TSTP Solution File: KLE011+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE011+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 17:23:48 EDT 2022
% Result : Theorem 3.69s 2.60s
% Output : Proof 3.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE011+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 07:54:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 3.69/2.60 % SZS status Theorem
% 3.69/2.60 % SZS output start Proof
% 3.69/2.60 tff(addition_type, type, (
% 3.69/2.60 addition: ( $i * $i ) > $i)).
% 3.69/2.60 tff(multiplication_type, type, (
% 3.69/2.60 multiplication: ( $i * $i ) > $i)).
% 3.69/2.60 tff(c_type, type, (
% 3.69/2.60 c: $i > $i)).
% 3.69/2.60 tff(tptp_fun_X1_1_type, type, (
% 3.69/2.60 tptp_fun_X1_1: $i)).
% 3.69/2.60 tff(tptp_fun_X0_2_type, type, (
% 3.69/2.60 tptp_fun_X0_2: $i)).
% 3.69/2.60 tff(one_type, type, (
% 3.69/2.60 one: $i)).
% 3.69/2.60 tff(zero_type, type, (
% 3.69/2.60 zero: $i)).
% 3.69/2.60 tff(complement_type, type, (
% 3.69/2.60 complement: ( $i * $i ) > $o)).
% 3.69/2.60 tff(test_type, type, (
% 3.69/2.60 test: $i > $o)).
% 3.69/2.60 tff(tptp_fun_X1_0_type, type, (
% 3.69/2.60 tptp_fun_X1_0: $i > $i)).
% 3.69/2.60 tff(1,plain,
% 3.69/2.60 (^[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)))),
% 3.69/2.60 inference(bind,[status(th)],[])).
% 3.69/2.60 tff(2,plain,
% 3.69/2.60 (![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))),
% 3.69/2.60 inference(quant_intro,[status(thm)],[1])).
% 3.69/2.60 tff(3,plain,
% 3.69/2.60 (![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))),
% 3.69/2.60 inference(rewrite,[status(thm)],[])).
% 3.69/2.60 tff(4,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')).
% 3.69/2.60 tff(5,plain,
% 3.69/2.60 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.69/2.60 tff(6,plain,(
% 3.69/2.60 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 3.69/2.60 inference(skolemize,[status(sab)],[5])).
% 3.69/2.60 tff(7,plain,
% 3.69/2.60 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.69/2.60 tff(8,plain,
% 3.69/2.60 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))))),
% 3.69/2.60 inference(quant_inst,[status(thm)],[])).
% 3.69/2.60 tff(9,plain,
% 3.69/2.60 (addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))),
% 3.69/2.60 inference(unit_resolution,[status(thm)],[8, 7])).
% 3.69/2.60 tff(10,plain,
% 3.69/2.60 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 3.69/2.60 inference(bind,[status(th)],[])).
% 3.69/2.60 tff(11,plain,
% 3.69/2.60 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.69/2.60 inference(quant_intro,[status(thm)],[10])).
% 3.69/2.60 tff(12,plain,
% 3.69/2.60 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.69/2.60 inference(rewrite,[status(thm)],[])).
% 3.69/2.60 tff(13,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 3.69/2.60 tff(14,plain,
% 3.69/2.60 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[13, 12])).
% 3.69/2.60 tff(15,plain,(
% 3.69/2.60 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.69/2.60 inference(skolemize,[status(sab)],[14])).
% 3.69/2.60 tff(16,plain,
% 3.69/2.60 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[15, 11])).
% 3.69/2.60 tff(17,plain,
% 3.69/2.60 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))))),
% 3.69/2.60 inference(quant_inst,[status(thm)],[])).
% 3.69/2.60 tff(18,plain,
% 3.69/2.60 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1)))),
% 3.69/2.60 inference(unit_resolution,[status(thm)],[17, 16])).
% 3.69/2.60 tff(19,plain,
% 3.69/2.60 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.69/2.60 inference(symmetry,[status(thm)],[18])).
% 3.69/2.60 tff(20,plain,
% 3.69/2.60 (addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.69/2.60 inference(monotonicity,[status(thm)],[19])).
% 3.69/2.60 tff(21,plain,
% 3.69/2.60 (addition(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))))),
% 3.69/2.60 inference(symmetry,[status(thm)],[20])).
% 3.69/2.60 tff(22,plain,
% 3.69/2.60 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.69/2.60 inference(quant_inst,[status(thm)],[])).
% 3.69/2.60 tff(23,plain,
% 3.69/2.60 (addition(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.69/2.60 inference(unit_resolution,[status(thm)],[22, 7])).
% 3.69/2.60 tff(24,plain,
% 3.69/2.60 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.69/2.60 inference(symmetry,[status(thm)],[23])).
% 3.69/2.60 tff(25,plain,
% 3.69/2.60 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, c(X0!2)) = addition(c(X0!2), X0!2))),
% 3.69/2.60 inference(quant_inst,[status(thm)],[])).
% 3.69/2.60 tff(26,plain,
% 3.69/2.60 (addition(X0!2, c(X0!2)) = addition(c(X0!2), X0!2)),
% 3.69/2.60 inference(unit_resolution,[status(thm)],[25, 16])).
% 3.69/2.60 tff(27,plain,
% 3.69/2.60 (addition(c(X0!2), X0!2) = addition(X0!2, c(X0!2))),
% 3.69/2.60 inference(symmetry,[status(thm)],[26])).
% 3.69/2.60 tff(28,plain,
% 3.69/2.60 (^[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))))))),
% 3.69/2.60 inference(bind,[status(th)],[])).
% 3.69/2.60 tff(29,plain,
% 3.69/2.60 (![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)))))),
% 3.69/2.60 inference(quant_intro,[status(thm)],[28])).
% 3.69/2.60 tff(30,plain,
% 3.69/2.60 (^[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))))))),
% 3.69/2.60 inference(bind,[status(th)],[])).
% 3.69/2.60 tff(31,plain,
% 3.69/2.60 (![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)))))),
% 3.69/2.60 inference(quant_intro,[status(thm)],[30])).
% 3.69/2.60 tff(32,plain,
% 3.69/2.60 (![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)))),
% 3.69/2.60 inference(rewrite,[status(thm)],[])).
% 3.69/2.60 tff(33,plain,
% 3.69/2.60 (^[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))))),
% 3.69/2.60 inference(bind,[status(th)],[])).
% 3.69/2.60 tff(34,plain,
% 3.69/2.60 (![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)))),
% 3.69/2.60 inference(quant_intro,[status(thm)],[33])).
% 3.69/2.60 tff(35,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')).
% 3.69/2.60 tff(36,plain,
% 3.69/2.60 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[35, 34])).
% 3.69/2.60 tff(37,plain,
% 3.69/2.60 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[36, 32])).
% 3.69/2.60 tff(38,plain,(
% 3.69/2.60 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 3.69/2.60 inference(skolemize,[status(sab)],[37])).
% 3.69/2.60 tff(39,plain,
% 3.69/2.60 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[38, 31])).
% 3.69/2.60 tff(40,plain,
% 3.69/2.60 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[39, 29])).
% 3.69/2.60 tff(41,plain,
% 3.69/2.60 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, c(X0!2)) <=> (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, c(X0!2)) <=> (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))))))),
% 3.69/2.60 inference(rewrite,[status(thm)],[])).
% 3.69/2.60 tff(42,plain,
% 3.69/2.60 ((complement(X0!2, c(X0!2)) <=> (~((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one))))) <=> (complement(X0!2, c(X0!2)) <=> (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one)))))),
% 3.69/2.60 inference(rewrite,[status(thm)],[])).
% 3.69/2.60 tff(43,plain,
% 3.69/2.60 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, c(X0!2)) <=> (~((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, c(X0!2)) <=> (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))))))),
% 3.69/2.60 inference(monotonicity,[status(thm)],[42])).
% 3.69/2.60 tff(44,plain,
% 3.69/2.60 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, c(X0!2)) <=> (~((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, c(X0!2)) <=> (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))))))),
% 3.69/2.60 inference(transitivity,[status(thm)],[43, 41])).
% 3.69/2.60 tff(45,plain,
% 3.69/2.60 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, c(X0!2)) <=> (~((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one)))))),
% 3.69/2.60 inference(quant_inst,[status(thm)],[])).
% 3.69/2.60 tff(46,plain,
% 3.69/2.60 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, c(X0!2)) <=> (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one)))))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[45, 44])).
% 3.69/2.60 tff(47,plain,
% 3.69/2.60 (complement(X0!2, c(X0!2)) <=> (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))))),
% 3.69/2.60 inference(unit_resolution,[status(thm)],[46, 40])).
% 3.69/2.60 tff(48,plain,
% 3.69/2.60 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1))))))),
% 3.69/2.60 inference(rewrite,[status(thm)],[])).
% 3.69/2.60 tff(49,plain,
% 3.69/2.60 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1))))))),
% 3.69/2.60 inference(rewrite,[status(thm)],[])).
% 3.69/2.60 tff(50,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 3.69/2.60 tff(51,plain,
% 3.69/2.60 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[50, 49])).
% 3.69/2.60 tff(52,plain,
% 3.69/2.60 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[51, 48])).
% 3.69/2.60 tff(53,plain,
% 3.69/2.60 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[52, 48])).
% 3.69/2.60 tff(54,plain,
% 3.69/2.60 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[53, 48])).
% 3.69/2.60 tff(55,plain,
% 3.69/2.60 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[54, 48])).
% 3.69/2.60 tff(56,plain,
% 3.69/2.60 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[55, 48])).
% 3.69/2.60 tff(57,plain,
% 3.69/2.60 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[56, 48])).
% 3.69/2.60 tff(58,plain,(
% 3.69/2.60 ~((~(test(X1!1) & test(X0!2))) | (one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 3.69/2.60 inference(skolemize,[status(sab)],[57])).
% 3.69/2.60 tff(59,plain,
% 3.69/2.60 (test(X1!1) & test(X0!2)),
% 3.69/2.60 inference(or_elim,[status(thm)],[58])).
% 3.69/2.60 tff(60,plain,
% 3.69/2.60 (test(X0!2)),
% 3.69/2.60 inference(and_elim,[status(thm)],[59])).
% 3.69/2.60 tff(61,plain,
% 3.69/2.60 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 3.69/2.60 inference(bind,[status(th)],[])).
% 3.69/2.60 tff(62,plain,
% 3.69/2.60 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.69/2.60 inference(quant_intro,[status(thm)],[61])).
% 3.69/2.60 tff(63,plain,
% 3.69/2.60 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.69/2.60 inference(rewrite,[status(thm)],[])).
% 3.69/2.60 tff(64,plain,
% 3.69/2.60 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 3.69/2.60 inference(bind,[status(th)],[])).
% 3.69/2.60 tff(65,plain,
% 3.69/2.60 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.69/2.60 inference(quant_intro,[status(thm)],[64])).
% 3.69/2.60 tff(66,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_3')).
% 3.69/2.60 tff(67,plain,
% 3.69/2.60 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[66, 65])).
% 3.69/2.60 tff(68,plain,
% 3.69/2.60 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[67, 63])).
% 3.69/2.60 tff(69,plain,(
% 3.69/2.60 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.69/2.60 inference(skolemize,[status(sab)],[68])).
% 3.69/2.60 tff(70,plain,
% 3.69/2.60 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.69/2.60 inference(modus_ponens,[status(thm)],[69, 62])).
% 3.69/2.60 tff(71,plain,
% 3.69/2.60 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | complement(X0!2, c(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | complement(X0!2, c(X0!2)))),
% 3.69/2.60 inference(rewrite,[status(thm)],[])).
% 3.69/2.60 tff(72,plain,
% 3.69/2.60 (((~test(X0!2)) | ((c(X0!2) = c(X0!2)) <=> complement(X0!2, c(X0!2)))) <=> ((~test(X0!2)) | complement(X0!2, c(X0!2)))),
% 3.69/2.60 inference(rewrite,[status(thm)],[])).
% 3.69/2.60 tff(73,plain,
% 3.69/2.60 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = c(X0!2)) <=> complement(X0!2, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | complement(X0!2, c(X0!2))))),
% 3.69/2.60 inference(monotonicity,[status(thm)],[72])).
% 3.69/2.61 tff(74,plain,
% 3.69/2.61 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = c(X0!2)) <=> complement(X0!2, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | complement(X0!2, c(X0!2)))),
% 3.69/2.61 inference(transitivity,[status(thm)],[73, 71])).
% 3.69/2.61 tff(75,plain,
% 3.69/2.61 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = c(X0!2)) <=> complement(X0!2, c(X0!2))))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(76,plain,
% 3.69/2.61 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | complement(X0!2, c(X0!2))),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[75, 74])).
% 3.69/2.61 tff(77,plain,
% 3.69/2.61 (complement(X0!2, c(X0!2))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[76, 70, 60])).
% 3.69/2.61 tff(78,plain,
% 3.69/2.61 ((~(complement(X0!2, c(X0!2)) <=> (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one)))))) | (~complement(X0!2, c(X0!2))) | (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))))),
% 3.69/2.61 inference(tautology,[status(thm)],[])).
% 3.69/2.61 tff(79,plain,
% 3.69/2.61 (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one)))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[78, 77, 47])).
% 3.69/2.61 tff(80,plain,
% 3.69/2.61 (((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) | (addition(c(X0!2), X0!2) = one)),
% 3.69/2.61 inference(tautology,[status(thm)],[])).
% 3.69/2.61 tff(81,plain,
% 3.69/2.61 (addition(c(X0!2), X0!2) = one),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[80, 79])).
% 3.69/2.61 tff(82,plain,
% 3.69/2.61 (one = addition(c(X0!2), X0!2)),
% 3.69/2.61 inference(symmetry,[status(thm)],[81])).
% 3.69/2.61 tff(83,plain,
% 3.69/2.61 (one = addition(X0!2, c(X0!2))),
% 3.69/2.61 inference(transitivity,[status(thm)],[82, 27])).
% 3.69/2.61 tff(84,plain,
% 3.69/2.61 (multiplication(one, X1!1) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 3.69/2.61 inference(monotonicity,[status(thm)],[83])).
% 3.69/2.61 tff(85,plain,
% 3.69/2.61 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 3.69/2.61 inference(bind,[status(th)],[])).
% 3.69/2.61 tff(86,plain,
% 3.69/2.61 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 3.69/2.61 inference(quant_intro,[status(thm)],[85])).
% 3.69/2.61 tff(87,plain,
% 3.69/2.61 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 3.69/2.61 inference(rewrite,[status(thm)],[])).
% 3.69/2.61 tff(88,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 3.69/2.61 tff(89,plain,
% 3.69/2.61 (![A: $i] : (multiplication(one, A) = A)),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[88, 87])).
% 3.69/2.61 tff(90,plain,(
% 3.69/2.61 ![A: $i] : (multiplication(one, A) = A)),
% 3.69/2.61 inference(skolemize,[status(sab)],[89])).
% 3.69/2.61 tff(91,plain,
% 3.69/2.61 (![A: $i] : (multiplication(one, A) = A)),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[90, 86])).
% 3.69/2.61 tff(92,plain,
% 3.69/2.61 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!1) = X1!1)),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(93,plain,
% 3.69/2.61 (multiplication(one, X1!1) = X1!1),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[92, 91])).
% 3.69/2.61 tff(94,plain,
% 3.69/2.61 (X1!1 = multiplication(one, X1!1)),
% 3.69/2.61 inference(symmetry,[status(thm)],[93])).
% 3.69/2.61 tff(95,plain,
% 3.69/2.61 (X1!1 = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 3.69/2.61 inference(transitivity,[status(thm)],[94, 84])).
% 3.69/2.61 tff(96,plain,
% 3.69/2.61 (c(X1!1) = c(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 3.69/2.61 inference(monotonicity,[status(thm)],[95])).
% 3.69/2.61 tff(97,plain,
% 3.69/2.61 (c(multiplication(addition(X0!2, c(X0!2)), X1!1)) = c(X1!1)),
% 3.69/2.61 inference(symmetry,[status(thm)],[96])).
% 3.69/2.61 tff(98,plain,
% 3.69/2.61 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 3.69/2.61 inference(bind,[status(th)],[])).
% 3.69/2.61 tff(99,plain,
% 3.69/2.61 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 3.69/2.61 inference(quant_intro,[status(thm)],[98])).
% 3.69/2.61 tff(100,plain,
% 3.69/2.61 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 3.69/2.61 inference(rewrite,[status(thm)],[])).
% 3.69/2.61 tff(101,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 3.69/2.61 tff(102,plain,
% 3.69/2.61 (![A: $i] : (multiplication(A, one) = A)),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[101, 100])).
% 3.69/2.61 tff(103,plain,(
% 3.69/2.61 ![A: $i] : (multiplication(A, one) = A)),
% 3.69/2.61 inference(skolemize,[status(sab)],[102])).
% 3.69/2.61 tff(104,plain,
% 3.69/2.61 (![A: $i] : (multiplication(A, one) = A)),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[103, 99])).
% 3.69/2.61 tff(105,plain,
% 3.69/2.61 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one) = c(multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(106,plain,
% 3.69/2.61 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one) = c(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[105, 104])).
% 3.69/2.61 tff(107,plain,
% 3.69/2.61 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one) = multiplication(c(X1!1), addition(X0!2, c(X0!2)))),
% 3.69/2.61 inference(monotonicity,[status(thm)],[97, 83])).
% 3.69/2.61 tff(108,plain,
% 3.69/2.61 (multiplication(c(X1!1), addition(X0!2, c(X0!2))) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one)),
% 3.69/2.61 inference(symmetry,[status(thm)],[107])).
% 3.69/2.61 tff(109,plain,
% 3.69/2.61 (^[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))))),
% 3.69/2.61 inference(bind,[status(th)],[])).
% 3.69/2.61 tff(110,plain,
% 3.69/2.61 (![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)))),
% 3.69/2.61 inference(quant_intro,[status(thm)],[109])).
% 3.69/2.61 tff(111,plain,
% 3.69/2.61 (![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)))),
% 3.69/2.61 inference(rewrite,[status(thm)],[])).
% 3.69/2.61 tff(112,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 3.69/2.61 tff(113,plain,
% 3.69/2.61 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[112, 111])).
% 3.69/2.61 tff(114,plain,(
% 3.69/2.61 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 3.69/2.61 inference(skolemize,[status(sab)],[113])).
% 3.69/2.61 tff(115,plain,
% 3.69/2.61 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[114, 110])).
% 3.69/2.61 tff(116,plain,
% 3.69/2.61 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(X1!1), addition(X0!2, c(X0!2))) = addition(multiplication(c(X1!1), X0!2), multiplication(c(X1!1), c(X0!2))))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(117,plain,
% 3.69/2.61 (multiplication(c(X1!1), addition(X0!2, c(X0!2))) = addition(multiplication(c(X1!1), X0!2), multiplication(c(X1!1), c(X0!2)))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[116, 115])).
% 3.69/2.61 tff(118,plain,
% 3.69/2.61 (addition(multiplication(c(X1!1), X0!2), multiplication(c(X1!1), c(X0!2))) = multiplication(c(X1!1), addition(X0!2, c(X0!2)))),
% 3.69/2.61 inference(symmetry,[status(thm)],[117])).
% 3.69/2.61 tff(119,plain,
% 3.69/2.61 (test(X1!1)),
% 3.69/2.61 inference(and_elim,[status(thm)],[59])).
% 3.69/2.61 tff(120,plain,
% 3.69/2.61 (^[X0: $i, X1: $i] : refl(((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))))),
% 3.69/2.61 inference(bind,[status(th)],[])).
% 3.69/2.61 tff(121,plain,
% 3.69/2.61 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 3.69/2.61 inference(quant_intro,[status(thm)],[120])).
% 3.69/2.61 tff(122,plain,
% 3.69/2.61 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((test(X0) & test(X1)) <=> (~((~test(X1)) | (~test(X0))))), ((~(test(X0) & test(X1))) <=> (~(~((~test(X1)) | (~test(X0))))))), rewrite((~(~((~test(X1)) | (~test(X0))))) <=> ((~test(X1)) | (~test(X0)))), ((~(test(X0) & test(X1))) <=> ((~test(X1)) | (~test(X0))))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> (((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))), rewrite((((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))))),
% 3.69/2.61 inference(bind,[status(th)],[])).
% 3.69/2.61 tff(123,plain,
% 3.69/2.61 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 3.69/2.61 inference(quant_intro,[status(thm)],[122])).
% 3.69/2.61 tff(124,plain,
% 3.69/2.61 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 3.69/2.61 inference(rewrite,[status(thm)],[])).
% 3.69/2.61 tff(125,plain,
% 3.69/2.61 (^[X0: $i, X1: $i] : rewrite(((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))),
% 3.69/2.61 inference(bind,[status(th)],[])).
% 3.69/2.61 tff(126,plain,
% 3.69/2.61 (![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 3.69/2.61 inference(quant_intro,[status(thm)],[125])).
% 3.69/2.61 tff(127,axiom,(![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax','test_deMorgan1')).
% 3.69/2.61 tff(128,plain,
% 3.69/2.61 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[127, 126])).
% 3.69/2.61 tff(129,plain,
% 3.69/2.61 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[128, 124])).
% 3.69/2.61 tff(130,plain,(
% 3.69/2.61 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 3.69/2.61 inference(skolemize,[status(sab)],[129])).
% 3.69/2.61 tff(131,plain,
% 3.69/2.61 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[130, 123])).
% 3.69/2.61 tff(132,plain,
% 3.69/2.61 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[131, 121])).
% 3.69/2.61 tff(133,plain,
% 3.69/2.61 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))),
% 3.69/2.61 inference(rewrite,[status(thm)],[])).
% 3.69/2.61 tff(134,plain,
% 3.69/2.61 (((~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))) | (~test(X0!2))) <=> ((~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))),
% 3.69/2.61 inference(rewrite,[status(thm)],[])).
% 3.69/2.61 tff(135,plain,
% 3.69/2.61 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1)))))),
% 3.69/2.61 inference(monotonicity,[status(thm)],[134])).
% 3.69/2.61 tff(136,plain,
% 3.69/2.61 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))),
% 3.69/2.61 inference(transitivity,[status(thm)],[135, 133])).
% 3.69/2.61 tff(137,plain,
% 3.69/2.61 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))) | (~test(X0!2)))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(138,plain,
% 3.69/2.61 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1)))),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[137, 136])).
% 3.69/2.61 tff(139,plain,
% 3.69/2.61 (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[138, 132, 119, 60])).
% 3.69/2.61 tff(140,plain,
% 3.69/2.61 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, X1!1) = addition(X1!1, X0!2))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(141,plain,
% 3.69/2.61 (addition(X0!2, X1!1) = addition(X1!1, X0!2)),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[140, 16])).
% 3.69/2.61 tff(142,plain,
% 3.69/2.61 (addition(X1!1, X0!2) = addition(X0!2, X1!1)),
% 3.69/2.61 inference(symmetry,[status(thm)],[141])).
% 3.69/2.61 tff(143,plain,
% 3.69/2.61 (c(addition(X1!1, X0!2)) = c(addition(X0!2, X1!1))),
% 3.69/2.61 inference(monotonicity,[status(thm)],[142])).
% 3.69/2.61 tff(144,plain,
% 3.69/2.61 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))))),
% 3.69/2.61 inference(rewrite,[status(thm)],[])).
% 3.69/2.61 tff(145,plain,
% 3.69/2.61 (((~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))) | (~test(X1!1))) <=> ((~test(X1!1)) | (~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))))),
% 3.69/2.61 inference(rewrite,[status(thm)],[])).
% 3.69/2.61 tff(146,plain,
% 3.69/2.61 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2)))))),
% 3.69/2.61 inference(monotonicity,[status(thm)],[145])).
% 3.69/2.61 tff(147,plain,
% 3.69/2.61 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))))),
% 3.69/2.61 inference(transitivity,[status(thm)],[146, 144])).
% 3.69/2.61 tff(148,plain,
% 3.69/2.61 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))) | (~test(X1!1)))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(149,plain,
% 3.69/2.61 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2)))),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[148, 147])).
% 3.69/2.61 tff(150,plain,
% 3.69/2.61 (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[149, 132, 119, 60])).
% 3.69/2.61 tff(151,plain,
% 3.69/2.61 (multiplication(c(X1!1), c(X0!2)) = c(addition(X1!1, X0!2))),
% 3.69/2.61 inference(symmetry,[status(thm)],[150])).
% 3.69/2.61 tff(152,plain,
% 3.69/2.61 (multiplication(c(X1!1), c(X0!2)) = multiplication(c(X0!2), c(X1!1))),
% 3.69/2.61 inference(transitivity,[status(thm)],[151, 143, 139])).
% 3.69/2.61 tff(153,plain,
% 3.69/2.61 (addition(multiplication(c(X1!1), X0!2), multiplication(c(X1!1), c(X0!2))) = addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1)))),
% 3.69/2.61 inference(monotonicity,[status(thm)],[152])).
% 3.69/2.61 tff(154,plain,
% 3.69/2.61 (addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X1!1), X0!2), multiplication(c(X1!1), c(X0!2)))),
% 3.69/2.61 inference(symmetry,[status(thm)],[153])).
% 3.69/2.61 tff(155,plain,
% 3.69/2.61 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(156,plain,
% 3.69/2.61 (addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[155, 16])).
% 3.69/2.61 tff(157,plain,
% 3.69/2.61 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1)))),
% 3.69/2.61 inference(symmetry,[status(thm)],[156])).
% 3.69/2.61 tff(158,plain,
% 3.69/2.61 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)) = c(X1!1)),
% 3.69/2.61 inference(transitivity,[status(thm)],[157, 154, 118, 108, 106, 97])).
% 3.69/2.61 tff(159,plain,
% 3.69/2.61 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!2) = X0!2)),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(160,plain,
% 3.69/2.61 (multiplication(one, X0!2) = X0!2),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[159, 91])).
% 3.69/2.61 tff(161,plain,
% 3.69/2.61 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!1, c(X1!1)) = addition(c(X1!1), X1!1))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(162,plain,
% 3.69/2.61 (addition(X1!1, c(X1!1)) = addition(c(X1!1), X1!1)),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[161, 16])).
% 3.69/2.61 tff(163,plain,
% 3.69/2.61 (addition(c(X1!1), X1!1) = addition(X1!1, c(X1!1))),
% 3.69/2.61 inference(symmetry,[status(thm)],[162])).
% 3.69/2.61 tff(164,plain,
% 3.69/2.61 (((~![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))))))),
% 3.69/2.61 inference(rewrite,[status(thm)],[])).
% 3.69/2.61 tff(165,plain,
% 3.69/2.61 ((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)))))),
% 3.69/2.61 inference(rewrite,[status(thm)],[])).
% 3.69/2.61 tff(166,plain,
% 3.69/2.61 (((~![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))))))),
% 3.69/2.61 inference(monotonicity,[status(thm)],[165])).
% 3.69/2.61 tff(167,plain,
% 3.69/2.61 (((~![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))))))),
% 3.69/2.61 inference(transitivity,[status(thm)],[166, 164])).
% 3.69/2.61 tff(168,plain,
% 3.69/2.61 ((~![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)))))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(169,plain,
% 3.69/2.61 ((~![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)))))),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[168, 167])).
% 3.69/2.61 tff(170,plain,
% 3.69/2.61 (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))))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[169, 40])).
% 3.69/2.61 tff(171,plain,
% 3.69/2.61 (((~![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)))),
% 3.69/2.61 inference(rewrite,[status(thm)],[])).
% 3.69/2.61 tff(172,plain,
% 3.69/2.61 (((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1)))) <=> ((~test(X1!1)) | complement(X1!1, c(X1!1)))),
% 3.69/2.61 inference(rewrite,[status(thm)],[])).
% 3.69/2.61 tff(173,plain,
% 3.69/2.61 (((~![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))))),
% 3.69/2.61 inference(monotonicity,[status(thm)],[172])).
% 3.69/2.61 tff(174,plain,
% 3.69/2.61 (((~![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)))),
% 3.69/2.61 inference(transitivity,[status(thm)],[173, 171])).
% 3.69/2.61 tff(175,plain,
% 3.69/2.61 ((~![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))))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(176,plain,
% 3.69/2.61 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | complement(X1!1, c(X1!1))),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[175, 174])).
% 3.69/2.61 tff(177,plain,
% 3.69/2.61 (complement(X1!1, c(X1!1))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[176, 70, 119])).
% 3.69/2.61 tff(178,plain,
% 3.69/2.61 ((~(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))))),
% 3.69/2.61 inference(tautology,[status(thm)],[])).
% 3.69/2.61 tff(179,plain,
% 3.69/2.61 (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one)))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[178, 177, 170])).
% 3.69/2.61 tff(180,plain,
% 3.69/2.61 (((~(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)),
% 3.69/2.61 inference(tautology,[status(thm)],[])).
% 3.69/2.61 tff(181,plain,
% 3.69/2.61 (addition(c(X1!1), X1!1) = one),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[180, 179])).
% 3.69/2.61 tff(182,plain,
% 3.69/2.61 (one = addition(c(X1!1), X1!1)),
% 3.69/2.61 inference(symmetry,[status(thm)],[181])).
% 3.69/2.61 tff(183,plain,
% 3.69/2.61 (one = addition(X1!1, c(X1!1))),
% 3.69/2.61 inference(transitivity,[status(thm)],[182, 163])).
% 3.69/2.61 tff(184,plain,
% 3.69/2.61 (multiplication(one, X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 3.69/2.61 inference(monotonicity,[status(thm)],[183])).
% 3.69/2.61 tff(185,plain,
% 3.69/2.61 (multiplication(addition(X1!1, c(X1!1)), X0!2) = multiplication(one, X0!2)),
% 3.69/2.61 inference(symmetry,[status(thm)],[184])).
% 3.69/2.61 tff(186,plain,
% 3.69/2.61 (^[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))))),
% 3.69/2.61 inference(bind,[status(th)],[])).
% 3.69/2.61 tff(187,plain,
% 3.69/2.61 (![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)))),
% 3.69/2.61 inference(quant_intro,[status(thm)],[186])).
% 3.69/2.61 tff(188,plain,
% 3.69/2.61 (![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)))),
% 3.69/2.61 inference(rewrite,[status(thm)],[])).
% 3.69/2.61 tff(189,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')).
% 3.69/2.61 tff(190,plain,
% 3.69/2.61 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[189, 188])).
% 3.69/2.61 tff(191,plain,(
% 3.69/2.61 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 3.69/2.61 inference(skolemize,[status(sab)],[190])).
% 3.69/2.61 tff(192,plain,
% 3.69/2.61 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 3.69/2.61 inference(modus_ponens,[status(thm)],[191, 187])).
% 3.69/2.61 tff(193,plain,
% 3.69/2.61 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X1!1, c(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(194,plain,
% 3.69/2.61 (multiplication(addition(X1!1, c(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[193, 192])).
% 3.69/2.61 tff(195,plain,
% 3.69/2.61 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 3.69/2.61 inference(symmetry,[status(thm)],[194])).
% 3.69/2.61 tff(196,plain,
% 3.69/2.61 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = X0!2),
% 3.69/2.61 inference(transitivity,[status(thm)],[195, 185, 160])).
% 3.69/2.61 tff(197,plain,
% 3.69/2.61 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))) = addition(X0!2, c(X1!1))),
% 3.69/2.61 inference(monotonicity,[status(thm)],[196, 158])).
% 3.69/2.61 tff(198,plain,
% 3.69/2.61 (addition(X0!2, c(X1!1)) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 3.69/2.61 inference(symmetry,[status(thm)],[197])).
% 3.69/2.61 tff(199,plain,
% 3.69/2.61 (c(multiplication(addition(X0!2, c(X0!2)), X1!1)) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one)),
% 3.69/2.61 inference(symmetry,[status(thm)],[106])).
% 3.69/2.61 tff(200,plain,
% 3.69/2.61 (c(X1!1) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))),
% 3.69/2.61 inference(transitivity,[status(thm)],[96, 199, 107, 117, 153, 156])).
% 3.69/2.61 tff(201,plain,
% 3.69/2.61 (X0!2 = multiplication(one, X0!2)),
% 3.69/2.61 inference(symmetry,[status(thm)],[160])).
% 3.69/2.61 tff(202,plain,
% 3.69/2.61 (X0!2 = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 3.69/2.61 inference(transitivity,[status(thm)],[201, 184])).
% 3.69/2.61 tff(203,plain,
% 3.69/2.61 (multiplication(X1!1, X0!2) = multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 3.69/2.61 inference(monotonicity,[status(thm)],[95, 202])).
% 3.69/2.61 tff(204,plain,
% 3.69/2.61 (multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = multiplication(X1!1, X0!2)),
% 3.69/2.61 inference(symmetry,[status(thm)],[203])).
% 3.69/2.61 tff(205,plain,
% 3.69/2.61 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))) = addition(multiplication(X1!1, X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 3.69/2.61 inference(monotonicity,[status(thm)],[204])).
% 3.69/2.61 tff(206,plain,
% 3.69/2.61 (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))) = addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 3.69/2.61 inference(symmetry,[status(thm)],[205])).
% 3.69/2.61 tff(207,plain,
% 3.69/2.61 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(208,plain,
% 3.69/2.61 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[207, 16])).
% 3.69/2.61 tff(209,plain,
% 3.69/2.61 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(210,plain,
% 3.69/2.61 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[209, 7])).
% 3.69/2.61 tff(211,plain,
% 3.69/2.61 ((~![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)))),
% 3.69/2.61 inference(quant_inst,[status(thm)],[])).
% 3.69/2.61 tff(212,plain,
% 3.69/2.61 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 3.69/2.61 inference(unit_resolution,[status(thm)],[211, 16])).
% 3.69/2.61 tff(213,plain,
% 3.69/2.61 (addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 3.69/2.62 inference(symmetry,[status(thm)],[212])).
% 3.69/2.62 tff(214,plain,
% 3.69/2.62 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.69/2.62 inference(monotonicity,[status(thm)],[213])).
% 3.69/2.62 tff(215,plain,
% 3.69/2.62 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 3.69/2.62 inference(symmetry,[status(thm)],[214])).
% 3.69/2.62 tff(216,plain,
% 3.69/2.62 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 3.69/2.62 inference(bind,[status(th)],[])).
% 3.69/2.62 tff(217,plain,
% 3.69/2.62 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 3.69/2.62 inference(quant_intro,[status(thm)],[216])).
% 3.69/2.62 tff(218,plain,
% 3.69/2.62 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 3.69/2.62 inference(rewrite,[status(thm)],[])).
% 3.69/2.62 tff(219,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 3.69/2.62 tff(220,plain,
% 3.69/2.62 (![A: $i] : (addition(A, zero) = A)),
% 3.69/2.62 inference(modus_ponens,[status(thm)],[219, 218])).
% 3.69/2.62 tff(221,plain,(
% 3.69/2.62 ![A: $i] : (addition(A, zero) = A)),
% 3.69/2.62 inference(skolemize,[status(sab)],[220])).
% 3.69/2.62 tff(222,plain,
% 3.69/2.62 (![A: $i] : (addition(A, zero) = A)),
% 3.69/2.62 inference(modus_ponens,[status(thm)],[221, 217])).
% 3.69/2.62 tff(223,plain,
% 3.69/2.62 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(X0!2, X0!2), zero) = multiplication(X0!2, X0!2))),
% 3.69/2.62 inference(quant_inst,[status(thm)],[])).
% 3.69/2.62 tff(224,plain,
% 3.69/2.62 (addition(multiplication(X0!2, X0!2), zero) = multiplication(X0!2, X0!2)),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[223, 222])).
% 3.69/2.62 tff(225,plain,
% 3.69/2.62 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(tptp_fun_X1_0(X0!2), X0!2) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))))),
% 3.69/2.62 inference(quant_inst,[status(thm)],[])).
% 3.69/2.62 tff(226,plain,
% 3.69/2.62 (complement(tptp_fun_X1_0(X0!2), X0!2) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[225, 40])).
% 3.69/2.62 tff(227,plain,
% 3.69/2.62 (^[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)))))))),
% 3.69/2.62 inference(bind,[status(th)],[])).
% 3.69/2.62 tff(228,plain,
% 3.69/2.62 (![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))))))),
% 3.69/2.62 inference(quant_intro,[status(thm)],[227])).
% 3.69/2.62 tff(229,plain,
% 3.69/2.62 (^[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)))))))),
% 3.69/2.62 inference(bind,[status(th)],[])).
% 3.69/2.62 tff(230,plain,
% 3.69/2.62 (![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))))))),
% 3.69/2.62 inference(quant_intro,[status(thm)],[229])).
% 3.69/2.62 tff(231,plain,
% 3.69/2.62 (![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))))))),
% 3.69/2.62 inference(transitivity,[status(thm)],[230, 228])).
% 3.69/2.62 tff(232,plain,
% 3.69/2.62 (^[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))))))))),
% 3.69/2.62 inference(bind,[status(th)],[])).
% 3.69/2.62 tff(233,plain,
% 3.69/2.62 (![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))))))),
% 3.69/2.62 inference(quant_intro,[status(thm)],[232])).
% 3.69/2.62 tff(234,plain,
% 3.69/2.62 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 3.69/2.62 inference(rewrite,[status(thm)],[])).
% 3.69/2.62 tff(235,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 3.69/2.62 tff(236,plain,
% 3.69/2.62 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 3.69/2.62 inference(modus_ponens,[status(thm)],[235, 234])).
% 3.69/2.62 tff(237,plain,(
% 3.69/2.62 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 3.69/2.62 inference(skolemize,[status(sab)],[236])).
% 3.69/2.62 tff(238,plain,
% 3.69/2.62 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 3.69/2.62 inference(modus_ponens,[status(thm)],[237, 233])).
% 3.69/2.62 tff(239,plain,
% 3.69/2.62 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 3.69/2.62 inference(modus_ponens,[status(thm)],[238, 231])).
% 3.69/2.62 tff(240,plain,
% 3.69/2.62 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2))))))),
% 3.69/2.62 inference(quant_inst,[status(thm)],[])).
% 3.69/2.62 tff(241,plain,
% 3.69/2.62 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[240, 239])).
% 3.69/2.62 tff(242,plain,
% 3.69/2.62 (((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2))))) | ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))),
% 3.69/2.62 inference(tautology,[status(thm)],[])).
% 3.69/2.62 tff(243,plain,
% 3.69/2.62 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[242, 241])).
% 3.69/2.62 tff(244,plain,
% 3.69/2.62 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 3.69/2.62 inference(tautology,[status(thm)],[])).
% 3.69/2.62 tff(245,plain,
% 3.69/2.62 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[244, 60])).
% 3.69/2.62 tff(246,plain,
% 3.69/2.62 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[245, 243])).
% 3.69/2.62 tff(247,plain,
% 3.69/2.62 ((~(complement(tptp_fun_X1_0(X0!2), X0!2) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))))) | (~complement(tptp_fun_X1_0(X0!2), X0!2)) | (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))))),
% 3.69/2.62 inference(tautology,[status(thm)],[])).
% 3.69/2.62 tff(248,plain,
% 3.69/2.62 ((~(complement(tptp_fun_X1_0(X0!2), X0!2) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))))) | (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[247, 246])).
% 3.69/2.62 tff(249,plain,
% 3.69/2.62 (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[248, 226])).
% 3.69/2.62 tff(250,plain,
% 3.69/2.62 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)),
% 3.69/2.62 inference(tautology,[status(thm)],[])).
% 3.69/2.62 tff(251,plain,
% 3.69/2.62 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[250, 249])).
% 3.69/2.62 tff(252,plain,
% 3.69/2.62 (zero = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 3.69/2.62 inference(symmetry,[status(thm)],[251])).
% 3.69/2.62 tff(253,plain,
% 3.69/2.62 (addition(multiplication(X0!2, X0!2), zero) = addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2))),
% 3.69/2.62 inference(monotonicity,[status(thm)],[252])).
% 3.69/2.62 tff(254,plain,
% 3.69/2.62 (addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2)) = addition(multiplication(X0!2, X0!2), zero)),
% 3.69/2.62 inference(symmetry,[status(thm)],[253])).
% 3.69/2.62 tff(255,plain,
% 3.69/2.62 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X0!2) = addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2)))),
% 3.69/2.62 inference(quant_inst,[status(thm)],[])).
% 3.69/2.62 tff(256,plain,
% 3.69/2.62 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X0!2) = addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[255, 192])).
% 3.69/2.62 tff(257,plain,
% 3.69/2.62 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (addition(X0!2, tptp_fun_X1_0(X0!2)) = one)),
% 3.69/2.62 inference(tautology,[status(thm)],[])).
% 3.69/2.62 tff(258,plain,
% 3.69/2.62 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[257, 249])).
% 3.69/2.62 tff(259,plain,
% 3.69/2.62 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(X1!1, c(X1!1))),
% 3.69/2.62 inference(transitivity,[status(thm)],[258, 182, 163])).
% 3.69/2.62 tff(260,plain,
% 3.69/2.62 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 3.69/2.62 inference(monotonicity,[status(thm)],[259])).
% 3.69/2.62 tff(261,plain,
% 3.69/2.62 (multiplication(addition(X1!1, c(X1!1)), X0!2) = multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X0!2)),
% 3.69/2.62 inference(symmetry,[status(thm)],[260])).
% 3.69/2.62 tff(262,plain,
% 3.69/2.62 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = multiplication(X0!2, X0!2)),
% 3.69/2.62 inference(transitivity,[status(thm)],[195, 261, 256, 254, 224])).
% 3.69/2.62 tff(263,plain,
% 3.69/2.62 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 3.69/2.62 inference(quant_inst,[status(thm)],[])).
% 3.69/2.62 tff(264,plain,
% 3.69/2.62 (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[263, 16])).
% 3.69/2.62 tff(265,plain,
% 3.69/2.62 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 3.69/2.62 inference(symmetry,[status(thm)],[264])).
% 3.69/2.62 tff(266,plain,
% 3.69/2.62 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X0!2, c(X0!2)), X1!1) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 3.69/2.62 inference(quant_inst,[status(thm)],[])).
% 3.69/2.62 tff(267,plain,
% 3.69/2.62 (multiplication(addition(X0!2, c(X0!2)), X1!1) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[266, 192])).
% 3.69/2.62 tff(268,plain,
% 3.69/2.62 (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 3.69/2.62 inference(symmetry,[status(thm)],[267])).
% 3.69/2.62 tff(269,plain,
% 3.69/2.62 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 3.69/2.62 inference(monotonicity,[status(thm)],[268, 195])).
% 3.69/2.62 tff(270,plain,
% 3.69/2.62 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 3.69/2.62 inference(transitivity,[status(thm)],[269, 265])).
% 3.69/2.62 tff(271,plain,
% 3.69/2.62 (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 3.69/2.62 inference(monotonicity,[status(thm)],[270])).
% 3.69/2.62 tff(272,plain,
% 3.69/2.62 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.69/2.62 inference(symmetry,[status(thm)],[269])).
% 3.69/2.62 tff(273,plain,
% 3.69/2.62 (addition(X0!2, X1!1) = addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 3.69/2.62 inference(monotonicity,[status(thm)],[202, 95])).
% 3.69/2.62 tff(274,plain,
% 3.69/2.62 (addition(X0!2, X1!1) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.69/2.62 inference(transitivity,[status(thm)],[273, 264, 272])).
% 3.69/2.62 tff(275,plain,
% 3.69/2.62 (c(addition(X0!2, X1!1)) = c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.69/2.62 inference(monotonicity,[status(thm)],[274])).
% 3.69/2.62 tff(276,plain,
% 3.69/2.62 (multiplication(c(X0!2), c(X1!1)) = c(addition(X0!2, X1!1))),
% 3.69/2.62 inference(symmetry,[status(thm)],[139])).
% 3.69/2.62 tff(277,plain,
% 3.69/2.62 (multiplication(c(X0!2), c(X1!1)) = c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 3.69/2.62 inference(transitivity,[status(thm)],[276, 275, 271])).
% 3.69/2.62 tff(278,plain,
% 3.69/2.62 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(X0!2, X0!2))),
% 3.69/2.62 inference(monotonicity,[status(thm)],[277, 262])).
% 3.69/2.62 tff(279,plain,
% 3.69/2.62 (addition(c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(X0!2, X0!2)) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.69/2.62 inference(symmetry,[status(thm)],[278])).
% 3.69/2.62 tff(280,plain,
% 3.69/2.62 (complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))) <=> complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1)))),
% 3.69/2.62 inference(monotonicity,[status(thm)],[269])).
% 3.69/2.62 tff(281,plain,
% 3.69/2.62 (complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))),
% 3.69/2.62 inference(symmetry,[status(thm)],[280])).
% 3.69/2.62 tff(282,plain,
% 3.69/2.62 ((~complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1)))) <=> (~complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))))),
% 3.69/2.62 inference(monotonicity,[status(thm)],[281])).
% 3.69/2.62 tff(283,plain,
% 3.69/2.62 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) <=> (~((~(multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)) | (~(multiplication(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one)))))),
% 3.69/2.62 inference(quant_inst,[status(thm)],[])).
% 3.69/2.62 tff(284,plain,
% 3.69/2.62 (complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) <=> (~((~(multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)) | (~(multiplication(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one))))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[283, 40])).
% 3.69/2.62 tff(285,plain,
% 3.69/2.62 ((addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))) = one) <=> (one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 3.69/2.62 inference(commutativity,[status(thm)],[])).
% 3.69/2.62 tff(286,plain,
% 3.69/2.62 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 3.69/2.62 inference(quant_inst,[status(thm)],[])).
% 3.69/2.62 tff(287,plain,
% 3.69/2.62 (addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[286, 16])).
% 3.69/2.62 tff(288,plain,
% 3.69/2.62 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 3.69/2.62 inference(symmetry,[status(thm)],[287])).
% 3.69/2.62 tff(289,plain,
% 3.69/2.62 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 3.69/2.62 inference(monotonicity,[status(thm)],[265])).
% 3.69/2.62 tff(290,plain,
% 3.69/2.62 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 3.69/2.62 inference(transitivity,[status(thm)],[289, 288])).
% 3.69/2.62 tff(291,plain,
% 3.69/2.62 ((addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one) <=> (addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))) = one)),
% 3.69/2.62 inference(monotonicity,[status(thm)],[290])).
% 3.69/2.62 tff(292,plain,
% 3.69/2.62 ((addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one) <=> (one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 3.69/2.62 inference(transitivity,[status(thm)],[291, 285])).
% 3.69/2.62 tff(293,plain,
% 3.69/2.62 ((one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one)),
% 3.69/2.62 inference(symmetry,[status(thm)],[292])).
% 3.69/2.62 tff(294,plain,
% 3.69/2.62 ((~(one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))))) <=> (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one))),
% 3.69/2.62 inference(monotonicity,[status(thm)],[293])).
% 3.69/2.62 tff(295,plain,
% 3.69/2.62 (~(one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 3.69/2.62 inference(or_elim,[status(thm)],[58])).
% 3.69/2.62 tff(296,plain,
% 3.69/2.62 (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one)),
% 3.69/2.62 inference(modus_ponens,[status(thm)],[295, 294])).
% 3.69/2.62 tff(297,plain,
% 3.69/2.62 (((~(multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)) | (~(multiplication(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one)),
% 3.69/2.62 inference(tautology,[status(thm)],[])).
% 3.69/2.62 tff(298,plain,
% 3.69/2.62 ((~(multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)) | (~(multiplication(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[297, 296])).
% 3.69/2.62 tff(299,plain,
% 3.69/2.62 ((~(complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) <=> (~((~(multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)) | (~(multiplication(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one)))))) | (~complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1)))) | (~((~(multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)) | (~(multiplication(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one))))),
% 3.69/2.62 inference(tautology,[status(thm)],[])).
% 3.69/2.62 tff(300,plain,
% 3.69/2.62 (~complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1)))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[299, 298, 284])).
% 3.69/2.62 tff(301,plain,
% 3.69/2.62 (~complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))),
% 3.69/2.62 inference(modus_ponens,[status(thm)],[300, 282])).
% 3.69/2.62 tff(302,plain,
% 3.69/2.62 (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = c(addition(X0!2, X1!1))),
% 3.69/2.62 inference(symmetry,[status(thm)],[275])).
% 3.69/2.62 tff(303,plain,
% 3.69/2.62 (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))),
% 3.69/2.62 inference(transitivity,[status(thm)],[302, 139])).
% 3.69/2.62 tff(304,plain,
% 3.69/2.62 ((~((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))))) | (~(c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1)))) | complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))),
% 3.69/2.62 inference(tautology,[status(thm)],[])).
% 3.69/2.62 tff(305,plain,
% 3.69/2.62 (~((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[304, 303, 301])).
% 3.69/2.62 tff(306,plain,
% 3.69/2.62 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | ((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | ((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))))),
% 3.69/2.62 inference(rewrite,[status(thm)],[])).
% 3.69/2.62 tff(307,plain,
% 3.69/2.62 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | ((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))))),
% 3.69/2.62 inference(quant_inst,[status(thm)],[])).
% 3.69/2.62 tff(308,plain,
% 3.69/2.62 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | ((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))))),
% 3.69/2.62 inference(modus_ponens,[status(thm)],[307, 306])).
% 3.69/2.62 tff(309,plain,
% 3.69/2.62 ((~test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | ((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[308, 70])).
% 3.69/2.62 tff(310,plain,
% 3.69/2.62 (~test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.69/2.62 inference(unit_resolution,[status(thm)],[309, 305])).
% 3.69/2.62 tff(311,plain,
% 3.69/2.62 (^[X0: $i] : refl((test(X0) | (c(X0) = zero)) <=> (test(X0) | (c(X0) = zero)))),
% 3.69/2.62 inference(bind,[status(th)],[])).
% 3.69/2.62 tff(312,plain,
% 3.69/2.62 (![X0: $i] : (test(X0) | (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 3.69/2.62 inference(quant_intro,[status(thm)],[311])).
% 3.69/2.62 tff(313,plain,
% 3.69/2.62 (![X0: $i] : (test(X0) | (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 3.69/2.62 inference(rewrite,[status(thm)],[])).
% 3.69/2.62 tff(314,plain,
% 3.69/2.62 (^[X0: $i] : rewrite(((~test(X0)) => (c(X0) = zero)) <=> (test(X0) | (c(X0) = zero)))),
% 3.69/2.62 inference(bind,[status(th)],[])).
% 3.69/2.62 tff(315,plain,
% 3.69/2.62 (![X0: $i] : ((~test(X0)) => (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 3.69/2.62 inference(quant_intro,[status(thm)],[314])).
% 3.69/2.62 tff(316,axiom,(![X0: $i] : ((~test(X0)) => (c(X0) = zero))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_4')).
% 3.69/2.62 tff(317,plain,
% 3.69/2.62 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 3.69/2.62 inference(modus_ponens,[status(thm)],[316, 315])).
% 3.69/2.63 tff(318,plain,
% 3.69/2.63 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 3.69/2.63 inference(modus_ponens,[status(thm)],[317, 313])).
% 3.69/2.63 tff(319,plain,(
% 3.69/2.63 ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 3.69/2.63 inference(skolemize,[status(sab)],[318])).
% 3.69/2.63 tff(320,plain,
% 3.69/2.63 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 3.69/2.63 inference(modus_ponens,[status(thm)],[319, 312])).
% 3.69/2.63 tff(321,plain,
% 3.69/2.63 (((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = zero))) <=> ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = zero))),
% 3.69/2.63 inference(rewrite,[status(thm)],[])).
% 3.69/2.63 tff(322,plain,
% 3.69/2.63 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = zero))),
% 3.69/2.63 inference(quant_inst,[status(thm)],[])).
% 3.69/2.63 tff(323,plain,
% 3.69/2.63 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = zero)),
% 3.69/2.63 inference(modus_ponens,[status(thm)],[322, 321])).
% 3.69/2.63 tff(324,plain,
% 3.69/2.63 (test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = zero)),
% 3.69/2.63 inference(unit_resolution,[status(thm)],[323, 320])).
% 3.69/2.63 tff(325,plain,
% 3.69/2.63 (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = zero),
% 3.69/2.63 inference(unit_resolution,[status(thm)],[324, 310])).
% 3.69/2.63 tff(326,plain,
% 3.69/2.63 (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.69/2.63 inference(symmetry,[status(thm)],[271])).
% 3.69/2.63 tff(327,plain,
% 3.69/2.63 (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 3.69/2.63 inference(transitivity,[status(thm)],[326, 325, 252])).
% 3.69/2.63 tff(328,plain,
% 3.69/2.63 (addition(c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(X0!2, X0!2)) = addition(multiplication(tptp_fun_X1_0(X0!2), X0!2), multiplication(X0!2, X0!2))),
% 3.69/2.63 inference(monotonicity,[status(thm)],[327])).
% 3.69/2.63 tff(329,plain,
% 3.69/2.63 (addition(multiplication(tptp_fun_X1_0(X0!2), X0!2), multiplication(X0!2, X0!2)) = addition(c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(X0!2, X0!2))),
% 3.69/2.63 inference(symmetry,[status(thm)],[328])).
% 3.69/2.63 tff(330,plain,
% 3.69/2.63 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2) = addition(multiplication(tptp_fun_X1_0(X0!2), X0!2), multiplication(X0!2, X0!2)))),
% 3.69/2.63 inference(quant_inst,[status(thm)],[])).
% 3.69/2.63 tff(331,plain,
% 3.69/2.63 (multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2) = addition(multiplication(tptp_fun_X1_0(X0!2), X0!2), multiplication(X0!2, X0!2))),
% 3.69/2.63 inference(unit_resolution,[status(thm)],[330, 192])).
% 3.69/2.63 tff(332,plain,
% 3.69/2.63 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 3.69/2.63 inference(quant_inst,[status(thm)],[])).
% 3.69/2.63 tff(333,plain,
% 3.69/2.63 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 3.69/2.63 inference(unit_resolution,[status(thm)],[332, 16])).
% 3.69/2.63 tff(334,plain,
% 3.69/2.63 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 3.69/2.63 inference(symmetry,[status(thm)],[333])).
% 3.69/2.63 tff(335,plain,
% 3.69/2.63 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X1!1, c(X1!1))),
% 3.69/2.63 inference(transitivity,[status(thm)],[334, 258, 182, 163])).
% 3.69/2.63 tff(336,plain,
% 3.69/2.63 (multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 3.69/2.63 inference(monotonicity,[status(thm)],[335])).
% 3.69/2.63 tff(337,plain,
% 3.69/2.63 (multiplication(addition(X1!1, c(X1!1)), X0!2) = multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2)),
% 3.69/2.63 inference(symmetry,[status(thm)],[336])).
% 3.69/2.63 tff(338,plain,
% 3.69/2.63 (X0!2 = addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 3.69/2.63 inference(transitivity,[status(thm)],[201, 184, 337, 331, 329, 279, 215, 210, 208, 206])).
% 3.69/2.63 tff(339,plain,
% 3.69/2.63 (addition(X0!2, c(X1!1)) = addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 3.69/2.63 inference(monotonicity,[status(thm)],[338, 200])).
% 3.69/2.63 tff(340,plain,
% 3.69/2.63 (addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))) = addition(X0!2, c(X1!1))),
% 3.69/2.63 inference(symmetry,[status(thm)],[339])).
% 3.69/2.63 tff(341,plain,
% 3.69/2.63 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))))),
% 3.69/2.63 inference(quant_inst,[status(thm)],[])).
% 3.69/2.63 tff(342,plain,
% 3.69/2.63 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 3.69/2.63 inference(unit_resolution,[status(thm)],[341, 7])).
% 3.69/2.63 tff(343,plain,
% 3.69/2.63 (addition(X1!1, c(X1!1)) = addition(X0!2, c(X0!2))),
% 3.69/2.63 inference(transitivity,[status(thm)],[162, 181, 82, 27])).
% 3.69/2.63 tff(344,plain,
% 3.69/2.63 (multiplication(addition(X1!1, c(X1!1)), X1!1) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 3.69/2.63 inference(monotonicity,[status(thm)],[343])).
% 3.69/2.63 tff(345,plain,
% 3.69/2.63 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X1!1, c(X1!1)), X1!1) = addition(multiplication(X1!1, X1!1), multiplication(c(X1!1), X1!1)))),
% 3.69/2.63 inference(quant_inst,[status(thm)],[])).
% 3.69/2.63 tff(346,plain,
% 3.69/2.63 (multiplication(addition(X1!1, c(X1!1)), X1!1) = addition(multiplication(X1!1, X1!1), multiplication(c(X1!1), X1!1))),
% 3.69/2.63 inference(unit_resolution,[status(thm)],[345, 192])).
% 3.69/2.63 tff(347,plain,
% 3.69/2.63 (addition(multiplication(X1!1, X1!1), multiplication(c(X1!1), X1!1)) = multiplication(addition(X1!1, c(X1!1)), X1!1)),
% 3.69/2.63 inference(symmetry,[status(thm)],[346])).
% 3.69/2.63 tff(348,plain,
% 3.69/2.63 (((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) | (multiplication(c(X1!1), X1!1) = zero)),
% 3.69/2.63 inference(tautology,[status(thm)],[])).
% 3.69/2.63 tff(349,plain,
% 3.69/2.63 (multiplication(c(X1!1), X1!1) = zero),
% 3.69/2.63 inference(unit_resolution,[status(thm)],[348, 179])).
% 3.69/2.63 tff(350,plain,
% 3.69/2.63 (zero = multiplication(c(X1!1), X1!1)),
% 3.69/2.63 inference(symmetry,[status(thm)],[349])).
% 3.69/2.63 tff(351,plain,
% 3.69/2.63 (addition(multiplication(X1!1, X1!1), zero) = addition(multiplication(X1!1, X1!1), multiplication(c(X1!1), X1!1))),
% 3.69/2.63 inference(monotonicity,[status(thm)],[350])).
% 3.69/2.63 tff(352,plain,
% 3.69/2.63 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(X1!1, X1!1), zero) = multiplication(X1!1, X1!1))),
% 3.69/2.63 inference(quant_inst,[status(thm)],[])).
% 3.69/2.63 tff(353,plain,
% 3.69/2.63 (addition(multiplication(X1!1, X1!1), zero) = multiplication(X1!1, X1!1)),
% 3.69/2.63 inference(unit_resolution,[status(thm)],[352, 222])).
% 3.69/2.63 tff(354,plain,
% 3.69/2.63 (multiplication(X1!1, X1!1) = addition(multiplication(X1!1, X1!1), zero)),
% 3.69/2.63 inference(symmetry,[status(thm)],[353])).
% 3.69/2.63 tff(355,plain,
% 3.69/2.63 (multiplication(addition(X0!2, c(X0!2)), X1!1) = multiplication(one, X1!1)),
% 3.69/2.63 inference(symmetry,[status(thm)],[84])).
% 3.69/2.63 tff(356,plain,
% 3.69/2.63 (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)) = X1!1),
% 3.69/2.63 inference(transitivity,[status(thm)],[268, 355, 93])).
% 3.69/2.63 tff(357,plain,
% 3.69/2.63 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(X1!1, X1!1)),
% 3.69/2.63 inference(monotonicity,[status(thm)],[356, 356])).
% 3.69/2.63 tff(358,plain,
% 3.69/2.63 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 3.69/2.63 inference(transitivity,[status(thm)],[357, 354, 351, 347, 344])).
% 3.69/2.63 tff(359,plain,
% 3.69/2.63 (c(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = c(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 3.69/2.63 inference(monotonicity,[status(thm)],[358])).
% 3.69/2.63 tff(360,plain,
% 3.69/2.63 (test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) <=> test(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 3.69/2.63 inference(monotonicity,[status(thm)],[268])).
% 3.69/2.63 tff(361,plain,
% 3.69/2.63 (test(multiplication(addition(X0!2, c(X0!2)), X1!1)) <=> test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 3.69/2.63 inference(symmetry,[status(thm)],[360])).
% 3.69/2.63 tff(362,plain,
% 3.69/2.63 (test(X1!1) <=> test(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 3.69/2.63 inference(monotonicity,[status(thm)],[95])).
% 3.69/2.63 tff(363,plain,
% 3.69/2.63 (test(X1!1) <=> test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 3.69/2.63 inference(transitivity,[status(thm)],[362, 361])).
% 3.69/2.63 tff(364,plain,
% 3.69/2.63 (test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 3.69/2.63 inference(modus_ponens,[status(thm)],[119, 363])).
% 3.69/2.63 tff(365,plain,
% 3.69/2.63 (^[X0: $i, X1: $i] : refl(((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))))),
% 3.69/2.63 inference(bind,[status(th)],[])).
% 3.69/2.63 tff(366,plain,
% 3.69/2.63 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 3.69/2.63 inference(quant_intro,[status(thm)],[365])).
% 3.69/2.63 tff(367,plain,
% 3.69/2.63 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((test(X0) & test(X1)) <=> (~((~test(X1)) | (~test(X0))))), ((~(test(X0) & test(X1))) <=> (~(~((~test(X1)) | (~test(X0))))))), rewrite((~(~((~test(X1)) | (~test(X0))))) <=> ((~test(X1)) | (~test(X0)))), ((~(test(X0) & test(X1))) <=> ((~test(X1)) | (~test(X0))))), (((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> (((~test(X1)) | (~test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))))), rewrite((((~test(X1)) | (~test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))), (((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))))),
% 3.69/2.63 inference(bind,[status(th)],[])).
% 3.69/2.63 tff(368,plain,
% 3.69/2.63 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 3.69/2.63 inference(quant_intro,[status(thm)],[367])).
% 3.69/2.63 tff(369,plain,
% 3.69/2.63 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 3.69/2.63 inference(rewrite,[status(thm)],[])).
% 3.69/2.63 tff(370,plain,
% 3.69/2.63 (^[X0: $i, X1: $i] : rewrite(((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))))),
% 3.69/2.63 inference(bind,[status(th)],[])).
% 3.69/2.63 tff(371,plain,
% 3.69/2.63 (![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 3.69/2.63 inference(quant_intro,[status(thm)],[370])).
% 3.69/2.63 tff(372,axiom,(![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax','test_deMorgan2')).
% 3.69/2.63 tff(373,plain,
% 3.69/2.63 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 3.69/2.63 inference(modus_ponens,[status(thm)],[372, 371])).
% 3.69/2.63 tff(374,plain,
% 3.69/2.63 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 3.69/2.63 inference(modus_ponens,[status(thm)],[373, 369])).
% 3.69/2.63 tff(375,plain,(
% 3.69/2.63 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 3.69/2.63 inference(skolemize,[status(sab)],[374])).
% 3.69/2.63 tff(376,plain,
% 3.69/2.63 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 3.69/2.63 inference(modus_ponens,[status(thm)],[375, 368])).
% 3.69/2.63 tff(377,plain,
% 3.69/2.63 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 3.69/2.63 inference(modus_ponens,[status(thm)],[376, 366])).
% 3.69/2.63 tff(378,plain,
% 3.69/2.63 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (c(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (c(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))))),
% 3.69/2.63 inference(rewrite,[status(thm)],[])).
% 3.69/2.63 tff(379,plain,
% 3.69/2.63 (((~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (c(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))) <=> ((~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (c(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))))),
% 3.69/2.63 inference(rewrite,[status(thm)],[])).
% 3.69/2.63 tff(380,plain,
% 3.69/2.63 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (c(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (c(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))))))),
% 3.69/2.63 inference(monotonicity,[status(thm)],[379])).
% 3.69/2.63 tff(381,plain,
% 3.69/2.63 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (c(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (c(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))))),
% 3.69/2.63 inference(transitivity,[status(thm)],[380, 378])).
% 3.69/2.63 tff(382,plain,
% 3.69/2.63 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (c(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))))),
% 3.69/2.63 inference(quant_inst,[status(thm)],[])).
% 3.69/2.63 tff(383,plain,
% 3.69/2.63 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (c(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))))),
% 3.69/2.63 inference(modus_ponens,[status(thm)],[382, 381])).
% 3.69/2.63 tff(384,plain,
% 3.69/2.63 (c(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 3.69/2.63 inference(unit_resolution,[status(thm)],[383, 377, 364])).
% 3.69/2.63 tff(385,plain,
% 3.69/2.63 (addition(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = c(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 3.69/2.63 inference(symmetry,[status(thm)],[384])).
% 3.69/2.63 tff(386,plain,
% 3.69/2.63 (c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = c(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 3.69/2.63 inference(monotonicity,[status(thm)],[268])).
% 3.69/2.63 tff(387,plain,
% 3.69/2.63 (c(multiplication(addition(X0!2, c(X0!2)), X1!1)) = c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 3.69/2.63 inference(symmetry,[status(thm)],[386])).
% 3.69/2.63 tff(388,plain,
% 3.69/2.63 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)) = c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 3.69/2.63 inference(transitivity,[status(thm)],[157, 154, 118, 108, 106, 387])).
% 3.69/2.63 tff(389,plain,
% 3.69/2.63 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))) = addition(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 3.69/2.63 inference(monotonicity,[status(thm)],[388, 388])).
% 3.69/2.63 tff(390,plain,
% 3.69/2.63 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))),
% 3.69/2.63 inference(transitivity,[status(thm)],[389, 385, 359, 199, 107, 117, 153, 156])).
% 3.69/2.63 tff(391,plain,
% 3.69/2.63 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))) = addition(multiplication(X1!1, X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 3.69/2.63 inference(monotonicity,[status(thm)],[204, 390])).
% 3.69/2.63 tff(392,plain,
% 3.69/2.63 (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))) = addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))))),
% 3.69/2.63 inference(symmetry,[status(thm)],[391])).
% 3.69/2.63 tff(393,plain,
% 3.69/2.63 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 3.69/2.63 inference(transitivity,[status(thm)],[195, 337, 331, 329, 279, 215, 210, 208, 392, 342, 340, 198])).
% 3.69/2.63 tff(394,plain,
% 3.69/2.63 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 3.69/2.63 inference(monotonicity,[status(thm)],[393])).
% 3.69/2.63 tff(395,plain,
% 3.69/2.63 (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 3.69/2.63 inference(symmetry,[status(thm)],[394])).
% 3.69/2.63 tff(396,plain,
% 3.69/2.63 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 3.69/2.63 inference(quant_inst,[status(thm)],[])).
% 3.69/2.63 tff(397,plain,
% 3.69/2.63 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 3.69/2.63 inference(unit_resolution,[status(thm)],[396, 7])).
% 3.69/2.63 tff(398,plain,
% 3.69/2.63 (addition(multiplication(tptp_fun_X1_0(X0!2), X0!2), multiplication(X0!2, X0!2)) = multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2)),
% 3.69/2.63 inference(symmetry,[status(thm)],[331])).
% 3.69/2.63 tff(399,plain,
% 3.69/2.63 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 3.69/2.63 inference(symmetry,[status(thm)],[210])).
% 3.69/2.63 tff(400,plain,
% 3.69/2.63 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2))),
% 3.69/2.63 inference(monotonicity,[status(thm)],[204])).
% 3.69/2.63 tff(401,plain,
% 3.69/2.63 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 3.69/2.63 inference(transitivity,[status(thm)],[400, 399, 214, 278, 328, 398, 336, 194])).
% 3.69/2.63 tff(402,plain,
% 3.69/2.63 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.69/2.63 inference(monotonicity,[status(thm)],[401])).
% 3.69/2.63 tff(403,plain,
% 3.69/2.63 (addition(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(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 3.73/2.64 inference(symmetry,[status(thm)],[402])).
% 3.73/2.64 tff(404,plain,
% 3.73/2.64 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 3.73/2.64 inference(bind,[status(th)],[])).
% 3.73/2.64 tff(405,plain,
% 3.73/2.64 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 3.73/2.64 inference(quant_intro,[status(thm)],[404])).
% 3.73/2.64 tff(406,plain,
% 3.73/2.64 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 3.73/2.64 inference(rewrite,[status(thm)],[])).
% 3.73/2.64 tff(407,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 3.73/2.64 tff(408,plain,
% 3.73/2.64 (![A: $i] : (addition(A, A) = A)),
% 3.73/2.64 inference(modus_ponens,[status(thm)],[407, 406])).
% 3.73/2.64 tff(409,plain,(
% 3.73/2.64 ![A: $i] : (addition(A, A) = A)),
% 3.73/2.64 inference(skolemize,[status(sab)],[408])).
% 3.73/2.64 tff(410,plain,
% 3.73/2.64 (![A: $i] : (addition(A, A) = A)),
% 3.73/2.64 inference(modus_ponens,[status(thm)],[409, 405])).
% 3.73/2.64 tff(411,plain,
% 3.73/2.64 ((~![A: $i] : (addition(A, A) = A)) | (addition(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(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(412,plain,
% 3.73/2.64 (addition(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(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[411, 410])).
% 3.73/2.64 tff(413,plain,
% 3.73/2.64 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.73/2.64 inference(symmetry,[status(thm)],[412])).
% 3.73/2.64 tff(414,plain,
% 3.73/2.64 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 3.73/2.64 inference(transitivity,[status(thm)],[413, 403, 397, 395])).
% 3.73/2.64 tff(415,plain,
% 3.73/2.64 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 3.73/2.64 inference(monotonicity,[status(thm)],[414])).
% 3.73/2.64 tff(416,plain,
% 3.73/2.64 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.73/2.64 inference(symmetry,[status(thm)],[415])).
% 3.73/2.64 tff(417,plain,
% 3.73/2.64 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(418,plain,
% 3.73/2.64 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[417, 7])).
% 3.73/2.64 tff(419,plain,
% 3.73/2.64 (addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 3.73/2.64 inference(symmetry,[status(thm)],[418])).
% 3.73/2.64 tff(420,plain,
% 3.73/2.64 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X1!1), X0!2)))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(421,plain,
% 3.73/2.64 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X1!1), X0!2))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[420, 7])).
% 3.73/2.64 tff(422,plain,
% 3.73/2.64 (((~![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))))),
% 3.73/2.64 inference(rewrite,[status(thm)],[])).
% 3.73/2.64 tff(423,plain,
% 3.73/2.64 ((~![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))))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(424,plain,
% 3.73/2.64 ((~![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)))),
% 3.73/2.64 inference(modus_ponens,[status(thm)],[423, 422])).
% 3.73/2.64 tff(425,plain,
% 3.73/2.64 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[424, 70, 119])).
% 3.73/2.64 tff(426,plain,
% 3.73/2.64 (((~![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))))))),
% 3.73/2.64 inference(rewrite,[status(thm)],[])).
% 3.73/2.64 tff(427,plain,
% 3.73/2.64 ((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)))))),
% 3.73/2.64 inference(rewrite,[status(thm)],[])).
% 3.73/2.64 tff(428,plain,
% 3.73/2.64 (((~![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))))))),
% 3.73/2.64 inference(monotonicity,[status(thm)],[427])).
% 3.73/2.64 tff(429,plain,
% 3.73/2.64 (((~![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))))))),
% 3.73/2.64 inference(transitivity,[status(thm)],[428, 426])).
% 3.73/2.64 tff(430,plain,
% 3.73/2.64 ((~![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)))))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(431,plain,
% 3.73/2.64 ((~![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)))))),
% 3.73/2.64 inference(modus_ponens,[status(thm)],[430, 429])).
% 3.73/2.64 tff(432,plain,
% 3.73/2.64 (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))))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[431, 40])).
% 3.73/2.64 tff(433,plain,
% 3.73/2.64 ((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))),
% 3.73/2.64 inference(commutativity,[status(thm)],[])).
% 3.73/2.64 tff(434,plain,
% 3.73/2.64 ((~![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)))))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(435,plain,
% 3.73/2.64 (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))))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[434, 40])).
% 3.73/2.64 tff(436,plain,
% 3.73/2.64 ((~![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))))))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(437,plain,
% 3.73/2.64 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[436, 239])).
% 3.73/2.64 tff(438,plain,
% 3.73/2.64 (((~((~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))),
% 3.73/2.64 inference(tautology,[status(thm)],[])).
% 3.73/2.64 tff(439,plain,
% 3.73/2.64 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[438, 437])).
% 3.73/2.64 tff(440,plain,
% 3.73/2.64 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 3.73/2.64 inference(tautology,[status(thm)],[])).
% 3.73/2.64 tff(441,plain,
% 3.73/2.64 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[440, 119])).
% 3.73/2.64 tff(442,plain,
% 3.73/2.64 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[441, 439])).
% 3.73/2.64 tff(443,plain,
% 3.73/2.64 ((~(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))))),
% 3.73/2.64 inference(tautology,[status(thm)],[])).
% 3.73/2.64 tff(444,plain,
% 3.73/2.64 ((~(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))))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[443, 442])).
% 3.73/2.64 tff(445,plain,
% 3.73/2.64 (~((~(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)))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[444, 435])).
% 3.73/2.64 tff(446,plain,
% 3.73/2.64 (((~(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)),
% 3.73/2.64 inference(tautology,[status(thm)],[])).
% 3.73/2.64 tff(447,plain,
% 3.73/2.64 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[446, 445])).
% 3.73/2.64 tff(448,plain,
% 3.73/2.64 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 3.73/2.64 inference(symmetry,[status(thm)],[447])).
% 3.73/2.64 tff(449,plain,
% 3.73/2.64 ((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)))),
% 3.73/2.64 inference(monotonicity,[status(thm)],[448])).
% 3.73/2.64 tff(450,plain,
% 3.73/2.64 ((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))),
% 3.73/2.64 inference(transitivity,[status(thm)],[449, 433])).
% 3.73/2.64 tff(451,plain,
% 3.73/2.64 ((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)),
% 3.73/2.64 inference(symmetry,[status(thm)],[450])).
% 3.73/2.64 tff(452,plain,
% 3.73/2.64 ((~![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))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(453,plain,
% 3.73/2.64 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[452, 16])).
% 3.73/2.64 tff(454,plain,
% 3.73/2.64 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 3.73/2.64 inference(modus_ponens,[status(thm)],[453, 451])).
% 3.73/2.64 tff(455,plain,
% 3.73/2.64 (((~(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)),
% 3.73/2.64 inference(tautology,[status(thm)],[])).
% 3.73/2.64 tff(456,plain,
% 3.73/2.64 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[455, 445])).
% 3.73/2.64 tff(457,plain,
% 3.73/2.64 (((~(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)),
% 3.73/2.64 inference(tautology,[status(thm)],[])).
% 3.73/2.64 tff(458,plain,
% 3.73/2.64 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[457, 445])).
% 3.73/2.64 tff(459,plain,
% 3.73/2.64 ((~((~(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))),
% 3.73/2.64 inference(tautology,[status(thm)],[])).
% 3.73/2.64 tff(460,plain,
% 3.73/2.64 ((~((~(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))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[459, 458, 456])).
% 3.73/2.64 tff(461,plain,
% 3.73/2.64 (~((~(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)))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[460, 454])).
% 3.73/2.64 tff(462,plain,
% 3.73/2.64 ((~(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)))),
% 3.73/2.64 inference(tautology,[status(thm)],[])).
% 3.73/2.64 tff(463,plain,
% 3.73/2.64 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[462, 461, 432])).
% 3.73/2.64 tff(464,plain,
% 3.73/2.64 ((~((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)))),
% 3.73/2.64 inference(tautology,[status(thm)],[])).
% 3.73/2.64 tff(465,plain,
% 3.73/2.64 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[464, 463, 425])).
% 3.73/2.64 tff(466,plain,
% 3.73/2.64 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)) = tptp_fun_X1_0(X1!1)),
% 3.73/2.64 inference(transitivity,[status(thm)],[157, 154, 118, 108, 106, 97, 465])).
% 3.73/2.64 tff(467,plain,
% 3.73/2.64 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 3.73/2.64 inference(monotonicity,[status(thm)],[356, 466])).
% 3.73/2.64 tff(468,plain,
% 3.73/2.64 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 3.73/2.64 inference(symmetry,[status(thm)],[467])).
% 3.73/2.64 tff(469,plain,
% 3.73/2.64 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(470,plain,
% 3.73/2.64 (addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[469, 16])).
% 3.73/2.64 tff(471,plain,
% 3.73/2.64 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(X0!2), addition(X1!1, c(X1!1))) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(472,plain,
% 3.73/2.64 (multiplication(c(X0!2), addition(X1!1, c(X1!1))) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[471, 115])).
% 3.73/2.64 tff(473,plain,
% 3.73/2.64 (multiplication(c(X0!2), one) = multiplication(c(X0!2), addition(X1!1, c(X1!1)))),
% 3.73/2.64 inference(monotonicity,[status(thm)],[183])).
% 3.73/2.64 tff(474,plain,
% 3.73/2.64 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(c(X0!2), one) = c(X0!2))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(475,plain,
% 3.73/2.64 (multiplication(c(X0!2), one) = c(X0!2)),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[474, 104])).
% 3.73/2.64 tff(476,plain,
% 3.73/2.64 (c(X0!2) = multiplication(c(X0!2), one)),
% 3.73/2.64 inference(symmetry,[status(thm)],[475])).
% 3.73/2.64 tff(477,plain,
% 3.73/2.64 (c(X0!2) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))),
% 3.73/2.64 inference(transitivity,[status(thm)],[476, 473, 472, 470])).
% 3.73/2.64 tff(478,plain,
% 3.73/2.64 (X0!2 = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 3.73/2.64 inference(transitivity,[status(thm)],[201, 184, 194])).
% 3.73/2.64 tff(479,plain,
% 3.73/2.64 (addition(X0!2, c(X0!2)) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 3.73/2.64 inference(monotonicity,[status(thm)],[478, 477])).
% 3.73/2.64 tff(480,plain,
% 3.73/2.64 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))) = addition(X0!2, c(X0!2))),
% 3.73/2.64 inference(symmetry,[status(thm)],[479])).
% 3.73/2.64 tff(481,plain,
% 3.73/2.64 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))) = addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), X1!1)))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(482,plain,
% 3.73/2.64 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))) = addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), X1!1))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[481, 7])).
% 3.73/2.64 tff(483,plain,
% 3.73/2.64 (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), X1!1)) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 3.73/2.64 inference(symmetry,[status(thm)],[482])).
% 3.73/2.64 tff(484,plain,
% 3.73/2.64 (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), X1!1)) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), X1!1))),
% 3.73/2.64 inference(monotonicity,[status(thm)],[19])).
% 3.73/2.64 tff(485,plain,
% 3.73/2.64 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), X1!1)) = addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), X1!1))),
% 3.73/2.64 inference(symmetry,[status(thm)],[484])).
% 3.73/2.64 tff(486,plain,
% 3.73/2.64 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(487,plain,
% 3.73/2.64 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[486, 7])).
% 3.73/2.64 tff(488,plain,
% 3.73/2.64 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), X1!1)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1))),
% 3.73/2.64 inference(monotonicity,[status(thm)],[487])).
% 3.73/2.64 tff(489,plain,
% 3.73/2.64 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1)) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), X1!1))),
% 3.73/2.64 inference(symmetry,[status(thm)],[488])).
% 3.73/2.64 tff(490,plain,
% 3.73/2.64 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2))))),
% 3.73/2.64 inference(quant_inst,[status(thm)],[])).
% 3.73/2.64 tff(491,plain,
% 3.73/2.64 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)))),
% 3.73/2.64 inference(unit_resolution,[status(thm)],[490, 16])).
% 3.73/2.64 tff(492,plain,
% 3.73/2.64 (addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1))),
% 3.73/2.64 inference(symmetry,[status(thm)],[491])).
% 3.73/2.64 tff(493,plain,
% 3.73/2.64 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.73/2.64 inference(symmetry,[status(thm)],[487])).
% 3.73/2.64 tff(494,plain,
% 3.73/2.64 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1)))),
% 3.73/2.64 inference(transitivity,[status(thm)],[493, 18])).
% 3.73/2.64 tff(495,plain,
% 3.73/2.64 (addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2))) = addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))))),
% 3.73/2.64 inference(monotonicity,[status(thm)],[494])).
% 3.73/2.64 tff(496,plain,
% 3.73/2.64 (addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)))),
% 3.73/2.64 inference(symmetry,[status(thm)],[495])).
% 3.73/2.64 tff(497,plain,
% 3.73/2.64 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X1!1), X0!2))),
% 3.73/2.64 inference(transitivity,[status(thm)],[24, 21, 496, 492, 489, 485, 483, 480, 26, 81, 448, 468, 421])).
% 3.73/2.65 tff(498,plain,
% 3.73/2.65 (addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2))),
% 3.73/2.65 inference(monotonicity,[status(thm)],[497, 204])).
% 3.73/2.65 tff(499,plain,
% 3.73/2.65 (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 3.73/2.65 inference(symmetry,[status(thm)],[498])).
% 3.73/2.65 tff(500,plain,
% 3.73/2.65 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)))),
% 3.73/2.65 inference(quant_inst,[status(thm)],[])).
% 3.73/2.65 tff(501,plain,
% 3.73/2.65 (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2))),
% 3.73/2.65 inference(unit_resolution,[status(thm)],[500, 7])).
% 3.73/2.65 tff(502,plain,
% 3.73/2.65 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 3.73/2.65 inference(quant_inst,[status(thm)],[])).
% 3.73/2.65 tff(503,plain,
% 3.73/2.65 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 3.73/2.65 inference(unit_resolution,[status(thm)],[502, 16])).
% 3.73/2.65 tff(504,plain,
% 3.73/2.65 (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.73/2.65 inference(monotonicity,[status(thm)],[503, 213])).
% 3.73/2.65 tff(505,plain,
% 3.73/2.65 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 3.73/2.65 inference(symmetry,[status(thm)],[504])).
% 3.73/2.65 tff(506,plain,
% 3.73/2.65 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.73/2.65 inference(quant_inst,[status(thm)],[])).
% 3.73/2.65 tff(507,plain,
% 3.73/2.65 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.73/2.65 inference(unit_resolution,[status(thm)],[506, 7])).
% 3.73/2.65 tff(508,plain,
% 3.73/2.65 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 3.73/2.65 inference(monotonicity,[status(thm)],[270])).
% 3.73/2.65 tff(509,plain,
% 3.73/2.65 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.73/2.65 inference(symmetry,[status(thm)],[508])).
% 3.73/2.65 tff(510,plain,
% 3.73/2.65 (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 3.73/2.65 inference(monotonicity,[status(thm)],[270])).
% 3.73/2.65 tff(511,plain,
% 3.73/2.65 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!2, X1!1), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.73/2.65 inference(quant_inst,[status(thm)],[])).
% 3.73/2.65 tff(512,plain,
% 3.73/2.65 (addition(multiplication(X0!2, X1!1), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.73/2.65 inference(unit_resolution,[status(thm)],[511, 7])).
% 3.73/2.65 tff(513,plain,
% 3.73/2.65 (addition(addition(multiplication(X0!2, X1!1), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))), multiplication(c(X0!2), c(X1!1))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))),
% 3.73/2.65 inference(monotonicity,[status(thm)],[512])).
% 3.73/2.65 tff(514,plain,
% 3.73/2.65 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!2, X1!1), addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(X0!2, X1!1), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))), multiplication(c(X0!2), c(X1!1))))),
% 3.73/2.65 inference(quant_inst,[status(thm)],[])).
% 3.73/2.65 tff(515,plain,
% 3.73/2.65 (addition(multiplication(X0!2, X1!1), addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(X0!2, X1!1), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))), multiplication(c(X0!2), c(X1!1)))),
% 3.73/2.65 inference(unit_resolution,[status(thm)],[514, 7])).
% 3.73/2.65 tff(516,plain,
% 3.73/2.65 (addition(multiplication(X0!2, X1!1), addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))),
% 3.73/2.65 inference(transitivity,[status(thm)],[515, 513, 510, 287, 509, 507, 505, 501, 499, 419, 416, 24, 21, 9])).
% 3.73/2.65 tff(517,plain,
% 3.73/2.65 (addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))))),
% 3.73/2.65 inference(symmetry,[status(thm)],[9])).
% 3.73/2.65 tff(518,plain,
% 3.73/2.65 (addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))) = one),
% 3.73/2.65 inference(transitivity,[status(thm)],[517, 496, 492, 489, 485, 483, 480, 26, 81])).
% 3.73/2.65 tff(519,plain,
% 3.73/2.65 (addition(multiplication(X0!2, X1!1), addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 3.73/2.65 inference(transitivity,[status(thm)],[515, 513, 510])).
% 3.73/2.65 tff(520,plain,
% 3.73/2.65 ((addition(multiplication(X0!2, X1!1), addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))) <=> (addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))) = one)),
% 3.73/2.65 inference(monotonicity,[status(thm)],[519, 518])).
% 3.73/2.65 tff(521,plain,
% 3.73/2.65 ((addition(multiplication(X0!2, X1!1), addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))) <=> (one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 3.73/2.65 inference(transitivity,[status(thm)],[520, 285])).
% 3.73/2.65 tff(522,plain,
% 3.73/2.65 ((one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(multiplication(X0!2, X1!1), addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))))),
% 3.73/2.65 inference(symmetry,[status(thm)],[521])).
% 3.73/2.65 tff(523,plain,
% 3.73/2.65 ((~(one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))))) <=> (~(addition(multiplication(X0!2, X1!1), addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))))),
% 3.73/2.65 inference(monotonicity,[status(thm)],[522])).
% 3.73/2.65 tff(524,plain,
% 3.73/2.65 (~(addition(multiplication(X0!2, X1!1), addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))))),
% 3.73/2.65 inference(modus_ponens,[status(thm)],[295, 523])).
% 3.73/2.65 tff(525,plain,
% 3.73/2.65 ($false),
% 3.73/2.65 inference(unit_resolution,[status(thm)],[524, 516])).
% 3.73/2.65 % SZS output end Proof
%------------------------------------------------------------------------------