15/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.15/0.38 tff(84,plain,(
% 0.15/0.38 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.15/0.38 inference(skolemize,[status(sab)],[83])).
% 0.15/0.38 tff(85,plain,
% 0.15/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.15/0.38 tff(86,plain,
% 0.15/0.38 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1))),
% 0.15/0.38 inference(quant_inst,[status(thm)],[])).
% 0.15/0.38 tff(87,plain,
% 0.15/0.38 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.15/0.38 tff(88,plain,
% 0.15/0.38 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[87, 78])).
% 0.15/0.38 tff(89,plain,
% 0.15/0.38 (((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) | (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)),
% 0.15/0.38 inference(tautology,[status(thm)],[])).
% 0.15/0.38 tff(90,plain,
% 0.15/0.38 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[89, 72])).
% 0.15/0.38 tff(91,plain,
% 0.15/0.38 (((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) | (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)),
% 0.15/0.38 inference(tautology,[status(thm)],[])).
% 0.15/0.38 tff(92,plain,
% 0.15/0.38 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[91, 72])).
% 0.15/0.38 tff(93,plain,
% 0.15/0.38 ((~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))),
% 0.15/0.38 inference(tautology,[status(thm)],[])).
% 0.15/0.38 tff(94,plain,
% 0.15/0.38 ((~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[93, 92, 90])).
% 0.15/0.38 tff(95,plain,
% 0.15/0.38 (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[94, 88])).
% 0.15/0.38 tff(96,plain,
% 0.15/0.38 ((~(complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))) | complement(X1!1, tptp_fun_X1_0(X1!1)) | ((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))),
% 0.15/0.38 inference(tautology,[status(thm)],[])).
% 0.15/0.38 tff(97,plain,
% 0.15/0.38 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[96, 95, 46])).
% 0.15/0.38 tff(98,plain,
% 0.15/0.38 ((~((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))) | (c(X1!1) = tptp_fun_X1_0(X1!1)) | (~complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 0.15/0.38 inference(tautology,[status(thm)],[])).
% 0.15/0.38 tff(99,plain,
% 0.15/0.38 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[98, 97, 26])).
% 0.15/0.38 tff(100,plain,
% 0.15/0.38 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 0.15/0.38 inference(symmetry,[status(thm)],[99])).
% 0.15/0.38 tff(101,plain,
% 0.15/0.38 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = multiplication(c(X1!1), X0!2)),
% 0.15/0.38 inference(monotonicity,[status(thm)],[100])).
% 0.15/0.38 tff(102,plain,
% 0.15/0.38 (multiplication(c(X1!1), X0!2) = multiplication(tptp_fun_X1_0(X1!1), X0!2)),
% 0.15/0.38 inference(symmetry,[status(thm)],[101])).
% 0.15/0.38 tff(103,plain,
% 0.15/0.38 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 0.15/0.38 inference(monotonicity,[status(thm)],[102])).
% 0.15/0.38 tff(104,plain,
% 0.15/0.38 (addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 0.15/0.38 inference(symmetry,[status(thm)],[103])).
% 0.15/0.38 tff(105,plain,
% 0.15/0.38 (^[A: $i, B: $i, C: $i] : refl((multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))))),
% 0.15/0.38 inference(bind,[status(th)],[])).
% 0.15/0.38 tff(106,plain,
% 0.15/0.38 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.15/0.38 inference(quant_intro,[status(thm)],[105])).
% 0.15/0.38 tff(107,plain,
% 0.15/0.38 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(108,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 0.15/0.38 tff(109,plain,
% 0.15/0.38 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.15/0.38 tff(110,plain,(
% 0.15/0.38 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.15/0.38 inference(skolemize,[status(sab)],[109])).
% 0.15/0.38 tff(111,plain,
% 0.15/0.38 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.15/0.38 tff(112,plain,
% 0.15/0.38 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 0.15/0.38 inference(quant_inst,[status(thm)],[])).
% 0.15/0.38 tff(113,plain,
% 0.15/0.38 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.15/0.38 tff(114,plain,
% 0.15/0.38 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = multiplication(one, X0!2)),
% 0.15/0.38 inference(monotonicity,[status(thm)],[74])).
% 0.15/0.38 tff(115,plain,
% 0.15/0.38 (multiplication(one, X0!2) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2)),
% 0.15/0.38 inference(symmetry,[status(thm)],[114])).
% 0.15/0.38 tff(116,plain,
% 0.15/0.38 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.15/0.38 inference(bind,[status(th)],[])).
% 0.15/0.38 tff(117,plain,
% 0.15/0.38 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.15/0.38 inference(quant_intro,[status(thm)],[116])).
% 0.15/0.38 tff(118,plain,
% 0.15/0.38 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(119,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 0.15/0.38 tff(120,plain,
% 0.15/0.38 (![A: $i] : (multiplication(one, A) = A)),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.15/0.38 tff(121,plain,(
% 0.15/0.38 ![A: $i] : (multiplication(one, A) = A)),
% 0.15/0.38 inference(skolemize,[status(sab)],[120])).
% 0.15/0.38 tff(122,plain,
% 0.15/0.38 (![A: $i] : (multiplication(one, A) = A)),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.15/0.38 tff(123,plain,
% 0.15/0.38 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!2) = X0!2)),
% 0.15/0.38 inference(quant_inst,[status(thm)],[])).
% 0.15/0.38 tff(124,plain,
% 0.15/0.38 (multiplication(one, X0!2) = X0!2),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.15/0.38 tff(125,plain,
% 0.15/0.38 (X0!2 = multiplication(one, X0!2)),
% 0.15/0.38 inference(symmetry,[status(thm)],[124])).
% 0.15/0.38 tff(126,plain,
% 0.15/0.38 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.15/0.38 inference(bind,[status(th)],[])).
% 0.15/0.38 tff(127,plain,
% 0.15/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.15/0.38 inference(quant_intro,[status(thm)],[126])).
% 0.15/0.38 tff(128,plain,
% 0.15/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(129,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','order')).
% 0.15/0.38 tff(130,plain,
% 0.15/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.15/0.38 tff(131,plain,(
% 0.15/0.38 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.15/0.38 inference(skolemize,[status(sab)],[130])).
% 0.15/0.38 tff(132,plain,
% 0.15/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.15/0.38 tff(133,plain,
% 0.15/0.38 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) <=> (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = X0!2))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(134,plain,
% 0.15/0.39 (leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) <=> (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = X0!2)),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.15/0.39 tff(135,plain,
% 0.15/0.39 (multiplication(one, X0!2) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2)),
% 0.15/0.39 inference(monotonicity,[status(thm)],[75])).
% 0.15/0.39 tff(136,plain,
% 0.15/0.39 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = multiplication(one, X0!2)),
% 0.15/0.39 inference(symmetry,[status(thm)],[135])).
% 0.15/0.39 tff(137,plain,
% 0.15/0.39 (addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2)),
% 0.15/0.39 inference(symmetry,[status(thm)],[113])).
% 0.15/0.39 tff(138,plain,
% 0.15/0.39 (addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 0.15/0.39 inference(monotonicity,[status(thm)],[101])).
% 0.15/0.39 tff(139,plain,
% 0.15/0.39 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 0.15/0.39 inference(symmetry,[status(thm)],[138])).
% 0.15/0.39 tff(140,plain,
% 0.15/0.39 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(141,plain,
% 0.15/0.39 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[140, 85])).
% 0.15/0.39 tff(142,plain,
% 0.15/0.39 (addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 0.15/0.39 inference(symmetry,[status(thm)],[141])).
% 0.15/0.39 tff(143,plain,
% 0.15/0.39 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.15/0.39 inference(bind,[status(th)],[])).
% 0.15/0.39 tff(144,plain,
% 0.15/0.39 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.15/0.39 inference(quant_intro,[status(thm)],[143])).
% 0.15/0.39 tff(145,plain,
% 0.15/0.39 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(146,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.15/0.39 tff(147,plain,
% 0.15/0.39 (![A: $i] : (addition(A, A) = A)),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.15/0.39 tff(148,plain,(
% 0.15/0.39 ![A: $i] : (addition(A, A) = A)),
% 0.15/0.39 inference(skolemize,[status(sab)],[147])).
% 0.15/0.39 tff(149,plain,
% 0.15/0.39 (![A: $i] : (addition(A, A) = A)),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.15/0.39 tff(150,plain,
% 0.15/0.39 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(151,plain,
% 0.15/0.39 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.15/0.39 tff(152,plain,
% 0.15/0.39 (X0!2 = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 0.15/0.39 inference(transitivity,[status(thm)],[125, 135, 113, 138, 141])).
% 0.15/0.39 tff(153,plain,
% 0.15/0.39 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 0.15/0.39 inference(monotonicity,[status(thm)],[141, 152])).
% 0.15/0.39 tff(154,plain,
% 0.15/0.39 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = X0!2),
% 0.15/0.39 inference(transitivity,[status(thm)],[153, 151, 142, 139, 137, 136, 124])).
% 0.15/0.39 tff(155,assumption,(~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)), introduced(assumption)).
% 0.15/0.39 tff(156,plain,
% 0.15/0.39 ((~(leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) <=> (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = X0!2))) | leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) | (~(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = X0!2))),
% 0.15/0.39 inference(tautology,[status(thm)],[])).
% 0.15/0.39 tff(157,plain,
% 0.15/0.39 ((~(leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) <=> (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = X0!2))) | (~(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = X0!2))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.15/0.39 tff(158,plain,
% 0.15/0.39 (~(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = X0!2)),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[157, 134])).
% 0.15/0.39 tff(159,plain,
% 0.15/0.39 ($false),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[158, 154])).
% 0.15/0.39 tff(160,plain,(leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.39 tff(161,plain,
% 0.15/0.39 ((~(leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) <=> (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = X0!2))) | (~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)) | (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = X0!2)),
% 0.15/0.39 inference(tautology,[status(thm)],[])).
% 0.15/0.39 tff(162,plain,
% 0.15/0.39 ((~(leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) <=> (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = X0!2))) | (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = X0!2)),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.15/0.39 tff(163,plain,
% 0.15/0.39 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) = X0!2),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[162, 134])).
% 0.15/0.39 tff(164,plain,
% 0.15/0.39 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), X0!2) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)),
% 0.15/0.39 inference(monotonicity,[status(thm)],[142])).
% 0.15/0.39 tff(165,plain,
% 0.15/0.39 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), X0!2) = addition(X0!2, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(166,plain,
% 0.15/0.39 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), X0!2) = addition(X0!2, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[165, 85])).
% 0.15/0.39 tff(167,plain,
% 0.15/0.39 (addition(X0!2, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), X0!2)),
% 0.15/0.39 inference(symmetry,[status(thm)],[166])).
% 0.15/0.39 tff(168,plain,
% 0.15/0.39 (addition(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(X0!2, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 0.15/0.39 inference(monotonicity,[status(thm)],[141])).
% 0.15/0.39 tff(169,plain,
% 0.15/0.39 (addition(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 0.15/0.39 inference(transitivity,[status(thm)],[168, 167, 164, 163, 125, 115, 113, 104])).
% 0.15/0.39 tff(170,plain,
% 0.15/0.39 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) <=> (addition(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(171,plain,
% 0.15/0.39 (leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) <=> (addition(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[170, 132])).
% 0.15/0.39 tff(172,plain,
% 0.15/0.39 ((~(~((~leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2))))) <=> ((~leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(173,plain,
% 0.15/0.39 ((leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) & leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)) <=> (~((~leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(174,plain,
% 0.15/0.39 ((~(leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) & leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2))) <=> (~(~((~leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)))))),
% 0.15/0.39 inference(monotonicity,[status(thm)],[173])).
% 0.15/0.39 tff(175,plain,
% 0.15/0.39 ((~(leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) & leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2))) <=> ((~leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)))),
% 0.15/0.39 inference(transitivity,[status(thm)],[174, 172])).
% 0.15/0.39 tff(176,plain,
% 0.15/0.39 (~(leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) & leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2))),
% 0.15/0.39 inference(or_elim,[status(thm)],[11])).
% 0.15/0.39 tff(177,plain,
% 0.15/0.39 ((~leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.15/0.39 tff(178,plain,
% 0.15/0.39 (~leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[177, 160])).
% 0.15/0.39 tff(179,plain,
% 0.15/0.39 ((~(leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) <=> (addition(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) | (~(addition(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 0.15/0.39 inference(tautology,[status(thm)],[])).
% 0.15/0.39 tff(180,plain,
% 0.15/0.39 ((~(leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) <=> (addition(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | (~(addition(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.15/0.39 tff(181,plain,
% 0.15/0.39 (~(addition(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[180, 171])).
% 0.15/0.40 tff(182,plain,
% 0.15/0.40 ($false),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[181, 169])).
% 0.15/0.40 % SZS output end Proof
%------------------------------------------------------------------------------