TSTP Solution File: KLE022+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE022+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 17:23:52 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KLE022+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 07:46:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(addition_type, type, (
% 0.12/0.38 addition: ( $i * $i ) > $i)).
% 0.12/0.38 tff(multiplication_type, type, (
% 0.12/0.38 multiplication: ( $i * $i ) > $i)).
% 0.12/0.38 tff(c_type, type, (
% 0.12/0.38 c: $i > $i)).
% 0.12/0.38 tff(tptp_fun_X1_1_type, type, (
% 0.12/0.38 tptp_fun_X1_1: $i)).
% 0.12/0.38 tff(tptp_fun_X0_2_type, type, (
% 0.12/0.38 tptp_fun_X0_2: $i)).
% 0.12/0.38 tff(one_type, type, (
% 0.12/0.38 one: $i)).
% 0.12/0.38 tff(zero_type, type, (
% 0.12/0.38 zero: $i)).
% 0.12/0.38 tff(complement_type, type, (
% 0.12/0.38 complement: ( $i * $i ) > $o)).
% 0.12/0.38 tff(test_type, type, (
% 0.12/0.38 test: $i > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,(
% 0.12/0.38 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.12/0.38 inference(skolemize,[status(sab)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))),
% 0.12/0.38 inference(symmetry,[status(thm)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.38 tff(16,plain,(
% 0.12/0.38 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(c(X1!1), X1!1)) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (multiplication(X0!2, addition(c(X1!1), X1!1)) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (^[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))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![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)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (^[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))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![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)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.38 tff(27,axiom,(![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_2')).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.12/0.38 tff(30,plain,(
% 0.12/0.38 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(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, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 ((complement(X1!1, c(X1!1)) <=> (~((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(X1!1), X1!1) = one))))) <=> (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(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, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[34])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(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, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[35, 33])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(X1!1), X1!1) = one)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 32])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 ((~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 ((~![X0: $i, X1: $i] : (test(X1) => (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(42,axiom,(~![X0: $i, X1: $i] : (test(X1) => (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[46, 40])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[48, 40])).
% 0.12/0.39 tff(50,plain,(
% 0.12/0.39 ~((~test(X1!1)) | (X0!2 = addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[49])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (test(X1!1)),
% 0.12/0.39 inference(or_elim,[status(thm)],[50])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.12/0.39 tff(57,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_3')).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.12/0.39 tff(60,plain,(
% 0.12/0.39 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[59])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | complement(X1!1, c(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | complement(X1!1, c(X1!1)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1)))) <=> ((~test(X1!1)) | complement(X1!1, c(X1!1)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | complement(X1!1, c(X1!1))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[63])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | complement(X1!1, c(X1!1)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[64, 62])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | complement(X1!1, c(X1!1))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (complement(X1!1, c(X1!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[67, 61, 51])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 ((~(complement(X1!1, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one)))))) | (~complement(X1!1, c(X1!1))) | (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[69, 68, 39])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) | (addition(c(X1!1), X1!1) = one)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (addition(c(X1!1), X1!1) = one),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (one = addition(c(X1!1), X1!1)),
% 0.12/0.39 inference(symmetry,[status(thm)],[72])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (multiplication(X0!2, one) = multiplication(X0!2, addition(c(X1!1), X1!1))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[73])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[75])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(78,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 (![A: $i] : (multiplication(A, one) = A)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.12/0.39 tff(80,plain,(
% 0.12/0.39 ![A: $i] : (multiplication(A, one) = A)),
% 0.12/0.39 inference(skolemize,[status(sab)],[79])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 (![A: $i] : (multiplication(A, one) = A)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X0!2, one) = X0!2)),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (multiplication(X0!2, one) = X0!2),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (X0!2 = multiplication(X0!2, one)),
% 0.12/0.39 inference(symmetry,[status(thm)],[83])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 (X0!2 = addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[84, 74, 19, 10])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 (~(X0!2 = addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))))),
% 0.12/0.39 inference(or_elim,[status(thm)],[50])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.12/0.39 % SZS output end Proof
%------------------------------------------------------------------------------