%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE011+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 Jun 21 05:12:51 AM UTC 2025
% Result : Theorem 5.66s 5.84s
% Output : Proof 5.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : KLE011+4 : TPTP v9.0.0. Released v4.0.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 18:51:47 EDT 2025
% 0.14/0.37 % CPUTime :
% 5.66/5.84 % SZS status Theorem
% 5.66/5.84 % SZS output start Proof
% 5.66/5.84 tff(one_type, type, (
% 5.66/5.84 one: $i)).
% 5.66/5.84 tff(addition_type, type, (
% 5.66/5.84 addition: ( $i * $i ) > $i)).
% 5.66/5.84 tff(multiplication_type, type, (
% 5.66/5.84 multiplication: ( $i * $i ) > $i)).
% 5.66/5.84 tff(tptp_fun_X1_1_type, type, (
% 5.66/5.84 tptp_fun_X1_1: $i)).
% 5.66/5.84 tff(c_type, type, (
% 5.66/5.84 c: $i > $i)).
% 5.66/5.84 tff(tptp_fun_X0_2_type, type, (
% 5.66/5.84 tptp_fun_X0_2: $i)).
% 5.66/5.84 tff(tptp_fun_X1_0_type, type, (
% 5.66/5.84 tptp_fun_X1_0: $i > $i)).
% 5.66/5.84 tff(complement_type, type, (
% 5.66/5.84 complement: ( $i * $i ) > $o)).
% 5.66/5.84 tff(test_type, type, (
% 5.66/5.84 test: $i > $o)).
% 5.66/5.84 tff(leq_type, type, (
% 5.66/5.84 leq: ( $i * $i ) > $o)).
% 5.66/5.84 tff(zero_type, type, (
% 5.66/5.84 zero: $i)).
% 5.66/5.84 tff(1,plain,
% 5.66/5.84 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 5.66/5.84 inference(bind,[status(th)],[])).
% 5.66/5.84 tff(2,plain,
% 5.66/5.84 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 5.66/5.84 inference(quant_intro,[status(thm)],[1])).
% 5.66/5.84 tff(3,plain,
% 5.66/5.84 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 5.66/5.84 inference(rewrite,[status(thm)],[])).
% 5.66/5.84 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 5.66/5.84 tff(5,plain,
% 5.66/5.84 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[4, 3])).
% 5.66/5.84 tff(6,plain,(
% 5.66/5.84 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 5.66/5.84 inference(skolemize,[status(sab)],[5])).
% 5.66/5.84 tff(7,plain,
% 5.66/5.84 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[6, 2])).
% 5.66/5.84 tff(8,plain,
% 5.66/5.84 ((~![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)))),
% 5.66/5.84 inference(quant_inst,[status(thm)],[])).
% 5.66/5.84 tff(9,plain,
% 5.66/5.84 (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))),
% 5.66/5.84 inference(unit_resolution,[status(thm)],[8, 7])).
% 5.66/5.84 tff(10,plain,
% 5.66/5.84 (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))),
% 5.66/5.84 inference(symmetry,[status(thm)],[9])).
% 5.66/5.84 tff(11,plain,
% 5.66/5.84 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1))), one)))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1))), one))))),
% 5.66/5.84 inference(rewrite,[status(thm)],[])).
% 5.66/5.84 tff(12,plain,
% 5.66/5.84 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (leq(one, addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1))), one)))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1))), one))))),
% 5.66/5.84 inference(rewrite,[status(thm)],[])).
% 5.66/5.84 tff(13,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (leq(one, addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1))), one)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 5.66/5.84 tff(14,plain,
% 5.66/5.84 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1))), one)))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[13, 12])).
% 5.66/5.84 tff(15,plain,
% 5.66/5.84 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1))), one)))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[14, 11])).
% 5.66/5.84 tff(16,plain,
% 5.66/5.84 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1))), one)))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[15, 11])).
% 5.66/5.84 tff(17,plain,
% 5.66/5.84 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1))), one)))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[16, 11])).
% 5.66/5.84 tff(18,plain,(
% 5.66/5.84 ~((~(test(X1!1) & test(X0!2))) | (leq(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)))) & leq(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)))),
% 5.66/5.84 inference(skolemize,[status(sab)],[17])).
% 5.66/5.84 tff(19,plain,
% 5.66/5.84 (test(X1!1) & test(X0!2)),
% 5.66/5.84 inference(or_elim,[status(thm)],[18])).
% 5.66/5.84 tff(20,plain,
% 5.66/5.84 (test(X1!1)),
% 5.66/5.84 inference(and_elim,[status(thm)],[19])).
% 5.66/5.84 tff(21,plain,
% 5.66/5.84 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 5.66/5.84 inference(bind,[status(th)],[])).
% 5.66/5.84 tff(22,plain,
% 5.66/5.84 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 5.66/5.84 inference(quant_intro,[status(thm)],[21])).
% 5.66/5.84 tff(23,plain,
% 5.66/5.84 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 5.66/5.84 inference(rewrite,[status(thm)],[])).
% 5.66/5.84 tff(24,plain,
% 5.66/5.84 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 5.66/5.84 inference(bind,[status(th)],[])).
% 5.66/5.84 tff(25,plain,
% 5.66/5.84 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 5.66/5.84 inference(quant_intro,[status(thm)],[24])).
% 5.66/5.84 tff(26,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_3')).
% 5.66/5.84 tff(27,plain,
% 5.66/5.84 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[26, 25])).
% 5.66/5.84 tff(28,plain,
% 5.66/5.84 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[27, 23])).
% 5.66/5.84 tff(29,plain,(
% 5.66/5.84 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 5.66/5.84 inference(skolemize,[status(sab)],[28])).
% 5.66/5.84 tff(30,plain,
% 5.66/5.84 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[29, 22])).
% 5.66/5.84 tff(31,plain,
% 5.66/5.84 (((~![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))))),
% 5.66/5.84 inference(rewrite,[status(thm)],[])).
% 5.66/5.84 tff(32,plain,
% 5.66/5.84 ((~![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))))),
% 5.66/5.84 inference(quant_inst,[status(thm)],[])).
% 5.66/5.84 tff(33,plain,
% 5.66/5.84 ((~![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)))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[32, 31])).
% 5.66/5.84 tff(34,plain,
% 5.66/5.84 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 5.66/5.84 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 5.66/5.84 tff(35,plain,
% 5.66/5.84 (^[X0: $i, X1: $i] : refl((~(((~(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))) <=> complement(X1, X0))))),
% 5.66/5.84 inference(bind,[status(th)],[])).
% 5.66/5.84 tff(36,plain,
% 5.66/5.84 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))) <=> ![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 5.66/5.84 inference(quant_intro,[status(thm)],[35])).
% 5.66/5.84 tff(37,plain,
% 5.66/5.84 (^[X0: $i, X1: $i] : trans(trans(monotonicity(rewrite(((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)) <=> (~((~(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))) <=> (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))))), rewrite((complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))), ((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))))), rewrite((~(((~(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))) <=> complement(X1, X0)))), ((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))))),
% 5.66/5.84 inference(bind,[status(th)],[])).
% 5.66/5.84 tff(38,plain,
% 5.66/5.84 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 5.66/5.84 inference(quant_intro,[status(thm)],[37])).
% 5.66/5.84 tff(39,plain,
% 5.66/5.84 (![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)))),
% 5.66/5.84 inference(rewrite,[status(thm)],[])).
% 5.66/5.84 tff(40,plain,
% 5.66/5.84 (^[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))))),
% 5.66/5.84 inference(bind,[status(th)],[])).
% 5.66/5.84 tff(41,plain,
% 5.66/5.84 (![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)))),
% 5.66/5.84 inference(quant_intro,[status(thm)],[40])).
% 5.66/5.84 tff(42,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')).
% 5.66/5.84 tff(43,plain,
% 5.66/5.84 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[42, 41])).
% 5.66/5.84 tff(44,plain,
% 5.66/5.84 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[43, 39])).
% 5.66/5.84 tff(45,plain,(
% 5.66/5.84 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 5.66/5.84 inference(skolemize,[status(sab)],[44])).
% 5.66/5.84 tff(46,plain,
% 5.66/5.84 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[45, 38])).
% 5.66/5.84 tff(47,plain,
% 5.66/5.84 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[46, 36])).
% 5.66/5.84 tff(48,plain,
% 5.66/5.84 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))))),
% 5.66/5.84 inference(rewrite,[status(thm)],[])).
% 5.66/5.84 tff(49,plain,
% 5.66/5.84 ((~(((~(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))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 5.66/5.84 inference(rewrite,[status(thm)],[])).
% 5.66/5.84 tff(50,plain,
% 5.66/5.84 ((((~(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))) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 5.66/5.84 inference(rewrite,[status(thm)],[])).
% 5.66/5.84 tff(51,plain,
% 5.66/5.84 ((~(((~(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))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 5.66/5.84 inference(monotonicity,[status(thm)],[50])).
% 5.66/5.84 tff(52,plain,
% 5.66/5.84 ((~(((~(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))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 5.66/5.84 inference(transitivity,[status(thm)],[51, 49])).
% 5.66/5.84 tff(53,plain,
% 5.66/5.84 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))))),
% 5.66/5.84 inference(monotonicity,[status(thm)],[52])).
% 5.66/5.84 tff(54,plain,
% 5.66/5.84 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))))),
% 5.66/5.84 inference(transitivity,[status(thm)],[53, 48])).
% 5.66/5.84 tff(55,plain,
% 5.66/5.84 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))),
% 5.66/5.84 inference(quant_inst,[status(thm)],[])).
% 5.66/5.84 tff(56,plain,
% 5.66/5.84 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[55, 54])).
% 5.66/5.84 tff(57,plain,
% 5.66/5.84 (~(((~(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)))),
% 5.66/5.84 inference(unit_resolution,[status(thm)],[56, 47])).
% 5.66/5.84 tff(58,plain,
% 5.66/5.84 ((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))),
% 5.66/5.84 inference(commutativity,[status(thm)],[])).
% 5.66/5.84 tff(59,plain,
% 5.66/5.84 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))),
% 5.66/5.84 inference(quant_inst,[status(thm)],[])).
% 5.66/5.84 tff(60,plain,
% 5.66/5.84 (~(((~(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))),
% 5.66/5.84 inference(unit_resolution,[status(thm)],[59, 47])).
% 5.66/5.84 tff(61,plain,
% 5.66/5.84 (^[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)))))))),
% 5.66/5.84 inference(bind,[status(th)],[])).
% 5.66/5.84 tff(62,plain,
% 5.66/5.84 (![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))))))),
% 5.66/5.84 inference(quant_intro,[status(thm)],[61])).
% 5.66/5.84 tff(63,plain,
% 5.66/5.84 (^[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)))))))),
% 5.66/5.84 inference(bind,[status(th)],[])).
% 5.66/5.84 tff(64,plain,
% 5.66/5.84 (![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))))))),
% 5.66/5.84 inference(quant_intro,[status(thm)],[63])).
% 5.66/5.84 tff(65,plain,
% 5.66/5.84 (![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))))))),
% 5.66/5.84 inference(transitivity,[status(thm)],[64, 62])).
% 5.66/5.84 tff(66,plain,
% 5.66/5.84 (^[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))))))))),
% 5.66/5.84 inference(bind,[status(th)],[])).
% 5.66/5.84 tff(67,plain,
% 5.66/5.84 (![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))))))),
% 5.66/5.84 inference(quant_intro,[status(thm)],[66])).
% 5.66/5.84 tff(68,plain,
% 5.66/5.84 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 5.66/5.84 inference(rewrite,[status(thm)],[])).
% 5.66/5.84 tff(69,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 5.66/5.84 tff(70,plain,
% 5.66/5.84 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[69, 68])).
% 5.66/5.84 tff(71,plain,(
% 5.66/5.84 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 5.66/5.84 inference(skolemize,[status(sab)],[70])).
% 5.66/5.84 tff(72,plain,
% 5.66/5.84 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[71, 67])).
% 5.66/5.84 tff(73,plain,
% 5.66/5.84 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 5.66/5.84 inference(modus_ponens,[status(thm)],[72, 65])).
% 5.66/5.84 tff(74,plain,
% 5.66/5.84 ((~![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))))))),
% 5.66/5.84 inference(quant_inst,[status(thm)],[])).
% 5.66/5.84 tff(75,plain,
% 5.66/5.84 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 5.66/5.84 inference(unit_resolution,[status(thm)],[74, 73])).
% 5.66/5.84 tff(76,plain,
% 5.66/5.84 (((~((~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))),
% 5.66/5.84 inference(tautology,[status(thm)],[])).
% 5.66/5.84 tff(77,plain,
% 5.66/5.84 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 5.66/5.84 inference(unit_resolution,[status(thm)],[76, 75])).
% 5.66/5.84 tff(78,plain,
% 5.66/5.84 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 5.66/5.84 inference(tautology,[status(thm)],[])).
% 5.66/5.84 tff(79,plain,
% 5.66/5.84 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 5.66/5.84 inference(unit_resolution,[status(thm)],[78, 20])).
% 5.66/5.84 tff(80,plain,
% 5.66/5.84 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 5.66/5.84 inference(unit_resolution,[status(thm)],[79, 77])).
% 5.66/5.84 tff(81,plain,
% 5.66/5.84 ((((~(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)))) | (~complement(tptp_fun_X1_0(X1!1), X1!1))),
% 5.66/5.84 inference(tautology,[status(thm)],[])).
% 5.66/5.84 tff(82,plain,
% 5.66/5.84 ((((~(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))))),
% 5.66/5.84 inference(unit_resolution,[status(thm)],[81, 80])).
% 5.66/5.84 tff(83,plain,
% 5.66/5.84 (~((~(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)))),
% 5.66/5.84 inference(unit_resolution,[status(thm)],[82, 60])).
% 5.66/5.84 tff(84,plain,
% 5.66/5.84 (((~(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)),
% 5.66/5.84 inference(tautology,[status(thm)],[])).
% 5.66/5.84 tff(85,plain,
% 5.66/5.84 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 5.66/5.84 inference(unit_resolution,[status(thm)],[84, 83])).
% 5.66/5.84 tff(86,plain,
% 5.66/5.84 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 5.66/5.84 inference(symmetry,[status(thm)],[85])).
% 5.66/5.84 tff(87,plain,
% 5.66/5.84 ((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)))),
% 5.66/5.84 inference(monotonicity,[status(thm)],[86])).
% 5.66/5.84 tff(88,plain,
% 5.66/5.84 ((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))),
% 5.66/5.84 inference(transitivity,[status(thm)],[87, 58])).
% 5.66/5.84 tff(89,plain,
% 5.66/5.84 ((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)),
% 5.66/5.84 inference(symmetry,[status(thm)],[88])).
% 5.66/5.84 tff(90,plain,
% 5.66/5.84 ((~![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))),
% 5.66/5.84 inference(quant_inst,[status(thm)],[])).
% 5.66/5.84 tff(91,plain,
% 5.66/5.84 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[90, 7])).
% 5.66/5.85 tff(92,plain,
% 5.66/5.85 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 5.66/5.85 inference(modus_ponens,[status(thm)],[91, 89])).
% 5.66/5.85 tff(93,plain,
% 5.66/5.85 (((~(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)),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(94,plain,
% 5.66/5.85 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[93, 83])).
% 5.66/5.85 tff(95,plain,
% 5.66/5.85 (((~(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)),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(96,plain,
% 5.66/5.85 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[95, 83])).
% 5.66/5.85 tff(97,plain,
% 5.66/5.85 ((~((~(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))),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(98,plain,
% 5.66/5.85 ((~((~(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))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[97, 96, 94])).
% 5.66/5.85 tff(99,plain,
% 5.66/5.85 (~((~(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)))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[98, 92])).
% 5.66/5.85 tff(100,plain,
% 5.66/5.85 ((((~(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))) | complement(X1!1, tptp_fun_X1_0(X1!1))),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(101,plain,
% 5.66/5.85 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[100, 99, 57])).
% 5.66/5.85 tff(102,plain,
% 5.66/5.85 ((~((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)))),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(103,plain,
% 5.66/5.85 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[102, 101, 34])).
% 5.66/5.85 tff(104,plain,
% 5.66/5.85 (addition(X1!1, c(X1!1)) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 5.66/5.85 inference(monotonicity,[status(thm)],[103])).
% 5.66/5.85 tff(105,plain,
% 5.66/5.85 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(X1!1, c(X1!1))),
% 5.66/5.85 inference(symmetry,[status(thm)],[104])).
% 5.66/5.85 tff(106,plain,
% 5.66/5.85 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))),
% 5.66/5.85 inference(quant_inst,[status(thm)],[])).
% 5.66/5.85 tff(107,plain,
% 5.66/5.85 (~(((~(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))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[106, 47])).
% 5.66/5.85 tff(108,plain,
% 5.66/5.85 ((~![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))))))),
% 5.66/5.85 inference(quant_inst,[status(thm)],[])).
% 5.66/5.85 tff(109,plain,
% 5.66/5.85 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[108, 73])).
% 5.66/5.85 tff(110,plain,
% 5.66/5.85 (((~((~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))),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(111,plain,
% 5.66/5.85 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[110, 109])).
% 5.66/5.85 tff(112,plain,
% 5.66/5.85 (test(X0!2)),
% 5.66/5.85 inference(and_elim,[status(thm)],[19])).
% 5.66/5.85 tff(113,plain,
% 5.66/5.85 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(114,plain,
% 5.66/5.85 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[113, 112])).
% 5.66/5.85 tff(115,plain,
% 5.66/5.85 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[114, 111])).
% 5.66/5.85 tff(116,plain,
% 5.66/5.85 ((((~(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)))) | (~complement(tptp_fun_X1_0(X0!2), X0!2))),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(117,plain,
% 5.66/5.85 ((((~(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))))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[116, 115])).
% 5.66/5.85 tff(118,plain,
% 5.66/5.85 (~((~(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)))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[117, 107])).
% 5.66/5.85 tff(119,plain,
% 5.66/5.85 (((~(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)),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(120,plain,
% 5.66/5.85 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[119, 118])).
% 5.66/5.85 tff(121,plain,
% 5.66/5.85 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(X1!1, c(X1!1))),
% 5.66/5.85 inference(transitivity,[status(thm)],[120, 86, 105])).
% 5.66/5.85 tff(122,plain,
% 5.66/5.85 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 5.66/5.85 inference(monotonicity,[status(thm)],[121])).
% 5.66/5.85 tff(123,plain,
% 5.66/5.85 (^[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))))),
% 5.66/5.85 inference(bind,[status(th)],[])).
% 5.66/5.85 tff(124,plain,
% 5.66/5.85 (![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)))),
% 5.66/5.85 inference(quant_intro,[status(thm)],[123])).
% 5.66/5.85 tff(125,plain,
% 5.66/5.85 (![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)))),
% 5.66/5.85 inference(rewrite,[status(thm)],[])).
% 5.66/5.85 tff(126,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')).
% 5.66/5.85 tff(127,plain,
% 5.66/5.85 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 5.66/5.85 inference(modus_ponens,[status(thm)],[126, 125])).
% 5.66/5.85 tff(128,plain,(
% 5.66/5.85 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 5.66/5.85 inference(skolemize,[status(sab)],[127])).
% 5.66/5.85 tff(129,plain,
% 5.66/5.85 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 5.66/5.85 inference(modus_ponens,[status(thm)],[128, 124])).
% 5.66/5.85 tff(130,plain,
% 5.66/5.85 ((~![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)))),
% 5.66/5.85 inference(quant_inst,[status(thm)],[])).
% 5.66/5.85 tff(131,plain,
% 5.66/5.85 (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))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[130, 129])).
% 5.66/5.85 tff(132,plain,
% 5.66/5.85 (addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X0!2)),
% 5.66/5.85 inference(symmetry,[status(thm)],[131])).
% 5.66/5.85 tff(133,plain,
% 5.66/5.85 (((~(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)),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(134,plain,
% 5.66/5.85 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[133, 118])).
% 5.66/5.85 tff(135,plain,
% 5.66/5.85 (zero = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 5.66/5.85 inference(symmetry,[status(thm)],[134])).
% 5.66/5.85 tff(136,plain,
% 5.66/5.85 (addition(multiplication(X0!2, X0!2), zero) = addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2))),
% 5.66/5.85 inference(monotonicity,[status(thm)],[135])).
% 5.66/5.85 tff(137,plain,
% 5.66/5.85 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 5.66/5.85 inference(bind,[status(th)],[])).
% 5.66/5.85 tff(138,plain,
% 5.66/5.85 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 5.66/5.85 inference(quant_intro,[status(thm)],[137])).
% 5.66/5.85 tff(139,plain,
% 5.66/5.85 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 5.66/5.85 inference(rewrite,[status(thm)],[])).
% 5.66/5.85 tff(140,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 5.66/5.85 tff(141,plain,
% 5.66/5.85 (![A: $i] : (addition(A, zero) = A)),
% 5.66/5.85 inference(modus_ponens,[status(thm)],[140, 139])).
% 5.66/5.85 tff(142,plain,(
% 5.66/5.85 ![A: $i] : (addition(A, zero) = A)),
% 5.66/5.85 inference(skolemize,[status(sab)],[141])).
% 5.66/5.85 tff(143,plain,
% 5.66/5.85 (![A: $i] : (addition(A, zero) = A)),
% 5.66/5.85 inference(modus_ponens,[status(thm)],[142, 138])).
% 5.66/5.85 tff(144,plain,
% 5.66/5.85 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(X0!2, X0!2), zero) = multiplication(X0!2, X0!2))),
% 5.66/5.85 inference(quant_inst,[status(thm)],[])).
% 5.66/5.85 tff(145,plain,
% 5.66/5.85 (addition(multiplication(X0!2, X0!2), zero) = multiplication(X0!2, X0!2)),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[144, 143])).
% 5.66/5.85 tff(146,plain,
% 5.66/5.85 (multiplication(X0!2, X0!2) = addition(multiplication(X0!2, X0!2), zero)),
% 5.66/5.85 inference(symmetry,[status(thm)],[145])).
% 5.66/5.85 tff(147,plain,
% 5.66/5.85 (multiplication(X0!2, X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 5.66/5.85 inference(transitivity,[status(thm)],[146, 136, 132, 122])).
% 5.66/5.85 tff(148,plain,
% 5.66/5.85 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 5.66/5.85 inference(rewrite,[status(thm)],[])).
% 5.66/5.85 tff(149,plain,
% 5.66/5.85 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 5.66/5.85 inference(quant_inst,[status(thm)],[])).
% 5.66/5.85 tff(150,plain,
% 5.66/5.85 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 5.66/5.85 inference(modus_ponens,[status(thm)],[149, 148])).
% 5.66/5.85 tff(151,plain,
% 5.66/5.85 ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[150, 30, 112])).
% 5.66/5.85 tff(152,plain,
% 5.66/5.85 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))))),
% 5.66/5.85 inference(rewrite,[status(thm)],[])).
% 5.66/5.85 tff(153,plain,
% 5.66/5.85 ((~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) <=> (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 5.66/5.85 inference(rewrite,[status(thm)],[])).
% 5.66/5.85 tff(154,plain,
% 5.66/5.85 ((((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))) <=> (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 5.66/5.85 inference(rewrite,[status(thm)],[])).
% 5.66/5.85 tff(155,plain,
% 5.66/5.85 ((~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) <=> (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 5.66/5.85 inference(monotonicity,[status(thm)],[154])).
% 5.66/5.85 tff(156,plain,
% 5.66/5.85 ((~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) <=> (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 5.66/5.85 inference(transitivity,[status(thm)],[155, 153])).
% 5.66/5.85 tff(157,plain,
% 5.66/5.85 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))))),
% 5.66/5.85 inference(monotonicity,[status(thm)],[156])).
% 5.66/5.85 tff(158,plain,
% 5.66/5.85 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))))),
% 5.66/5.85 inference(transitivity,[status(thm)],[157, 152])).
% 5.66/5.85 tff(159,plain,
% 5.66/5.85 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 5.66/5.85 inference(quant_inst,[status(thm)],[])).
% 5.66/5.85 tff(160,plain,
% 5.66/5.85 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 5.66/5.85 inference(modus_ponens,[status(thm)],[159, 158])).
% 5.66/5.85 tff(161,plain,
% 5.66/5.85 (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[160, 47])).
% 5.66/5.85 tff(162,plain,
% 5.66/5.85 ((addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))) <=> (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 5.66/5.85 inference(commutativity,[status(thm)],[])).
% 5.66/5.85 tff(163,plain,
% 5.66/5.85 (one = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 5.66/5.85 inference(symmetry,[status(thm)],[120])).
% 5.66/5.85 tff(164,plain,
% 5.66/5.85 ((addition(tptp_fun_X1_0(X0!2), X0!2) = one) <=> (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2)))),
% 5.66/5.85 inference(monotonicity,[status(thm)],[163])).
% 5.66/5.85 tff(165,plain,
% 5.66/5.85 ((addition(tptp_fun_X1_0(X0!2), X0!2) = one) <=> (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 5.66/5.85 inference(transitivity,[status(thm)],[164, 162])).
% 5.66/5.85 tff(166,plain,
% 5.66/5.85 ((addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)) <=> (addition(tptp_fun_X1_0(X0!2), X0!2) = one)),
% 5.66/5.85 inference(symmetry,[status(thm)],[165])).
% 5.66/5.85 tff(167,plain,
% 5.66/5.85 ((~![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))),
% 5.66/5.85 inference(quant_inst,[status(thm)],[])).
% 5.66/5.85 tff(168,plain,
% 5.66/5.85 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[167, 7])).
% 5.66/5.85 tff(169,plain,
% 5.66/5.85 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 5.66/5.85 inference(modus_ponens,[status(thm)],[168, 166])).
% 5.66/5.85 tff(170,plain,
% 5.66/5.85 (((~(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)),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(171,plain,
% 5.66/5.85 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[170, 118])).
% 5.66/5.85 tff(172,plain,
% 5.66/5.85 ((~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(173,plain,
% 5.66/5.85 ((~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[172, 171, 134])).
% 5.66/5.85 tff(174,plain,
% 5.66/5.85 (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[173, 169])).
% 5.66/5.85 tff(175,plain,
% 5.66/5.85 ((((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))) | ((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) | complement(X0!2, tptp_fun_X1_0(X0!2))),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(176,plain,
% 5.66/5.85 (complement(X0!2, tptp_fun_X1_0(X0!2))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[175, 174, 161])).
% 5.66/5.85 tff(177,plain,
% 5.66/5.85 ((~((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) | (c(X0!2) = tptp_fun_X1_0(X0!2)) | (~complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 5.66/5.85 inference(tautology,[status(thm)],[])).
% 5.66/5.85 tff(178,plain,
% 5.66/5.85 (c(X0!2) = tptp_fun_X1_0(X0!2)),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[177, 176, 151])).
% 5.66/5.85 tff(179,plain,
% 5.66/5.85 (addition(X0!2, c(X0!2)) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 5.66/5.85 inference(monotonicity,[status(thm)],[178])).
% 5.66/5.85 tff(180,plain,
% 5.66/5.85 (addition(X0!2, c(X0!2)) = one),
% 5.66/5.85 inference(transitivity,[status(thm)],[179, 120])).
% 5.66/5.85 tff(181,plain,
% 5.66/5.85 (multiplication(addition(X0!2, c(X0!2)), X1!1) = multiplication(one, X1!1)),
% 5.66/5.85 inference(monotonicity,[status(thm)],[180])).
% 5.66/5.85 tff(182,plain,
% 5.66/5.85 (multiplication(one, X1!1) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 5.66/5.85 inference(symmetry,[status(thm)],[181])).
% 5.66/5.85 tff(183,plain,
% 5.66/5.85 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 5.66/5.85 inference(bind,[status(th)],[])).
% 5.66/5.85 tff(184,plain,
% 5.66/5.85 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 5.66/5.85 inference(quant_intro,[status(thm)],[183])).
% 5.66/5.85 tff(185,plain,
% 5.66/5.85 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 5.66/5.85 inference(rewrite,[status(thm)],[])).
% 5.66/5.85 tff(186,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 5.66/5.85 tff(187,plain,
% 5.66/5.85 (![A: $i] : (multiplication(one, A) = A)),
% 5.66/5.85 inference(modus_ponens,[status(thm)],[186, 185])).
% 5.66/5.85 tff(188,plain,(
% 5.66/5.85 ![A: $i] : (multiplication(one, A) = A)),
% 5.66/5.85 inference(skolemize,[status(sab)],[187])).
% 5.66/5.85 tff(189,plain,
% 5.66/5.85 (![A: $i] : (multiplication(one, A) = A)),
% 5.66/5.85 inference(modus_ponens,[status(thm)],[188, 184])).
% 5.66/5.85 tff(190,plain,
% 5.66/5.85 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!1) = X1!1)),
% 5.66/5.85 inference(quant_inst,[status(thm)],[])).
% 5.66/5.85 tff(191,plain,
% 5.66/5.85 (multiplication(one, X1!1) = X1!1),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[190, 189])).
% 5.66/5.85 tff(192,plain,
% 5.66/5.85 (X1!1 = multiplication(one, X1!1)),
% 5.66/5.85 inference(symmetry,[status(thm)],[191])).
% 5.66/5.85 tff(193,plain,
% 5.66/5.85 (X1!1 = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 5.66/5.85 inference(transitivity,[status(thm)],[192, 182])).
% 5.66/5.85 tff(194,plain,
% 5.66/5.85 (addition(X1!1, multiplication(X0!2, X0!2)) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 5.66/5.85 inference(monotonicity,[status(thm)],[193, 147])).
% 5.66/5.85 tff(195,plain,
% 5.66/5.85 (addition(X1!1, addition(multiplication(X0!2, X0!2), zero)) = addition(X1!1, multiplication(X0!2, X0!2))),
% 5.66/5.85 inference(monotonicity,[status(thm)],[145])).
% 5.66/5.85 tff(196,plain,
% 5.66/5.85 (^[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)))),
% 5.66/5.85 inference(bind,[status(th)],[])).
% 5.66/5.85 tff(197,plain,
% 5.66/5.85 (![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))),
% 5.66/5.85 inference(quant_intro,[status(thm)],[196])).
% 5.66/5.85 tff(198,plain,
% 5.66/5.85 (![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))),
% 5.66/5.85 inference(rewrite,[status(thm)],[])).
% 5.66/5.85 tff(199,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')).
% 5.66/5.85 tff(200,plain,
% 5.66/5.85 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 5.66/5.85 inference(modus_ponens,[status(thm)],[199, 198])).
% 5.66/5.85 tff(201,plain,(
% 5.66/5.85 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 5.66/5.85 inference(skolemize,[status(sab)],[200])).
% 5.66/5.85 tff(202,plain,
% 5.66/5.85 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 5.66/5.85 inference(modus_ponens,[status(thm)],[201, 197])).
% 5.66/5.85 tff(203,plain,
% 5.66/5.85 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X1!1, addition(multiplication(X0!2, X0!2), zero)) = addition(addition(X1!1, multiplication(X0!2, X0!2)), zero))),
% 5.66/5.85 inference(quant_inst,[status(thm)],[])).
% 5.66/5.85 tff(204,plain,
% 5.66/5.85 (addition(X1!1, addition(multiplication(X0!2, X0!2), zero)) = addition(addition(X1!1, multiplication(X0!2, X0!2)), zero)),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[203, 202])).
% 5.66/5.85 tff(205,plain,
% 5.66/5.85 (addition(addition(X1!1, multiplication(X0!2, X0!2)), zero) = addition(X1!1, addition(multiplication(X0!2, X0!2), zero))),
% 5.66/5.85 inference(symmetry,[status(thm)],[204])).
% 5.66/5.85 tff(206,plain,
% 5.66/5.85 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))))),
% 5.66/5.85 inference(quant_inst,[status(thm)],[])).
% 5.66/5.85 tff(207,plain,
% 5.66/5.85 (~(((~(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))))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[206, 47])).
% 5.66/5.85 tff(208,plain,
% 5.66/5.85 ((~![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))))),
% 5.66/5.85 inference(quant_inst,[status(thm)],[])).
% 5.66/5.85 tff(209,plain,
% 5.66/5.85 (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)))),
% 5.66/5.85 inference(unit_resolution,[status(thm)],[208, 7])).
% 5.66/5.85 tff(210,plain,
% 5.66/5.85 (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)))),
% 5.66/5.85 inference(symmetry,[status(thm)],[209])).
% 5.66/5.85 tff(211,plain,
% 5.66/5.85 (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)))),
% 5.66/5.85 inference(monotonicity,[status(thm)],[10])).
% 5.66/5.85 tff(212,plain,
% 5.66/5.85 (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)))),
% 5.66/5.85 inference(transitivity,[status(thm)],[211, 210])).
% 5.66/5.85 tff(213,plain,
% 5.66/5.85 ((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)),
% 5.66/5.85 inference(monotonicity,[status(thm)],[212])).
% 5.66/5.85 tff(214,plain,
% 5.66/5.85 ((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) <=> (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)),
% 5.66/5.86 inference(symmetry,[status(thm)],[213])).
% 5.66/5.86 tff(215,plain,
% 5.66/5.86 ((~(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)) <=> (~(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))),
% 5.66/5.86 inference(monotonicity,[status(thm)],[214])).
% 5.66/5.86 tff(216,plain,
% 5.66/5.86 ((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(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)),
% 5.66/5.86 inference(commutativity,[status(thm)],[])).
% 5.66/5.86 tff(217,plain,
% 5.66/5.86 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 5.66/5.86 inference(bind,[status(th)],[])).
% 5.66/5.86 tff(218,plain,
% 5.66/5.86 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 5.66/5.86 inference(quant_intro,[status(thm)],[217])).
% 5.66/5.86 tff(219,plain,
% 5.66/5.86 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 5.66/5.86 inference(rewrite,[status(thm)],[])).
% 5.66/5.86 tff(220,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','order')).
% 5.66/5.86 tff(221,plain,
% 5.66/5.86 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 5.66/5.86 inference(modus_ponens,[status(thm)],[220, 219])).
% 5.66/5.86 tff(222,plain,(
% 5.66/5.86 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 5.66/5.86 inference(skolemize,[status(sab)],[221])).
% 5.66/5.86 tff(223,plain,
% 5.66/5.86 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 5.66/5.86 inference(modus_ponens,[status(thm)],[222, 218])).
% 5.66/5.86 tff(224,plain,
% 5.66/5.86 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(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) <=> (addition(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))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(225,plain,
% 5.66/5.86 (leq(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) <=> (addition(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)),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[224, 223])).
% 5.66/5.86 tff(226,plain,
% 5.66/5.86 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 5.66/5.86 inference(symmetry,[status(thm)],[168])).
% 5.66/5.86 tff(227,plain,
% 5.66/5.86 (tptp_fun_X1_0(X0!2) = c(X0!2)),
% 5.66/5.86 inference(symmetry,[status(thm)],[178])).
% 5.66/5.86 tff(228,plain,
% 5.66/5.86 (addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = addition(c(X0!2), c(X0!2))),
% 5.66/5.86 inference(monotonicity,[status(thm)],[227, 227])).
% 5.66/5.86 tff(229,plain,
% 5.66/5.86 (addition(c(X0!2), c(X0!2)) = addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))),
% 5.66/5.86 inference(symmetry,[status(thm)],[228])).
% 5.66/5.86 tff(230,plain,
% 5.66/5.86 (^[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))))),
% 5.66/5.86 inference(bind,[status(th)],[])).
% 5.66/5.86 tff(231,plain,
% 5.66/5.86 (![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)))),
% 5.66/5.86 inference(quant_intro,[status(thm)],[230])).
% 5.66/5.86 tff(232,plain,
% 5.66/5.86 (^[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)))))),
% 5.66/5.86 inference(bind,[status(th)],[])).
% 5.66/5.86 tff(233,plain,
% 5.66/5.86 (![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)))),
% 5.66/5.86 inference(quant_intro,[status(thm)],[232])).
% 5.66/5.86 tff(234,plain,
% 5.66/5.86 (![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))))),
% 5.66/5.86 inference(rewrite,[status(thm)],[])).
% 5.66/5.86 tff(235,plain,
% 5.66/5.86 (^[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)))))),
% 5.66/5.86 inference(bind,[status(th)],[])).
% 5.66/5.86 tff(236,plain,
% 5.66/5.86 (![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))))),
% 5.66/5.86 inference(quant_intro,[status(thm)],[235])).
% 5.66/5.86 tff(237,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')).
% 5.66/5.86 tff(238,plain,
% 5.66/5.86 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 5.66/5.86 inference(modus_ponens,[status(thm)],[237, 236])).
% 5.66/5.86 tff(239,plain,
% 5.66/5.86 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 5.66/5.86 inference(modus_ponens,[status(thm)],[238, 234])).
% 5.66/5.86 tff(240,plain,(
% 5.66/5.86 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 5.66/5.86 inference(skolemize,[status(sab)],[239])).
% 5.66/5.86 tff(241,plain,
% 5.66/5.86 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 5.66/5.86 inference(modus_ponens,[status(thm)],[240, 233])).
% 5.66/5.86 tff(242,plain,
% 5.66/5.86 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 5.66/5.86 inference(modus_ponens,[status(thm)],[241, 231])).
% 5.66/5.86 tff(243,plain,
% 5.66/5.86 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(multiplication(X0!2, X0!2)) = addition(c(X0!2), c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (c(multiplication(X0!2, X0!2)) = addition(c(X0!2), c(X0!2))))),
% 5.66/5.86 inference(rewrite,[status(thm)],[])).
% 5.66/5.86 tff(244,plain,
% 5.66/5.86 (((~test(X0!2)) | (c(multiplication(X0!2, X0!2)) = addition(c(X0!2), c(X0!2))) | (~test(X0!2))) <=> ((~test(X0!2)) | (c(multiplication(X0!2, X0!2)) = addition(c(X0!2), c(X0!2))))),
% 5.66/5.86 inference(rewrite,[status(thm)],[])).
% 5.66/5.86 tff(245,plain,
% 5.66/5.86 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(multiplication(X0!2, X0!2)) = addition(c(X0!2), c(X0!2))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(multiplication(X0!2, X0!2)) = addition(c(X0!2), c(X0!2)))))),
% 5.66/5.86 inference(monotonicity,[status(thm)],[244])).
% 5.66/5.86 tff(246,plain,
% 5.66/5.86 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(multiplication(X0!2, X0!2)) = addition(c(X0!2), c(X0!2))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (c(multiplication(X0!2, X0!2)) = addition(c(X0!2), c(X0!2))))),
% 5.66/5.86 inference(transitivity,[status(thm)],[245, 243])).
% 5.66/5.86 tff(247,plain,
% 5.66/5.86 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(multiplication(X0!2, X0!2)) = addition(c(X0!2), c(X0!2))) | (~test(X0!2)))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(248,plain,
% 5.66/5.86 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (c(multiplication(X0!2, X0!2)) = addition(c(X0!2), c(X0!2)))),
% 5.66/5.86 inference(modus_ponens,[status(thm)],[247, 246])).
% 5.66/5.86 tff(249,plain,
% 5.66/5.86 (c(multiplication(X0!2, X0!2)) = addition(c(X0!2), c(X0!2))),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[248, 242, 112])).
% 5.66/5.86 tff(250,plain,
% 5.66/5.86 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!2) = X0!2)),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(251,plain,
% 5.66/5.86 (multiplication(one, X0!2) = X0!2),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[250, 189])).
% 5.66/5.86 tff(252,plain,
% 5.66/5.86 (addition(X1!1, c(X1!1)) = one),
% 5.66/5.86 inference(transitivity,[status(thm)],[104, 85])).
% 5.66/5.86 tff(253,plain,
% 5.66/5.86 (multiplication(addition(X1!1, c(X1!1)), X0!2) = multiplication(one, X0!2)),
% 5.66/5.86 inference(monotonicity,[status(thm)],[252])).
% 5.66/5.86 tff(254,plain,
% 5.66/5.86 (multiplication(X0!2, X0!2) = X0!2),
% 5.66/5.86 inference(transitivity,[status(thm)],[146, 136, 132, 122, 253, 251])).
% 5.66/5.86 tff(255,plain,
% 5.66/5.86 (c(multiplication(X0!2, X0!2)) = c(X0!2)),
% 5.66/5.86 inference(monotonicity,[status(thm)],[254])).
% 5.66/5.86 tff(256,plain,
% 5.66/5.86 (c(X0!2) = c(multiplication(X0!2, X0!2))),
% 5.66/5.86 inference(symmetry,[status(thm)],[255])).
% 5.66/5.86 tff(257,plain,
% 5.66/5.86 (tptp_fun_X1_0(X0!2) = addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))),
% 5.66/5.86 inference(transitivity,[status(thm)],[227, 256, 249, 229])).
% 5.66/5.86 tff(258,plain,
% 5.66/5.86 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), X0!2)),
% 5.66/5.86 inference(monotonicity,[status(thm)],[257])).
% 5.66/5.86 tff(259,plain,
% 5.66/5.86 (addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), X0!2) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 5.66/5.86 inference(symmetry,[status(thm)],[258])).
% 5.66/5.86 tff(260,plain,
% 5.66/5.86 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), X0!2)) = addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), X0!2))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(261,plain,
% 5.66/5.86 (addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), X0!2)) = addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), X0!2)),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[260, 202])).
% 5.66/5.86 tff(262,plain,
% 5.66/5.86 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 5.66/5.86 inference(transitivity,[status(thm)],[226, 120])).
% 5.66/5.86 tff(263,plain,
% 5.66/5.86 (addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), X0!2)) = addition(tptp_fun_X1_0(X0!2), one)),
% 5.66/5.86 inference(monotonicity,[status(thm)],[262])).
% 5.66/5.86 tff(264,plain,
% 5.66/5.86 (addition(tptp_fun_X1_0(X0!2), one) = addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), X0!2))),
% 5.66/5.86 inference(symmetry,[status(thm)],[263])).
% 5.66/5.86 tff(265,plain,
% 5.66/5.86 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(266,plain,
% 5.66/5.86 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[265, 7])).
% 5.66/5.86 tff(267,plain,
% 5.66/5.86 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.86 inference(symmetry,[status(thm)],[266])).
% 5.66/5.86 tff(268,plain,
% 5.66/5.86 (multiplication(tptp_fun_X1_0(X0!2), X1!1) = multiplication(tptp_fun_X1_0(X0!2), multiplication(one, X1!1))),
% 5.66/5.86 inference(monotonicity,[status(thm)],[192])).
% 5.66/5.86 tff(269,plain,
% 5.66/5.86 (multiplication(tptp_fun_X1_0(X0!2), multiplication(one, X1!1)) = multiplication(tptp_fun_X1_0(X0!2), X1!1)),
% 5.66/5.86 inference(symmetry,[status(thm)],[268])).
% 5.66/5.86 tff(270,plain,
% 5.66/5.86 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)))),
% 5.66/5.86 inference(bind,[status(th)],[])).
% 5.66/5.86 tff(271,plain,
% 5.66/5.86 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 5.66/5.86 inference(quant_intro,[status(thm)],[270])).
% 5.66/5.86 tff(272,plain,
% 5.66/5.86 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 5.66/5.86 inference(rewrite,[status(thm)],[])).
% 5.66/5.86 tff(273,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_associativity')).
% 5.66/5.86 tff(274,plain,
% 5.66/5.86 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 5.66/5.86 inference(modus_ponens,[status(thm)],[273, 272])).
% 5.66/5.86 tff(275,plain,(
% 5.66/5.86 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 5.66/5.86 inference(skolemize,[status(sab)],[274])).
% 5.66/5.86 tff(276,plain,
% 5.66/5.86 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 5.66/5.86 inference(modus_ponens,[status(thm)],[275, 271])).
% 5.66/5.86 tff(277,plain,
% 5.66/5.86 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X0!2), multiplication(one, X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(278,plain,
% 5.66/5.86 (multiplication(tptp_fun_X1_0(X0!2), multiplication(one, X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[277, 276])).
% 5.66/5.86 tff(279,plain,
% 5.66/5.86 (multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1) = multiplication(tptp_fun_X1_0(X0!2), multiplication(one, X1!1))),
% 5.66/5.86 inference(symmetry,[status(thm)],[278])).
% 5.66/5.86 tff(280,plain,
% 5.66/5.86 (multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1) = multiplication(tptp_fun_X1_0(X0!2), X1!1)),
% 5.66/5.86 inference(transitivity,[status(thm)],[279, 269])).
% 5.66/5.86 tff(281,plain,
% 5.66/5.86 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 5.66/5.86 inference(symmetry,[status(thm)],[103])).
% 5.66/5.86 tff(282,plain,
% 5.66/5.86 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 5.66/5.86 inference(monotonicity,[status(thm)],[227, 281])).
% 5.66/5.86 tff(283,plain,
% 5.66/5.86 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 5.66/5.86 inference(symmetry,[status(thm)],[282])).
% 5.66/5.86 tff(284,plain,
% 5.66/5.86 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 5.66/5.86 inference(monotonicity,[status(thm)],[283, 280])).
% 5.66/5.86 tff(285,plain,
% 5.66/5.86 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))),
% 5.66/5.86 inference(symmetry,[status(thm)],[284])).
% 5.66/5.86 tff(286,plain,
% 5.66/5.86 (^[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))))),
% 5.66/5.86 inference(bind,[status(th)],[])).
% 5.66/5.86 tff(287,plain,
% 5.66/5.86 (![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)))),
% 5.66/5.86 inference(quant_intro,[status(thm)],[286])).
% 5.66/5.86 tff(288,plain,
% 5.66/5.86 (![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)))),
% 5.66/5.86 inference(rewrite,[status(thm)],[])).
% 5.66/5.86 tff(289,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')).
% 5.66/5.86 tff(290,plain,
% 5.66/5.86 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 5.66/5.86 inference(modus_ponens,[status(thm)],[289, 288])).
% 5.66/5.86 tff(291,plain,(
% 5.66/5.86 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 5.66/5.86 inference(skolemize,[status(sab)],[290])).
% 5.66/5.86 tff(292,plain,
% 5.66/5.86 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 5.66/5.86 inference(modus_ponens,[status(thm)],[291, 287])).
% 5.66/5.86 tff(293,plain,
% 5.66/5.86 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1)))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(294,plain,
% 5.66/5.86 (multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[293, 292])).
% 5.66/5.86 tff(295,plain,
% 5.66/5.86 (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 5.66/5.86 inference(symmetry,[status(thm)],[91])).
% 5.66/5.86 tff(296,plain,
% 5.66/5.86 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 5.66/5.86 inference(transitivity,[status(thm)],[295, 85])).
% 5.66/5.86 tff(297,plain,
% 5.66/5.86 (multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(tptp_fun_X1_0(X0!2), one)),
% 5.66/5.86 inference(monotonicity,[status(thm)],[296])).
% 5.66/5.86 tff(298,plain,
% 5.66/5.86 (multiplication(tptp_fun_X1_0(X0!2), one) = multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), X1!1))),
% 5.66/5.86 inference(symmetry,[status(thm)],[297])).
% 5.66/5.86 tff(299,plain,
% 5.66/5.86 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 5.66/5.86 inference(bind,[status(th)],[])).
% 5.66/5.86 tff(300,plain,
% 5.66/5.86 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 5.66/5.86 inference(quant_intro,[status(thm)],[299])).
% 5.66/5.86 tff(301,plain,
% 5.66/5.86 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 5.66/5.86 inference(rewrite,[status(thm)],[])).
% 5.66/5.86 tff(302,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 5.66/5.86 tff(303,plain,
% 5.66/5.86 (![A: $i] : (multiplication(A, one) = A)),
% 5.66/5.86 inference(modus_ponens,[status(thm)],[302, 301])).
% 5.66/5.86 tff(304,plain,(
% 5.66/5.86 ![A: $i] : (multiplication(A, one) = A)),
% 5.66/5.86 inference(skolemize,[status(sab)],[303])).
% 5.66/5.86 tff(305,plain,
% 5.66/5.86 (![A: $i] : (multiplication(A, one) = A)),
% 5.66/5.86 inference(modus_ponens,[status(thm)],[304, 300])).
% 5.66/5.86 tff(306,plain,
% 5.66/5.86 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(307,plain,
% 5.66/5.86 (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2)),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[306, 305])).
% 5.66/5.86 tff(308,plain,
% 5.66/5.86 (tptp_fun_X1_0(X0!2) = multiplication(tptp_fun_X1_0(X0!2), one)),
% 5.66/5.86 inference(symmetry,[status(thm)],[307])).
% 5.66/5.86 tff(309,plain,
% 5.66/5.86 (tptp_fun_X1_0(X0!2) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.86 inference(transitivity,[status(thm)],[308, 298, 294, 285, 267])).
% 5.66/5.86 tff(310,plain,
% 5.66/5.86 (addition(tptp_fun_X1_0(X0!2), one) = addition(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(c(X0!2), c(X1!1))), one)),
% 5.66/5.86 inference(monotonicity,[status(thm)],[309])).
% 5.66/5.86 tff(311,plain,
% 5.66/5.86 (addition(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(c(X0!2), c(X1!1))), one) = addition(tptp_fun_X1_0(X0!2), one)),
% 5.66/5.86 inference(symmetry,[status(thm)],[310])).
% 5.66/5.86 tff(312,plain,
% 5.66/5.86 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), addition(multiplication(c(X0!2), c(X1!1)), one)) = addition(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(c(X0!2), c(X1!1))), one))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(313,plain,
% 5.66/5.86 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), addition(multiplication(c(X0!2), c(X1!1)), one)) = addition(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(c(X0!2), c(X1!1))), one)),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[312, 202])).
% 5.66/5.86 tff(314,plain,
% 5.66/5.86 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), c(X1!1)), one) = addition(one, multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(315,plain,
% 5.66/5.86 (addition(multiplication(c(X0!2), c(X1!1)), one) = addition(one, multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[314, 7])).
% 5.66/5.86 tff(316,plain,
% 5.66/5.86 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), addition(multiplication(c(X0!2), c(X1!1)), one)) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), addition(one, multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.86 inference(monotonicity,[status(thm)],[315])).
% 5.66/5.86 tff(317,plain,
% 5.66/5.86 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), addition(one, multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), addition(multiplication(c(X0!2), c(X1!1)), one))),
% 5.66/5.86 inference(symmetry,[status(thm)],[316])).
% 5.66/5.86 tff(318,plain,
% 5.66/5.86 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), addition(one, multiplication(c(X0!2), c(X1!1)))) = addition(addition(one, multiplication(c(X0!2), c(X1!1))), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(319,plain,
% 5.66/5.86 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), addition(one, multiplication(c(X0!2), c(X1!1)))) = addition(addition(one, multiplication(c(X0!2), c(X1!1))), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[318, 7])).
% 5.66/5.86 tff(320,plain,
% 5.66/5.86 (addition(addition(one, multiplication(c(X0!2), c(X1!1))), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), addition(one, multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.86 inference(symmetry,[status(thm)],[319])).
% 5.66/5.86 tff(321,plain,
% 5.66/5.86 ((~![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(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1))), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(322,plain,
% 5.66/5.86 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1))), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[321, 202])).
% 5.66/5.86 tff(323,plain,
% 5.66/5.86 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(X0!2, c(X0!2))),
% 5.66/5.86 inference(symmetry,[status(thm)],[179])).
% 5.66/5.86 tff(324,plain,
% 5.66/5.86 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 5.66/5.86 inference(monotonicity,[status(thm)],[323])).
% 5.66/5.86 tff(325,plain,
% 5.66/5.86 ((~![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)), X1!1) = addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(326,plain,
% 5.66/5.86 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1) = addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[325, 129])).
% 5.66/5.86 tff(327,plain,
% 5.66/5.86 (addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1)),
% 5.66/5.86 inference(symmetry,[status(thm)],[326])).
% 5.66/5.86 tff(328,plain,
% 5.66/5.86 (addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = X1!1),
% 5.66/5.86 inference(transitivity,[status(thm)],[327, 324, 181, 191])).
% 5.66/5.86 tff(329,plain,
% 5.66/5.86 (addition(tptp_fun_X1_0(X1!1), addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1))) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 5.66/5.86 inference(monotonicity,[status(thm)],[328])).
% 5.66/5.86 tff(330,plain,
% 5.66/5.86 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X1!1), addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1))) = addition(addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1)))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(331,plain,
% 5.66/5.86 (addition(tptp_fun_X1_0(X1!1), addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1))) = addition(addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[330, 202])).
% 5.66/5.86 tff(332,plain,
% 5.66/5.86 (addition(addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = addition(tptp_fun_X1_0(X1!1), addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)))),
% 5.66/5.86 inference(symmetry,[status(thm)],[331])).
% 5.66/5.86 tff(333,plain,
% 5.66/5.86 (addition(addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)) = addition(addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 5.66/5.86 inference(monotonicity,[status(thm)],[280])).
% 5.66/5.86 tff(334,plain,
% 5.66/5.86 (addition(addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)) = one),
% 5.66/5.86 inference(transitivity,[status(thm)],[333, 332, 329, 295, 85])).
% 5.66/5.86 tff(335,plain,
% 5.66/5.86 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), one)),
% 5.66/5.86 inference(monotonicity,[status(thm)],[334])).
% 5.66/5.86 tff(336,plain,
% 5.66/5.86 (addition(multiplication(c(X0!2), c(X1!1)), one) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)))),
% 5.66/5.86 inference(symmetry,[status(thm)],[335])).
% 5.66/5.86 tff(337,plain,
% 5.66/5.86 (addition(one, multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), one)),
% 5.66/5.86 inference(symmetry,[status(thm)],[315])).
% 5.66/5.86 tff(338,plain,
% 5.66/5.86 (addition(one, multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1))), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))),
% 5.66/5.86 inference(transitivity,[status(thm)],[337, 336, 322])).
% 5.66/5.86 tff(339,plain,
% 5.66/5.86 (addition(addition(one, multiplication(c(X0!2), c(X1!1))), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1))), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))),
% 5.66/5.86 inference(monotonicity,[status(thm)],[338])).
% 5.66/5.86 tff(340,plain,
% 5.66/5.86 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1))), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)) = addition(addition(one, multiplication(c(X0!2), c(X1!1))), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))),
% 5.66/5.86 inference(symmetry,[status(thm)],[339])).
% 5.66/5.86 tff(341,plain,
% 5.66/5.86 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1))), addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1))), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(342,plain,
% 5.66/5.86 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1))), addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1))), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[341, 202])).
% 5.66/5.86 tff(343,plain,
% 5.66/5.86 (addition(c(X0!2), c(X0!2)) = c(multiplication(X0!2, X0!2))),
% 5.66/5.86 inference(symmetry,[status(thm)],[249])).
% 5.66/5.86 tff(344,plain,
% 5.66/5.86 (addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = tptp_fun_X1_0(X0!2)),
% 5.66/5.86 inference(transitivity,[status(thm)],[228, 343, 255, 178])).
% 5.66/5.86 tff(345,plain,
% 5.66/5.86 (multiplication(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), X1!1) = multiplication(tptp_fun_X1_0(X0!2), X1!1)),
% 5.66/5.86 inference(monotonicity,[status(thm)],[344])).
% 5.66/5.86 tff(346,plain,
% 5.66/5.86 ((~![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), tptp_fun_X1_0(X0!2)), X1!1) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(347,plain,
% 5.66/5.86 (multiplication(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), X1!1) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[346, 129])).
% 5.66/5.86 tff(348,plain,
% 5.66/5.86 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), X1!1)),
% 5.66/5.86 inference(symmetry,[status(thm)],[347])).
% 5.66/5.86 tff(349,plain,
% 5.66/5.86 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 5.66/5.86 inference(monotonicity,[status(thm)],[280, 280])).
% 5.66/5.86 tff(350,plain,
% 5.66/5.86 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)),
% 5.66/5.86 inference(transitivity,[status(thm)],[349, 348, 345, 268, 278])).
% 5.66/5.86 tff(351,plain,
% 5.66/5.86 ((~![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(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1)))),
% 5.66/5.86 inference(quant_inst,[status(thm)],[])).
% 5.66/5.86 tff(352,plain,
% 5.66/5.86 (addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1))),
% 5.66/5.86 inference(unit_resolution,[status(thm)],[351, 202])).
% 5.66/5.86 tff(353,plain,
% 5.66/5.86 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1))), addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))),
% 5.66/5.86 inference(monotonicity,[status(thm)],[352, 350])).
% 5.66/5.86 tff(354,plain,
% 5.66/5.86 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), multiplication(X0!2, X1!1))), addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)))),
% 5.66/5.87 inference(symmetry,[status(thm)],[353])).
% 5.66/5.87 tff(355,plain,
% 5.66/5.87 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(356,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[355, 202])).
% 5.66/5.87 tff(357,plain,
% 5.66/5.87 (addition(multiplication(X0!2, X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 5.66/5.87 inference(monotonicity,[status(thm)],[280])).
% 5.66/5.87 tff(358,plain,
% 5.66/5.87 (addition(multiplication(X0!2, X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)) = X1!1),
% 5.66/5.87 inference(transitivity,[status(thm)],[357, 327, 324, 181, 191])).
% 5.66/5.87 tff(359,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), X1!1)),
% 5.66/5.87 inference(monotonicity,[status(thm)],[358])).
% 5.66/5.87 tff(360,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), X1!1) = addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)))),
% 5.66/5.87 inference(symmetry,[status(thm)],[359])).
% 5.66/5.87 tff(361,plain,
% 5.66/5.87 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 5.66/5.87 inference(bind,[status(th)],[])).
% 5.66/5.87 tff(362,plain,
% 5.66/5.87 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 5.66/5.87 inference(quant_intro,[status(thm)],[361])).
% 5.66/5.87 tff(363,plain,
% 5.66/5.87 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 5.66/5.87 inference(rewrite,[status(thm)],[])).
% 5.66/5.87 tff(364,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 5.66/5.87 tff(365,plain,
% 5.66/5.87 (![A: $i] : (addition(A, A) = A)),
% 5.66/5.87 inference(modus_ponens,[status(thm)],[364, 363])).
% 5.66/5.87 tff(366,plain,(
% 5.66/5.87 ![A: $i] : (addition(A, A) = A)),
% 5.66/5.87 inference(skolemize,[status(sab)],[365])).
% 5.66/5.87 tff(367,plain,
% 5.66/5.87 (![A: $i] : (addition(A, A) = A)),
% 5.66/5.87 inference(modus_ponens,[status(thm)],[366, 362])).
% 5.66/5.87 tff(368,plain,
% 5.66/5.87 ((~![A: $i] : (addition(A, A) = A)) | (addition(X1!1, X1!1) = X1!1)),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(369,plain,
% 5.66/5.87 (addition(X1!1, X1!1) = X1!1),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[368, 367])).
% 5.66/5.87 tff(370,plain,
% 5.66/5.87 (X1!1 = addition(X1!1, X1!1)),
% 5.66/5.87 inference(symmetry,[status(thm)],[369])).
% 5.66/5.87 tff(371,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), X1!1) = addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), addition(X1!1, X1!1))),
% 5.66/5.87 inference(monotonicity,[status(thm)],[370])).
% 5.66/5.87 tff(372,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), addition(X1!1, X1!1)) = addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), X1!1)),
% 5.66/5.87 inference(symmetry,[status(thm)],[371])).
% 5.66/5.87 tff(373,plain,
% 5.66/5.87 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), addition(X1!1, X1!1)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), X1!1), X1!1))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(374,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), addition(X1!1, X1!1)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), X1!1), X1!1)),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[373, 202])).
% 5.66/5.87 tff(375,plain,
% 5.66/5.87 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), X1!1), X1!1) = addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), addition(X1!1, X1!1))),
% 5.66/5.87 inference(symmetry,[status(thm)],[374])).
% 5.66/5.87 tff(376,plain,
% 5.66/5.87 ((~![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(X1!1, tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), tptp_fun_X1_0(X1!1)))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(377,plain,
% 5.66/5.87 (addition(multiplication(c(X0!2), c(X1!1)), addition(X1!1, tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), tptp_fun_X1_0(X1!1))),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[376, 202])).
% 5.66/5.87 tff(378,plain,
% 5.66/5.87 (addition(multiplication(c(X0!2), c(X1!1)), addition(X1!1, tptp_fun_X1_0(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), one)),
% 5.66/5.87 inference(monotonicity,[status(thm)],[85])).
% 5.66/5.87 tff(379,plain,
% 5.66/5.87 (addition(multiplication(c(X0!2), c(X1!1)), one) = addition(multiplication(c(X0!2), c(X1!1)), addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 5.66/5.87 inference(symmetry,[status(thm)],[378])).
% 5.66/5.87 tff(380,plain,
% 5.66/5.87 (one = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 5.66/5.87 inference(transitivity,[status(thm)],[86, 91])).
% 5.66/5.87 tff(381,plain,
% 5.66/5.87 (addition(multiplication(c(X0!2), c(X1!1)), one) = addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), X1!1))),
% 5.66/5.87 inference(monotonicity,[status(thm)],[380])).
% 5.66/5.87 tff(382,plain,
% 5.66/5.87 (addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), X1!1)) = addition(multiplication(c(X0!2), c(X1!1)), one)),
% 5.66/5.87 inference(symmetry,[status(thm)],[381])).
% 5.66/5.87 tff(383,plain,
% 5.66/5.87 ((~![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(tptp_fun_X1_0(X1!1), X1!1)) = addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), X1!1))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(384,plain,
% 5.66/5.87 (addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), X1!1)) = addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), X1!1)),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[383, 202])).
% 5.66/5.87 tff(385,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), X1!1) = addition(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X1!1), X1!1))),
% 5.66/5.87 inference(symmetry,[status(thm)],[384])).
% 5.66/5.87 tff(386,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), X1!1) = addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), tptp_fun_X1_0(X1!1))),
% 5.66/5.87 inference(transitivity,[status(thm)],[385, 382, 379, 377])).
% 5.66/5.87 tff(387,plain,
% 5.66/5.87 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), X1!1), X1!1) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), tptp_fun_X1_0(X1!1)), X1!1)),
% 5.66/5.87 inference(monotonicity,[status(thm)],[386])).
% 5.66/5.87 tff(388,plain,
% 5.66/5.87 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), tptp_fun_X1_0(X1!1)), X1!1) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), X1!1), X1!1)),
% 5.66/5.87 inference(symmetry,[status(thm)],[387])).
% 5.66/5.87 tff(389,plain,
% 5.66/5.87 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), addition(tptp_fun_X1_0(X1!1), X1!1)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), tptp_fun_X1_0(X1!1)), X1!1))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(390,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), addition(tptp_fun_X1_0(X1!1), X1!1)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), tptp_fun_X1_0(X1!1)), X1!1)),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[389, 202])).
% 5.66/5.87 tff(391,plain,
% 5.66/5.87 (multiplication(addition(X0!2, c(X0!2)), X1!1) = X1!1),
% 5.66/5.87 inference(transitivity,[status(thm)],[181, 191])).
% 5.66/5.87 tff(392,plain,
% 5.66/5.87 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(X1!1, multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.87 inference(monotonicity,[status(thm)],[391])).
% 5.66/5.87 tff(393,plain,
% 5.66/5.87 (addition(X1!1, multiplication(c(X0!2), c(X1!1))) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.87 inference(symmetry,[status(thm)],[392])).
% 5.66/5.87 tff(394,plain,
% 5.66/5.87 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!1, multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), X1!1))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(395,plain,
% 5.66/5.87 (addition(X1!1, multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), X1!1)),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[394, 7])).
% 5.66/5.87 tff(396,plain,
% 5.66/5.87 (addition(multiplication(c(X0!2), c(X1!1)), X1!1) = addition(X1!1, multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.87 inference(symmetry,[status(thm)],[395])).
% 5.66/5.87 tff(397,plain,
% 5.66/5.87 (addition(multiplication(c(X0!2), c(X1!1)), X1!1) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.87 inference(transitivity,[status(thm)],[396, 393])).
% 5.66/5.87 tff(398,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), addition(tptp_fun_X1_0(X1!1), X1!1)) = addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))), one)),
% 5.66/5.87 inference(monotonicity,[status(thm)],[397, 296])).
% 5.66/5.87 tff(399,plain,
% 5.66/5.87 (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))), one) = addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), addition(tptp_fun_X1_0(X1!1), X1!1))),
% 5.66/5.87 inference(symmetry,[status(thm)],[398])).
% 5.66/5.87 tff(400,plain,
% 5.66/5.87 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(401,plain,
% 5.66/5.87 (addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[400, 202])).
% 5.66/5.87 tff(402,plain,
% 5.66/5.87 (addition(addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.87 inference(symmetry,[status(thm)],[401])).
% 5.66/5.87 tff(403,plain,
% 5.66/5.87 (addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 5.66/5.87 inference(transitivity,[status(thm)],[327, 324])).
% 5.66/5.87 tff(404,plain,
% 5.66/5.87 (addition(addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.87 inference(monotonicity,[status(thm)],[403])).
% 5.66/5.87 tff(405,plain,
% 5.66/5.87 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.87 inference(symmetry,[status(thm)],[404])).
% 5.66/5.87 tff(406,plain,
% 5.66/5.87 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.87 inference(transitivity,[status(thm)],[405, 402])).
% 5.66/5.87 tff(407,plain,
% 5.66/5.87 (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))), one) = addition(addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), one)),
% 5.66/5.87 inference(monotonicity,[status(thm)],[406])).
% 5.66/5.87 tff(408,plain,
% 5.66/5.87 (addition(addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), one) = addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))), one)),
% 5.66/5.87 inference(symmetry,[status(thm)],[407])).
% 5.66/5.87 tff(409,plain,
% 5.66/5.87 ((~![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(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one)) = addition(addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), one))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(410,plain,
% 5.66/5.87 (addition(multiplication(X0!2, X1!1), addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one)) = addition(addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), one)),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[409, 202])).
% 5.66/5.87 tff(411,plain,
% 5.66/5.87 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), X1!1))),
% 5.66/5.87 inference(symmetry,[status(thm)],[294])).
% 5.66/5.87 tff(412,plain,
% 5.66/5.87 (multiplication(tptp_fun_X1_0(X0!2), X1!1) = multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)),
% 5.66/5.87 inference(transitivity,[status(thm)],[268, 278])).
% 5.66/5.87 tff(413,plain,
% 5.66/5.87 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.87 inference(monotonicity,[status(thm)],[412])).
% 5.66/5.87 tff(414,plain,
% 5.66/5.87 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = tptp_fun_X1_0(X0!2)),
% 5.66/5.87 inference(transitivity,[status(thm)],[413, 266, 284, 411, 297, 307])).
% 5.66/5.87 tff(415,plain,
% 5.66/5.87 (addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one) = addition(tptp_fun_X1_0(X0!2), one)),
% 5.66/5.87 inference(monotonicity,[status(thm)],[414])).
% 5.66/5.87 tff(416,plain,
% 5.66/5.87 (addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one) = one),
% 5.66/5.87 inference(transitivity,[status(thm)],[415, 264, 261, 259, 226, 120])).
% 5.66/5.87 tff(417,plain,
% 5.66/5.87 (addition(multiplication(X0!2, X1!1), addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one)) = addition(multiplication(X0!2, X1!1), one)),
% 5.66/5.87 inference(monotonicity,[status(thm)],[416])).
% 5.66/5.87 tff(418,plain,
% 5.66/5.87 (addition(multiplication(X0!2, X1!1), one) = addition(multiplication(X0!2, X1!1), addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one))),
% 5.66/5.87 inference(symmetry,[status(thm)],[417])).
% 5.66/5.87 tff(419,plain,
% 5.66/5.87 (addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 5.66/5.87 inference(monotonicity,[status(thm)],[414])).
% 5.66/5.87 tff(420,plain,
% 5.66/5.87 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2)),
% 5.66/5.87 inference(symmetry,[status(thm)],[419])).
% 5.66/5.87 tff(421,plain,
% 5.66/5.87 (one = addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2)),
% 5.66/5.87 inference(transitivity,[status(thm)],[163, 168, 420])).
% 5.66/5.87 tff(422,plain,
% 5.66/5.87 (addition(multiplication(X0!2, X1!1), one) = addition(multiplication(X0!2, X1!1), addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2))),
% 5.66/5.87 inference(monotonicity,[status(thm)],[421])).
% 5.66/5.87 tff(423,plain,
% 5.66/5.87 (addition(multiplication(X0!2, X1!1), addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2)) = addition(multiplication(X0!2, X1!1), one)),
% 5.66/5.87 inference(symmetry,[status(thm)],[422])).
% 5.66/5.87 tff(424,plain,
% 5.66/5.87 ((~![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(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2)) = addition(addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), X0!2))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(425,plain,
% 5.66/5.87 (addition(multiplication(X0!2, X1!1), addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2)) = addition(addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), X0!2)),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[424, 202])).
% 5.66/5.87 tff(426,plain,
% 5.66/5.87 (addition(addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), X0!2) = addition(multiplication(X0!2, X1!1), addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2))),
% 5.66/5.87 inference(symmetry,[status(thm)],[425])).
% 5.66/5.87 tff(427,plain,
% 5.66/5.87 (addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(c(X0!2), c(X1!1)), X1!1)),
% 5.66/5.87 inference(transitivity,[status(thm)],[401, 404, 392, 395])).
% 5.66/5.87 tff(428,plain,
% 5.66/5.87 (addition(addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), X0!2) = addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2)),
% 5.66/5.87 inference(monotonicity,[status(thm)],[427])).
% 5.66/5.87 tff(429,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2) = addition(addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), X0!2)),
% 5.66/5.87 inference(symmetry,[status(thm)],[428])).
% 5.66/5.87 tff(430,plain,
% 5.66/5.87 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!2, X0!2) = X0!2)),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(431,plain,
% 5.66/5.87 (addition(X0!2, X0!2) = X0!2),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[430, 367])).
% 5.66/5.87 tff(432,plain,
% 5.66/5.87 (X0!2 = addition(X0!2, X0!2)),
% 5.66/5.87 inference(symmetry,[status(thm)],[431])).
% 5.66/5.87 tff(433,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2) = addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), addition(X0!2, X0!2))),
% 5.66/5.87 inference(monotonicity,[status(thm)],[432])).
% 5.66/5.87 tff(434,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), addition(X0!2, X0!2)) = addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2)),
% 5.66/5.87 inference(symmetry,[status(thm)],[433])).
% 5.66/5.87 tff(435,plain,
% 5.66/5.87 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), addition(X0!2, X0!2)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2), X0!2))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(436,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), addition(X0!2, X0!2)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2), X0!2)),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[435, 202])).
% 5.66/5.87 tff(437,plain,
% 5.66/5.87 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2), X0!2) = addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), addition(X0!2, X0!2))),
% 5.66/5.87 inference(symmetry,[status(thm)],[436])).
% 5.66/5.87 tff(438,plain,
% 5.66/5.87 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), 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))))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(439,plain,
% 5.66/5.87 (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), 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)))),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[438, 202])).
% 5.66/5.87 tff(440,plain,
% 5.66/5.87 (multiplication(addition(X1!1, c(X1!1)), X0!2) = X0!2),
% 5.66/5.87 inference(transitivity,[status(thm)],[253, 251])).
% 5.66/5.87 tff(441,plain,
% 5.66/5.87 (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(X0!2, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.87 inference(monotonicity,[status(thm)],[440])).
% 5.66/5.87 tff(442,plain,
% 5.66/5.87 (addition(X0!2, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(addition(X1!1, c(X1!1)), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.87 inference(symmetry,[status(thm)],[441])).
% 5.66/5.87 tff(443,plain,
% 5.66/5.87 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(444,plain,
% 5.66/5.87 (addition(X0!2, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2)),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[443, 7])).
% 5.66/5.87 tff(445,plain,
% 5.66/5.87 (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2) = addition(X0!2, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.87 inference(symmetry,[status(thm)],[444])).
% 5.66/5.87 tff(446,plain,
% 5.66/5.87 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), X1!1)),
% 5.66/5.87 inference(transitivity,[status(thm)],[392, 395])).
% 5.66/5.87 tff(447,plain,
% 5.66/5.87 (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2) = addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2)),
% 5.66/5.87 inference(monotonicity,[status(thm)],[446])).
% 5.66/5.87 tff(448,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2) = addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2)),
% 5.66/5.87 inference(symmetry,[status(thm)],[447])).
% 5.66/5.87 tff(449,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), 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)))),
% 5.66/5.87 inference(transitivity,[status(thm)],[448, 445, 442, 439])).
% 5.66/5.87 tff(450,plain,
% 5.66/5.87 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2), X0!2) = addition(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))), X0!2)),
% 5.66/5.87 inference(monotonicity,[status(thm)],[449])).
% 5.66/5.87 tff(451,plain,
% 5.66/5.87 (addition(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))), X0!2) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2), X0!2)),
% 5.66/5.87 inference(symmetry,[status(thm)],[450])).
% 5.66/5.87 tff(452,plain,
% 5.66/5.87 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), one) = addition(one, addition(multiplication(c(X0!2), c(X1!1)), X1!1)))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(453,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), one) = addition(one, addition(multiplication(c(X0!2), c(X1!1)), X1!1))),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[452, 7])).
% 5.66/5.87 tff(454,plain,
% 5.66/5.87 (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), one) = addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))), one)),
% 5.66/5.87 inference(monotonicity,[status(thm)],[397])).
% 5.66/5.87 tff(455,plain,
% 5.66/5.87 (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))), one) = addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), one)),
% 5.66/5.87 inference(symmetry,[status(thm)],[454])).
% 5.66/5.87 tff(456,plain,
% 5.66/5.87 (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(addition(X1!1, c(X1!1)), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.87 inference(symmetry,[status(thm)],[439])).
% 5.66/5.87 tff(457,plain,
% 5.66/5.87 (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(one, addition(multiplication(c(X0!2), c(X1!1)), X1!1))),
% 5.66/5.87 inference(transitivity,[status(thm)],[456, 441, 444, 447, 429, 426, 423, 418, 410, 408, 455, 453])).
% 5.66/5.87 tff(458,plain,
% 5.66/5.87 (addition(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))), X0!2) = addition(addition(one, addition(multiplication(c(X0!2), c(X1!1)), X1!1)), X0!2)),
% 5.66/5.87 inference(monotonicity,[status(thm)],[457])).
% 5.66/5.87 tff(459,plain,
% 5.66/5.87 (addition(addition(one, addition(multiplication(c(X0!2), c(X1!1)), X1!1)), X0!2) = addition(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))), X0!2)),
% 5.66/5.87 inference(symmetry,[status(thm)],[458])).
% 5.66/5.87 tff(460,plain,
% 5.66/5.87 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2)) = addition(addition(one, addition(multiplication(c(X0!2), c(X1!1)), X1!1)), X0!2))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(461,plain,
% 5.66/5.87 (addition(one, addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2)) = addition(addition(one, addition(multiplication(c(X0!2), c(X1!1)), X1!1)), X0!2)),
% 5.66/5.87 inference(unit_resolution,[status(thm)],[460, 202])).
% 5.66/5.87 tff(462,plain,
% 5.66/5.87 (addition(one, addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2)) = addition(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))))),
% 5.66/5.87 inference(monotonicity,[status(thm)],[449])).
% 5.66/5.87 tff(463,plain,
% 5.66/5.87 (addition(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(one, addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2))),
% 5.66/5.87 inference(symmetry,[status(thm)],[462])).
% 5.66/5.87 tff(464,plain,
% 5.66/5.87 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(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) = addition(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)))))),
% 5.66/5.87 inference(quant_inst,[status(thm)],[])).
% 5.66/5.87 tff(465,plain,
% 5.66/5.87 (addition(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) = addition(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))))),
% 5.66/5.88 inference(unit_resolution,[status(thm)],[464, 7])).
% 5.66/5.88 tff(466,plain,
% 5.66/5.88 (addition(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),
% 5.66/5.88 inference(transitivity,[status(thm)],[465, 463, 461, 459, 451, 437, 434, 429, 426, 423, 418, 410, 408, 399, 390, 388, 375, 372, 360, 356, 354, 342, 340, 320, 317, 313, 311, 264, 261, 259, 226, 120])).
% 5.66/5.88 tff(467,assumption,(~leq(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)), introduced(assumption)).
% 5.66/5.88 tff(468,plain,
% 5.66/5.88 ((~(leq(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) <=> (addition(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))) | leq(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) | (~(addition(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))),
% 5.66/5.88 inference(tautology,[status(thm)],[])).
% 5.66/5.88 tff(469,plain,
% 5.66/5.88 ((~(leq(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) <=> (addition(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(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))),
% 5.66/5.88 inference(unit_resolution,[status(thm)],[468, 467])).
% 5.66/5.88 tff(470,plain,
% 5.66/5.88 (~(addition(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)),
% 5.66/5.88 inference(unit_resolution,[status(thm)],[469, 225])).
% 5.66/5.88 tff(471,plain,
% 5.66/5.88 ($false),
% 5.66/5.88 inference(unit_resolution,[status(thm)],[470, 466])).
% 5.66/5.88 tff(472,plain,(leq(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)), inference(lemma,lemma(discharge,[]))).
% 5.66/5.88 tff(473,plain,
% 5.66/5.88 ((~(leq(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) <=> (addition(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))) | (~leq(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)) | (addition(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)),
% 5.66/5.88 inference(tautology,[status(thm)],[])).
% 5.66/5.88 tff(474,plain,
% 5.66/5.88 ((~(leq(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) <=> (addition(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(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)),
% 5.66/5.88 inference(unit_resolution,[status(thm)],[473, 472])).
% 5.66/5.88 tff(475,plain,
% 5.66/5.88 (addition(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),
% 5.66/5.88 inference(unit_resolution,[status(thm)],[474, 225])).
% 5.66/5.88 tff(476,plain,
% 5.66/5.88 (addition(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(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)),
% 5.66/5.88 inference(symmetry,[status(thm)],[465])).
% 5.66/5.88 tff(477,plain,
% 5.66/5.88 (addition(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),
% 5.66/5.88 inference(transitivity,[status(thm)],[476, 475])).
% 5.66/5.88 tff(478,plain,
% 5.66/5.88 ((addition(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(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 = 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))))),
% 5.66/5.88 inference(monotonicity,[status(thm)],[477])).
% 5.66/5.88 tff(479,plain,
% 5.66/5.88 ((addition(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(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(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)),
% 5.66/5.88 inference(transitivity,[status(thm)],[478, 216])).
% 5.66/5.88 tff(480,plain,
% 5.66/5.88 ((~(addition(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(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(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))),
% 5.66/5.88 inference(monotonicity,[status(thm)],[479])).
% 5.66/5.88 tff(481,plain,
% 5.66/5.88 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(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(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(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)))))),
% 5.66/5.88 inference(quant_inst,[status(thm)],[])).
% 5.66/5.88 tff(482,plain,
% 5.66/5.88 (leq(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(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(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))))),
% 5.66/5.88 inference(unit_resolution,[status(thm)],[481, 223])).
% 5.66/5.88 tff(483,plain,
% 5.66/5.88 ((~(~((~leq(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))))) | (~leq(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))))) <=> ((~leq(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))))) | (~leq(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)))),
% 5.66/5.88 inference(rewrite,[status(thm)],[])).
% 5.66/5.88 tff(484,plain,
% 5.66/5.88 ((leq(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)))) & leq(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)) <=> (~((~leq(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))))) | (~leq(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))))),
% 5.66/5.88 inference(rewrite,[status(thm)],[])).
% 5.66/5.88 tff(485,plain,
% 5.66/5.88 ((~(leq(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)))) & leq(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))) <=> (~(~((~leq(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))))) | (~leq(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)))))),
% 5.66/5.88 inference(monotonicity,[status(thm)],[484])).
% 5.66/5.88 tff(486,plain,
% 5.66/5.88 ((~(leq(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)))) & leq(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))) <=> ((~leq(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))))) | (~leq(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)))),
% 5.66/5.88 inference(transitivity,[status(thm)],[485, 483])).
% 5.66/5.88 tff(487,plain,
% 5.66/5.88 (~(leq(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)))) & leq(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))),
% 5.66/5.88 inference(or_elim,[status(thm)],[18])).
% 5.66/5.88 tff(488,plain,
% 5.66/5.88 ((~leq(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))))) | (~leq(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))),
% 5.66/5.88 inference(modus_ponens,[status(thm)],[487, 486])).
% 5.66/5.88 tff(489,plain,
% 5.66/5.88 (~leq(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))))),
% 5.66/5.88 inference(unit_resolution,[status(thm)],[488, 472])).
% 5.66/5.88 tff(490,plain,
% 5.66/5.88 ((~(leq(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(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(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)))))) | leq(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(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(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)))))),
% 5.66/5.88 inference(tautology,[status(thm)],[])).
% 5.66/5.88 tff(491,plain,
% 5.66/5.88 ((~(leq(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(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(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(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(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)))))),
% 5.66/5.88 inference(unit_resolution,[status(thm)],[490, 489])).
% 5.66/5.88 tff(492,plain,
% 5.66/5.88 (~(addition(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(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))))),
% 5.66/5.88 inference(unit_resolution,[status(thm)],[491, 482])).
% 5.66/5.88 tff(493,plain,
% 5.66/5.88 (~(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)),
% 5.66/5.88 inference(modus_ponens,[status(thm)],[492, 480])).
% 5.66/5.88 tff(494,plain,
% 5.66/5.88 (~(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)),
% 5.66/5.88 inference(modus_ponens,[status(thm)],[493, 215])).
% 5.66/5.88 tff(495,plain,
% 5.66/5.88 (((~(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)),
% 5.66/5.88 inference(tautology,[status(thm)],[])).
% 5.66/5.88 tff(496,plain,
% 5.66/5.88 ((~(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))),
% 5.66/5.88 inference(unit_resolution,[status(thm)],[495, 494])).
% 5.66/5.88 tff(497,plain,
% 5.66/5.88 ((((~(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)))) | (~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))))),
% 5.66/5.88 inference(tautology,[status(thm)],[])).
% 5.66/5.88 tff(498,plain,
% 5.66/5.88 (~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)))),
% 5.66/5.88 inference(unit_resolution,[status(thm)],[497, 496, 207])).
% 5.66/5.88 tff(499,plain,
% 5.66/5.88 (c(multiplication(addition(X0!2, c(X0!2)), X1!1)) = c(X1!1)),
% 5.66/5.88 inference(monotonicity,[status(thm)],[391])).
% 5.66/5.88 tff(500,plain,
% 5.66/5.88 (c(X1!1) = c(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 5.66/5.88 inference(symmetry,[status(thm)],[499])).
% 5.66/5.88 tff(501,plain,
% 5.66/5.88 (c(multiplication(addition(X1!1, c(X1!1)), X0!2)) = c(X0!2)),
% 5.66/5.88 inference(monotonicity,[status(thm)],[440])).
% 5.66/5.88 tff(502,plain,
% 5.66/5.88 (c(X0!2) = c(multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 5.66/5.88 inference(symmetry,[status(thm)],[501])).
% 5.66/5.88 tff(503,plain,
% 5.66/5.88 (multiplication(c(X0!2), c(X1!1)) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 5.66/5.88 inference(monotonicity,[status(thm)],[502, 500])).
% 5.66/5.88 tff(504,plain,
% 5.66/5.88 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(X0!2), c(X1!1))),
% 5.66/5.88 inference(symmetry,[status(thm)],[503])).
% 5.66/5.88 tff(505,plain,
% 5.66/5.88 (test(multiplication(addition(X1!1, c(X1!1)), X0!2)) <=> test(X0!2)),
% 5.66/5.88 inference(monotonicity,[status(thm)],[440])).
% 5.66/5.88 tff(506,plain,
% 5.66/5.88 (test(X0!2) <=> test(multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 5.66/5.88 inference(symmetry,[status(thm)],[505])).
% 5.66/5.88 tff(507,plain,
% 5.66/5.88 (test(multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 5.66/5.88 inference(modus_ponens,[status(thm)],[112, 506])).
% 5.66/5.88 tff(508,plain,
% 5.66/5.88 (test(multiplication(addition(X0!2, c(X0!2)), X1!1)) <=> test(X1!1)),
% 5.66/5.88 inference(monotonicity,[status(thm)],[391])).
% 5.66/5.88 tff(509,plain,
% 5.66/5.88 (test(X1!1) <=> test(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 5.66/5.88 inference(symmetry,[status(thm)],[508])).
% 5.66/5.88 tff(510,plain,
% 5.66/5.88 (test(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 5.66/5.88 inference(modus_ponens,[status(thm)],[20, 509])).
% 5.66/5.88 tff(511,plain,
% 5.66/5.88 (^[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))))),
% 5.66/5.88 inference(bind,[status(th)],[])).
% 5.66/5.88 tff(512,plain,
% 5.66/5.88 (![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)))),
% 5.66/5.88 inference(quant_intro,[status(thm)],[511])).
% 5.66/5.88 tff(513,plain,
% 5.66/5.88 (^[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)))))),
% 5.66/5.88 inference(bind,[status(th)],[])).
% 5.66/5.88 tff(514,plain,
% 5.66/5.88 (![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)))),
% 5.66/5.88 inference(quant_intro,[status(thm)],[513])).
% 5.66/5.88 tff(515,plain,
% 5.66/5.88 (![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))))),
% 5.66/5.88 inference(rewrite,[status(thm)],[])).
% 5.66/5.88 tff(516,plain,
% 5.66/5.88 (^[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)))))),
% 5.66/5.88 inference(bind,[status(th)],[])).
% 5.66/5.88 tff(517,plain,
% 5.66/5.88 (![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))))),
% 5.66/5.88 inference(quant_intro,[status(thm)],[516])).
% 5.66/5.88 tff(518,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')).
% 5.66/5.88 tff(519,plain,
% 5.66/5.88 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 5.66/5.88 inference(modus_ponens,[status(thm)],[518, 517])).
% 5.66/5.88 tff(520,plain,
% 5.66/5.88 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 5.66/5.88 inference(modus_ponens,[status(thm)],[519, 515])).
% 5.66/5.88 tff(521,plain,(
% 5.66/5.88 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 5.66/5.88 inference(skolemize,[status(sab)],[520])).
% 5.66/5.88 tff(522,plain,
% 5.66/5.88 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 5.66/5.88 inference(modus_ponens,[status(thm)],[521, 514])).
% 5.66/5.88 tff(523,plain,
% 5.66/5.88 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 5.66/5.88 inference(modus_ponens,[status(thm)],[522, 512])).
% 5.66/5.88 tff(524,plain,
% 5.66/5.88 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(multiplication(addition(X0!2, c(X0!2)), X1!1))) | (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) | (~test(multiplication(addition(X1!1, c(X1!1)), X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(multiplication(addition(X0!2, c(X0!2)), X1!1))) | (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) | (~test(multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 5.66/5.88 inference(rewrite,[status(thm)],[])).
% 5.66/5.88 tff(525,plain,
% 5.66/5.88 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(multiplication(addition(X0!2, c(X0!2)), X1!1))) | (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) | (~test(multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 5.66/5.88 inference(quant_inst,[status(thm)],[])).
% 5.66/5.88 tff(526,plain,
% 5.66/5.88 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(multiplication(addition(X0!2, c(X0!2)), X1!1))) | (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) | (~test(multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 5.66/5.88 inference(modus_ponens,[status(thm)],[525, 524])).
% 5.66/5.89 tff(527,plain,
% 5.66/5.89 ((~test(multiplication(addition(X0!2, c(X0!2)), X1!1))) | (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) | (~test(multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[526, 523])).
% 5.66/5.89 tff(528,plain,
% 5.66/5.89 (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[527, 510, 507])).
% 5.66/5.89 tff(529,plain,
% 5.66/5.89 (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = c(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 5.66/5.89 inference(monotonicity,[status(thm)],[9])).
% 5.66/5.89 tff(530,plain,
% 5.66/5.89 (c(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, 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)))),
% 5.66/5.89 inference(symmetry,[status(thm)],[529])).
% 5.66/5.89 tff(531,plain,
% 5.66/5.89 (c(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))),
% 5.66/5.89 inference(transitivity,[status(thm)],[530, 528, 504])).
% 5.66/5.89 tff(532,plain,
% 5.66/5.89 ((~((c(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(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))))) | (~(c(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(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)))),
% 5.66/5.89 inference(tautology,[status(thm)],[])).
% 5.66/5.89 tff(533,plain,
% 5.66/5.89 ((~((c(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(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(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)))),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[532, 531])).
% 5.66/5.89 tff(534,plain,
% 5.66/5.89 (~((c(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(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))))),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[533, 498])).
% 5.66/5.89 tff(535,plain,
% 5.66/5.89 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) | ((c(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(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)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) | ((c(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(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)))))),
% 5.66/5.89 inference(rewrite,[status(thm)],[])).
% 5.66/5.89 tff(536,plain,
% 5.66/5.89 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) | ((c(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(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)))))),
% 5.66/5.89 inference(quant_inst,[status(thm)],[])).
% 5.66/5.89 tff(537,plain,
% 5.66/5.89 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) | ((c(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(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))))),
% 5.66/5.89 inference(modus_ponens,[status(thm)],[536, 535])).
% 5.66/5.89 tff(538,plain,
% 5.66/5.89 ((~test(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) | ((c(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(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))))),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[537, 30])).
% 5.66/5.89 tff(539,plain,
% 5.66/5.89 (~test(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[538, 534])).
% 5.66/5.89 tff(540,plain,
% 5.66/5.89 (^[X0: $i] : refl((test(X0) | (c(X0) = zero)) <=> (test(X0) | (c(X0) = zero)))),
% 5.66/5.89 inference(bind,[status(th)],[])).
% 5.66/5.89 tff(541,plain,
% 5.66/5.89 (![X0: $i] : (test(X0) | (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 5.66/5.89 inference(quant_intro,[status(thm)],[540])).
% 5.66/5.89 tff(542,plain,
% 5.66/5.89 (![X0: $i] : (test(X0) | (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 5.66/5.89 inference(rewrite,[status(thm)],[])).
% 5.66/5.89 tff(543,plain,
% 5.66/5.89 (^[X0: $i] : rewrite(((~test(X0)) => (c(X0) = zero)) <=> (test(X0) | (c(X0) = zero)))),
% 5.66/5.89 inference(bind,[status(th)],[])).
% 5.66/5.89 tff(544,plain,
% 5.66/5.89 (![X0: $i] : ((~test(X0)) => (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 5.66/5.89 inference(quant_intro,[status(thm)],[543])).
% 5.66/5.89 tff(545,axiom,(![X0: $i] : ((~test(X0)) => (c(X0) = zero))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_4')).
% 5.66/5.89 tff(546,plain,
% 5.66/5.89 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 5.66/5.89 inference(modus_ponens,[status(thm)],[545, 544])).
% 5.66/5.89 tff(547,plain,
% 5.66/5.89 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 5.66/5.89 inference(modus_ponens,[status(thm)],[546, 542])).
% 5.66/5.89 tff(548,plain,(
% 5.66/5.89 ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 5.66/5.89 inference(skolemize,[status(sab)],[547])).
% 5.66/5.89 tff(549,plain,
% 5.66/5.89 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 5.66/5.89 inference(modus_ponens,[status(thm)],[548, 541])).
% 5.66/5.89 tff(550,plain,
% 5.66/5.89 (((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) | (c(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero))) <=> ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) | (c(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero))),
% 5.66/5.89 inference(rewrite,[status(thm)],[])).
% 5.66/5.89 tff(551,plain,
% 5.66/5.89 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) | (c(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero))),
% 5.66/5.89 inference(quant_inst,[status(thm)],[])).
% 5.66/5.89 tff(552,plain,
% 5.66/5.89 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) | (c(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)),
% 5.66/5.89 inference(modus_ponens,[status(thm)],[551, 550])).
% 5.66/5.89 tff(553,plain,
% 5.66/5.89 (test(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) | (c(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[552, 549])).
% 5.66/5.89 tff(554,plain,
% 5.66/5.89 (c(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[553, 539])).
% 5.66/5.89 tff(555,plain,
% 5.66/5.89 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))) = c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 5.66/5.89 inference(symmetry,[status(thm)],[528])).
% 5.66/5.89 tff(556,plain,
% 5.66/5.89 (multiplication(c(X0!2), c(X1!1)) = zero),
% 5.66/5.89 inference(transitivity,[status(thm)],[503, 555, 529, 554])).
% 5.66/5.89 tff(557,plain,
% 5.66/5.89 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = addition(X1!1, multiplication(X0!2, X0!2))),
% 5.66/5.89 inference(symmetry,[status(thm)],[194])).
% 5.66/5.89 tff(558,plain,
% 5.66/5.89 (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = addition(X1!1, multiplication(X0!2, X0!2))),
% 5.66/5.89 inference(transitivity,[status(thm)],[9, 557])).
% 5.66/5.89 tff(559,plain,
% 5.66/5.89 (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(addition(X1!1, multiplication(X0!2, X0!2)), zero)),
% 5.66/5.89 inference(monotonicity,[status(thm)],[558, 556])).
% 5.66/5.89 tff(560,plain,
% 5.66/5.89 (multiplication(one, X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 5.66/5.89 inference(symmetry,[status(thm)],[253])).
% 5.66/5.89 tff(561,plain,
% 5.66/5.89 (X0!2 = multiplication(one, X0!2)),
% 5.66/5.89 inference(symmetry,[status(thm)],[251])).
% 5.66/5.89 tff(562,plain,
% 5.66/5.89 (X0!2 = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 5.66/5.89 inference(transitivity,[status(thm)],[561, 560])).
% 5.66/5.89 tff(563,plain,
% 5.66/5.89 (addition(X0!2, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(addition(X1!1, c(X1!1)), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.89 inference(monotonicity,[status(thm)],[562])).
% 5.66/5.89 tff(564,plain,
% 5.66/5.89 (addition(X1!1, multiplication(c(X0!2), c(X1!1))) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.89 inference(monotonicity,[status(thm)],[193])).
% 5.66/5.89 tff(565,plain,
% 5.66/5.89 (addition(multiplication(c(X0!2), c(X1!1)), X1!1) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.89 inference(transitivity,[status(thm)],[396, 564])).
% 5.66/5.89 tff(566,plain,
% 5.66/5.89 (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2) = addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2)),
% 5.66/5.89 inference(monotonicity,[status(thm)],[565])).
% 5.66/5.89 tff(567,plain,
% 5.66/5.89 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(X1!1, multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.89 inference(symmetry,[status(thm)],[564])).
% 5.66/5.89 tff(568,plain,
% 5.66/5.89 (addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(c(X0!2), c(X1!1)), X1!1)),
% 5.66/5.89 inference(transitivity,[status(thm)],[401, 404, 567, 395])).
% 5.66/5.89 tff(569,plain,
% 5.66/5.89 (addition(addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), X0!2) = addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), X0!2)),
% 5.66/5.89 inference(monotonicity,[status(thm)],[568])).
% 5.66/5.89 tff(570,plain,
% 5.66/5.89 (multiplication(tptp_fun_X1_0(X0!2), multiplication(one, X1!1)) = multiplication(tptp_fun_X1_0(X0!2), X1!1)),
% 5.66/5.89 inference(monotonicity,[status(thm)],[191])).
% 5.66/5.89 tff(571,plain,
% 5.66/5.89 (multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1) = multiplication(tptp_fun_X1_0(X0!2), X1!1)),
% 5.66/5.89 inference(transitivity,[status(thm)],[279, 570])).
% 5.66/5.89 tff(572,plain,
% 5.66/5.89 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 5.66/5.89 inference(monotonicity,[status(thm)],[283, 571])).
% 5.66/5.89 tff(573,plain,
% 5.66/5.89 (multiplication(tptp_fun_X1_0(X0!2), X1!1) = multiplication(tptp_fun_X1_0(X0!2), multiplication(one, X1!1))),
% 5.66/5.89 inference(symmetry,[status(thm)],[570])).
% 5.66/5.89 tff(574,plain,
% 5.66/5.89 (multiplication(tptp_fun_X1_0(X0!2), X1!1) = multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1)),
% 5.66/5.89 inference(transitivity,[status(thm)],[573, 278])).
% 5.66/5.89 tff(575,plain,
% 5.66/5.89 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), one), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 5.66/5.89 inference(monotonicity,[status(thm)],[574])).
% 5.66/5.89 tff(576,plain,
% 5.66/5.89 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = tptp_fun_X1_0(X0!2)),
% 5.66/5.89 inference(transitivity,[status(thm)],[575, 266, 572, 411, 297, 307])).
% 5.66/5.89 tff(577,plain,
% 5.66/5.89 (addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 5.66/5.89 inference(monotonicity,[status(thm)],[576])).
% 5.66/5.89 tff(578,plain,
% 5.66/5.89 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2)),
% 5.66/5.89 inference(symmetry,[status(thm)],[577])).
% 5.66/5.89 tff(579,plain,
% 5.66/5.89 (one = addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2)),
% 5.66/5.89 inference(transitivity,[status(thm)],[163, 168, 578])).
% 5.66/5.89 tff(580,plain,
% 5.66/5.89 (addition(multiplication(X0!2, X1!1), one) = addition(multiplication(X0!2, X1!1), addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), X0!2))),
% 5.66/5.89 inference(monotonicity,[status(thm)],[579])).
% 5.66/5.89 tff(581,plain,
% 5.66/5.89 (addition(addition(tptp_fun_X1_0(X0!2), 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)))) = addition(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))))),
% 5.66/5.89 inference(monotonicity,[status(thm)],[262])).
% 5.66/5.89 tff(582,plain,
% 5.66/5.89 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(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))))) = addition(addition(tptp_fun_X1_0(X0!2), 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)))))),
% 5.66/5.89 inference(quant_inst,[status(thm)],[])).
% 5.66/5.89 tff(583,plain,
% 5.66/5.89 (addition(tptp_fun_X1_0(X0!2), addition(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))))) = addition(addition(tptp_fun_X1_0(X0!2), 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))))),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[582, 202])).
% 5.66/5.89 tff(584,plain,
% 5.66/5.89 (addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), addition(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))))) = addition(tptp_fun_X1_0(X0!2), addition(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)))))),
% 5.66/5.89 inference(monotonicity,[status(thm)],[344])).
% 5.66/5.89 tff(585,plain,
% 5.66/5.89 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), addition(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)))))) = addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), addition(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))))))),
% 5.66/5.89 inference(quant_inst,[status(thm)],[])).
% 5.66/5.89 tff(586,plain,
% 5.66/5.89 (addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), addition(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)))))) = addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), addition(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)))))),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[585, 202])).
% 5.66/5.89 tff(587,plain,
% 5.66/5.89 (addition(addition(tptp_fun_X1_0(X0!2), 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)))) = addition(tptp_fun_X1_0(X0!2), addition(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)))))),
% 5.66/5.89 inference(symmetry,[status(thm)],[583])).
% 5.66/5.89 tff(588,plain,
% 5.66/5.89 (addition(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(addition(tptp_fun_X1_0(X0!2), 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))))),
% 5.66/5.89 inference(symmetry,[status(thm)],[581])).
% 5.66/5.89 tff(589,plain,
% 5.66/5.89 (one = addition(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)),
% 5.66/5.89 inference(symmetry,[status(thm)],[475])).
% 5.66/5.89 tff(590,plain,
% 5.66/5.89 (one = addition(tptp_fun_X1_0(X0!2), addition(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)))))),
% 5.66/5.89 inference(transitivity,[status(thm)],[589, 465, 588, 587])).
% 5.66/5.89 tff(591,plain,
% 5.66/5.89 (addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one) = addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), addition(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))))))),
% 5.66/5.89 inference(monotonicity,[status(thm)],[576, 590])).
% 5.66/5.89 tff(592,plain,
% 5.66/5.89 (addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one) = one),
% 5.66/5.89 inference(transitivity,[status(thm)],[591, 586, 584, 583, 581, 476, 475])).
% 5.66/5.89 tff(593,plain,
% 5.66/5.89 (addition(multiplication(X0!2, X1!1), addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one)) = addition(multiplication(X0!2, X1!1), one)),
% 5.66/5.89 inference(monotonicity,[status(thm)],[592])).
% 5.66/5.89 tff(594,plain,
% 5.66/5.89 (addition(addition(multiplication(X0!2, X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), one) = addition(multiplication(X0!2, X1!1), addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one))),
% 5.66/5.89 inference(symmetry,[status(thm)],[410])).
% 5.66/5.89 tff(595,plain,
% 5.66/5.89 (addition(addition(tptp_fun_X1_0(X1!1), 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)))) = addition(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))))),
% 5.66/5.89 inference(monotonicity,[status(thm)],[296])).
% 5.66/5.89 tff(596,plain,
% 5.66/5.89 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X1!1), addition(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))))) = addition(addition(tptp_fun_X1_0(X1!1), 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)))))),
% 5.66/5.89 inference(quant_inst,[status(thm)],[])).
% 5.66/5.89 tff(597,plain,
% 5.66/5.89 (addition(tptp_fun_X1_0(X1!1), addition(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))))) = addition(addition(tptp_fun_X1_0(X1!1), 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))))),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[596, 202])).
% 5.66/5.89 tff(598,plain,
% 5.66/5.89 (addition(tptp_fun_X1_0(X1!1), addition(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),
% 5.66/5.89 inference(transitivity,[status(thm)],[597, 595, 476, 475])).
% 5.66/5.89 tff(599,plain,
% 5.66/5.89 (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), addition(tptp_fun_X1_0(X1!1), addition(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)))))) = addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))), one)),
% 5.66/5.89 inference(monotonicity,[status(thm)],[565, 598])).
% 5.66/5.89 tff(600,plain,
% 5.66/5.89 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), addition(tptp_fun_X1_0(X1!1), addition(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)))))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), tptp_fun_X1_0(X1!1)), addition(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))))))),
% 5.66/5.89 inference(quant_inst,[status(thm)],[])).
% 5.66/5.89 tff(601,plain,
% 5.66/5.89 (addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), addition(tptp_fun_X1_0(X1!1), addition(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)))))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), tptp_fun_X1_0(X1!1)), addition(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)))))),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[600, 202])).
% 5.66/5.89 tff(602,plain,
% 5.66/5.89 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), tptp_fun_X1_0(X1!1)), addition(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))))) = addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), addition(tptp_fun_X1_0(X1!1), addition(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))))))),
% 5.66/5.89 inference(symmetry,[status(thm)],[601])).
% 5.66/5.89 tff(603,plain,
% 5.66/5.89 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X1!1, X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 5.66/5.89 inference(quant_inst,[status(thm)],[])).
% 5.66/5.89 tff(604,plain,
% 5.66/5.89 (addition(multiplication(X1!1, X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[603, 202])).
% 5.66/5.89 tff(605,plain,
% 5.66/5.89 (addition(addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(X1!1, X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 5.66/5.89 inference(symmetry,[status(thm)],[604])).
% 5.66/5.89 tff(606,plain,
% 5.66/5.89 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 5.66/5.89 inference(monotonicity,[status(thm)],[105])).
% 5.66/5.89 tff(607,plain,
% 5.66/5.89 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 5.66/5.89 inference(quant_inst,[status(thm)],[])).
% 5.66/5.89 tff(608,plain,
% 5.66/5.89 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 5.66/5.89 inference(unit_resolution,[status(thm)],[607, 129])).
% 5.66/5.89 tff(609,plain,
% 5.66/5.89 (addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2)),
% 5.66/5.89 inference(symmetry,[status(thm)],[608])).
% 5.66/5.89 tff(610,plain,
% 5.66/5.89 (addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 5.66/5.89 inference(transitivity,[status(thm)],[609, 606])).
% 5.66/5.89 tff(611,plain,
% 5.66/5.89 (addition(addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(addition(X1!1, c(X1!1)), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.89 inference(monotonicity,[status(thm)],[610])).
% 5.66/5.89 tff(612,plain,
% 5.66/5.89 (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 5.66/5.89 inference(symmetry,[status(thm)],[611])).
% 5.66/5.89 tff(613,plain,
% 5.66/5.89 (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(X1!1, X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 5.66/5.89 inference(transitivity,[status(thm)],[456, 612, 605])).
% 5.66/5.89 tff(614,plain,
% 5.66/5.89 (addition(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)))) = addition(X1!1, addition(multiplication(X1!1, X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))))),
% 5.66/5.89 inference(monotonicity,[status(thm)],[613])).
% 5.66/5.89 tff(615,plain,
% 5.66/5.89 (addition(X1!1, addition(multiplication(X1!1, X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))))) = addition(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))))),
% 5.66/5.90 inference(symmetry,[status(thm)],[614])).
% 5.66/5.90 tff(616,plain,
% 5.66/5.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X1!1, addition(multiplication(X1!1, X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))))) = addition(addition(X1!1, multiplication(X1!1, X0!2)), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))))),
% 5.66/5.90 inference(quant_inst,[status(thm)],[])).
% 5.66/5.90 tff(617,plain,
% 5.66/5.90 (addition(X1!1, addition(multiplication(X1!1, X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))))) = addition(addition(X1!1, multiplication(X1!1, X0!2)), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 5.66/5.90 inference(unit_resolution,[status(thm)],[616, 202])).
% 5.66/5.90 tff(618,plain,
% 5.66/5.90 (addition(addition(X1!1, multiplication(X1!1, X0!2)), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(X1!1, addition(multiplication(X1!1, X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))))),
% 5.66/5.90 inference(symmetry,[status(thm)],[617])).
% 5.66/5.90 tff(619,plain,
% 5.66/5.90 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(tptp_fun_X1_0(X1!1), one) = tptp_fun_X1_0(X1!1))),
% 5.66/5.90 inference(quant_inst,[status(thm)],[])).
% 5.66/5.90 tff(620,plain,
% 5.66/5.90 (multiplication(tptp_fun_X1_0(X1!1), one) = tptp_fun_X1_0(X1!1)),
% 5.66/5.90 inference(unit_resolution,[status(thm)],[619, 305])).
% 5.66/5.90 tff(621,plain,
% 5.66/5.90 (multiplication(tptp_fun_X1_0(X1!1), addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X1!1), one)),
% 5.66/5.90 inference(monotonicity,[status(thm)],[120])).
% 5.66/5.90 tff(622,plain,
% 5.66/5.90 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(tptp_fun_X1_0(X1!1), addition(X0!2, tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))))),
% 5.66/5.90 inference(quant_inst,[status(thm)],[])).
% 5.66/5.90 tff(623,plain,
% 5.66/5.90 (multiplication(tptp_fun_X1_0(X1!1), addition(X0!2, tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 5.66/5.90 inference(unit_resolution,[status(thm)],[622, 292])).
% 5.66/5.90 tff(624,plain,
% 5.66/5.90 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X1!1), addition(X0!2, tptp_fun_X1_0(X0!2)))),
% 5.66/5.90 inference(symmetry,[status(thm)],[623])).
% 5.66/5.90 tff(625,plain,
% 5.66/5.90 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(c(X1!1), c(X0!2))),
% 5.66/5.90 inference(monotonicity,[status(thm)],[281, 227])).
% 5.66/5.90 tff(626,plain,
% 5.66/5.90 (multiplication(c(X1!1), c(X0!2)) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 5.66/5.90 inference(symmetry,[status(thm)],[625])).
% 5.66/5.90 tff(627,plain,
% 5.66/5.90 (((~![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))))),
% 5.66/5.90 inference(rewrite,[status(thm)],[])).
% 5.74/5.90 tff(628,plain,
% 5.74/5.90 (((~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))))),
% 5.74/5.90 inference(rewrite,[status(thm)],[])).
% 5.74/5.90 tff(629,plain,
% 5.74/5.90 (((~![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)))))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[628])).
% 5.74/5.90 tff(630,plain,
% 5.74/5.90 (((~![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))))),
% 5.74/5.90 inference(transitivity,[status(thm)],[629, 627])).
% 5.74/5.90 tff(631,plain,
% 5.74/5.90 ((~![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)))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(632,plain,
% 5.74/5.90 ((~![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)))),
% 5.74/5.90 inference(modus_ponens,[status(thm)],[631, 630])).
% 5.74/5.90 tff(633,plain,
% 5.74/5.90 (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[632, 523, 20, 112])).
% 5.74/5.90 tff(634,plain,
% 5.74/5.90 (addition(X1!1, X0!2) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[193, 562])).
% 5.74/5.90 tff(635,plain,
% 5.74/5.90 (addition(X1!1, X0!2) = addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 5.74/5.90 inference(transitivity,[status(thm)],[634, 10])).
% 5.74/5.90 tff(636,plain,
% 5.74/5.90 (c(addition(X1!1, X0!2)) = c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[635])).
% 5.74/5.90 tff(637,plain,
% 5.74/5.90 (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = c(addition(X1!1, X0!2))),
% 5.74/5.90 inference(symmetry,[status(thm)],[636])).
% 5.74/5.90 tff(638,plain,
% 5.74/5.90 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 5.74/5.90 inference(transitivity,[status(thm)],[503, 555, 637, 633, 626])).
% 5.74/5.90 tff(639,plain,
% 5.74/5.90 (multiplication(tptp_fun_X1_0(X1!1), multiplication(one, X0!2)) = multiplication(tptp_fun_X1_0(X1!1), X0!2)),
% 5.74/5.90 inference(monotonicity,[status(thm)],[251])).
% 5.74/5.90 tff(640,plain,
% 5.74/5.90 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X1!1), multiplication(one, X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(641,plain,
% 5.74/5.90 (multiplication(tptp_fun_X1_0(X1!1), multiplication(one, X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[640, 276])).
% 5.74/5.90 tff(642,plain,
% 5.74/5.90 (multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2) = multiplication(tptp_fun_X1_0(X1!1), multiplication(one, X0!2))),
% 5.74/5.90 inference(symmetry,[status(thm)],[641])).
% 5.74/5.90 tff(643,plain,
% 5.74/5.90 (multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2) = multiplication(tptp_fun_X1_0(X1!1), X0!2)),
% 5.74/5.90 inference(transitivity,[status(thm)],[642, 639])).
% 5.74/5.90 tff(644,plain,
% 5.74/5.90 (addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[643, 638])).
% 5.74/5.90 tff(645,plain,
% 5.74/5.90 (addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), multiplication(c(X0!2), c(X1!1))) = tptp_fun_X1_0(X1!1)),
% 5.74/5.90 inference(transitivity,[status(thm)],[644, 624, 621, 620])).
% 5.74/5.90 tff(646,plain,
% 5.74/5.90 (addition(addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), multiplication(c(X0!2), c(X1!1))), X1!1) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 5.74/5.90 inference(monotonicity,[status(thm)],[645])).
% 5.74/5.90 tff(647,plain,
% 5.74/5.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(c(X0!2), c(X1!1)), X1!1)) = addition(addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), multiplication(c(X0!2), c(X1!1))), X1!1))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(648,plain,
% 5.74/5.90 (addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(c(X0!2), c(X1!1)), X1!1)) = addition(addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), multiplication(c(X0!2), c(X1!1))), X1!1)),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[647, 202])).
% 5.74/5.90 tff(649,plain,
% 5.74/5.90 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), X1!1)),
% 5.74/5.90 inference(transitivity,[status(thm)],[567, 395])).
% 5.74/5.90 tff(650,plain,
% 5.74/5.90 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = multiplication(tptp_fun_X1_0(X1!1), multiplication(one, X0!2))),
% 5.74/5.90 inference(symmetry,[status(thm)],[639])).
% 5.74/5.90 tff(651,plain,
% 5.74/5.90 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)),
% 5.74/5.90 inference(transitivity,[status(thm)],[650, 641])).
% 5.74/5.90 tff(652,plain,
% 5.74/5.90 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(c(X0!2), c(X1!1)), X1!1))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[651, 649])).
% 5.74/5.90 tff(653,plain,
% 5.74/5.90 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = one),
% 5.74/5.90 inference(transitivity,[status(thm)],[652, 648, 646, 295, 85])).
% 5.74/5.90 tff(654,plain,
% 5.74/5.90 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!1, multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), X1!1))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(655,plain,
% 5.74/5.90 (addition(X1!1, multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), X1!1)),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[654, 7])).
% 5.74/5.90 tff(656,plain,
% 5.74/5.90 (addition(addition(X1!1, multiplication(X1!1, X0!2)), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(X1!1, X0!2), X1!1), one)),
% 5.74/5.90 inference(monotonicity,[status(thm)],[655, 653])).
% 5.74/5.90 tff(657,plain,
% 5.74/5.90 (addition(addition(multiplication(X1!1, X0!2), X1!1), one) = addition(addition(X1!1, multiplication(X1!1, X0!2)), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 5.74/5.90 inference(symmetry,[status(thm)],[656])).
% 5.74/5.90 tff(658,plain,
% 5.74/5.90 (addition(addition(tptp_fun_X1_0(X1!1), 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)))) = addition(tptp_fun_X1_0(X1!1), addition(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)))))),
% 5.74/5.90 inference(symmetry,[status(thm)],[597])).
% 5.74/5.90 tff(659,plain,
% 5.74/5.90 (addition(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(addition(tptp_fun_X1_0(X1!1), 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))))),
% 5.74/5.90 inference(symmetry,[status(thm)],[595])).
% 5.74/5.90 tff(660,plain,
% 5.74/5.90 (one = addition(tptp_fun_X1_0(X1!1), addition(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)))))),
% 5.74/5.90 inference(transitivity,[status(thm)],[589, 465, 659, 658])).
% 5.74/5.90 tff(661,plain,
% 5.74/5.90 (multiplication(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(tptp_fun_X1_0(X1!1), one)),
% 5.74/5.90 inference(monotonicity,[status(thm)],[262])).
% 5.74/5.90 tff(662,plain,
% 5.74/5.90 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(663,plain,
% 5.74/5.90 (multiplication(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[662, 292])).
% 5.74/5.90 tff(664,plain,
% 5.74/5.90 (addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), X0!2))),
% 5.74/5.90 inference(symmetry,[status(thm)],[663])).
% 5.74/5.90 tff(665,plain,
% 5.74/5.90 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[638, 643])).
% 5.74/5.90 tff(666,plain,
% 5.74/5.90 (zero = c(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 5.74/5.90 inference(symmetry,[status(thm)],[554])).
% 5.74/5.90 tff(667,plain,
% 5.74/5.90 (zero = multiplication(c(X0!2), c(X1!1))),
% 5.74/5.90 inference(transitivity,[status(thm)],[666, 530, 528, 504])).
% 5.74/5.90 tff(668,plain,
% 5.74/5.90 (addition(zero, multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[667])).
% 5.74/5.90 tff(669,plain,
% 5.74/5.90 (multiplication(tptp_fun_X1_0(X1!1), multiplication(X0!2, X0!2)) = multiplication(tptp_fun_X1_0(X1!1), X0!2)),
% 5.74/5.90 inference(monotonicity,[status(thm)],[254])).
% 5.74/5.90 tff(670,plain,
% 5.74/5.90 (multiplication(tptp_fun_X1_0(X1!1), multiplication(X0!2, X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)),
% 5.74/5.90 inference(transitivity,[status(thm)],[669, 650, 641])).
% 5.74/5.90 tff(671,plain,
% 5.74/5.90 (^[A: $i] : refl((multiplication(A, zero) = zero) <=> (multiplication(A, zero) = zero))),
% 5.74/5.90 inference(bind,[status(th)],[])).
% 5.74/5.90 tff(672,plain,
% 5.74/5.90 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 5.74/5.90 inference(quant_intro,[status(thm)],[671])).
% 5.74/5.90 tff(673,plain,
% 5.74/5.90 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 5.74/5.90 inference(rewrite,[status(thm)],[])).
% 5.74/5.90 tff(674,axiom,(![A: $i] : (multiplication(A, zero) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_annihilation')).
% 5.74/5.90 tff(675,plain,
% 5.74/5.90 (![A: $i] : (multiplication(A, zero) = zero)),
% 5.74/5.90 inference(modus_ponens,[status(thm)],[674, 673])).
% 5.74/5.90 tff(676,plain,(
% 5.74/5.90 ![A: $i] : (multiplication(A, zero) = zero)),
% 5.74/5.90 inference(skolemize,[status(sab)],[675])).
% 5.74/5.90 tff(677,plain,
% 5.74/5.90 (![A: $i] : (multiplication(A, zero) = zero)),
% 5.74/5.90 inference(modus_ponens,[status(thm)],[676, 672])).
% 5.74/5.90 tff(678,plain,
% 5.74/5.90 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(tptp_fun_X1_0(X1!1), zero) = zero)),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(679,plain,
% 5.74/5.90 (multiplication(tptp_fun_X1_0(X1!1), zero) = zero),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[678, 677])).
% 5.74/5.90 tff(680,plain,
% 5.74/5.90 (addition(multiplication(tptp_fun_X1_0(X1!1), zero), multiplication(tptp_fun_X1_0(X1!1), multiplication(X0!2, X0!2))) = addition(zero, multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[679, 670])).
% 5.74/5.90 tff(681,plain,
% 5.74/5.90 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(tptp_fun_X1_0(X1!1), addition(zero, multiplication(X0!2, X0!2))) = addition(multiplication(tptp_fun_X1_0(X1!1), zero), multiplication(tptp_fun_X1_0(X1!1), multiplication(X0!2, X0!2))))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(682,plain,
% 5.74/5.90 (multiplication(tptp_fun_X1_0(X1!1), addition(zero, multiplication(X0!2, X0!2))) = addition(multiplication(tptp_fun_X1_0(X1!1), zero), multiplication(tptp_fun_X1_0(X1!1), multiplication(X0!2, X0!2)))),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[681, 292])).
% 5.74/5.90 tff(683,plain,
% 5.74/5.90 (addition(zero, multiplication(X0!2, X0!2)) = addition(multiplication(tptp_fun_X1_0(X0!2), X0!2), multiplication(X0!2, X0!2))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[135])).
% 5.74/5.90 tff(684,plain,
% 5.74/5.90 (addition(multiplication(tptp_fun_X1_0(X0!2), X0!2), multiplication(X0!2, X0!2)) = addition(zero, multiplication(X0!2, X0!2))),
% 5.74/5.90 inference(symmetry,[status(thm)],[683])).
% 5.74/5.90 tff(685,plain,
% 5.74/5.90 ((~![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)))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(686,plain,
% 5.74/5.90 (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))),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[685, 129])).
% 5.74/5.90 tff(687,plain,
% 5.74/5.90 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X1!1, c(X1!1))),
% 5.74/5.90 inference(transitivity,[status(thm)],[226, 120, 86, 105])).
% 5.74/5.90 tff(688,plain,
% 5.74/5.90 (multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 5.74/5.90 inference(monotonicity,[status(thm)],[687])).
% 5.74/5.90 tff(689,plain,
% 5.74/5.90 (multiplication(addition(X1!1, c(X1!1)), X0!2) = multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2)),
% 5.74/5.90 inference(symmetry,[status(thm)],[688])).
% 5.74/5.90 tff(690,plain,
% 5.74/5.90 (X0!2 = addition(zero, multiplication(X0!2, X0!2))),
% 5.74/5.90 inference(transitivity,[status(thm)],[561, 560, 689, 686, 684])).
% 5.74/5.90 tff(691,plain,
% 5.74/5.90 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = multiplication(tptp_fun_X1_0(X1!1), addition(zero, multiplication(X0!2, X0!2)))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[690])).
% 5.74/5.90 tff(692,plain,
% 5.74/5.90 (multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2) = tptp_fun_X1_0(X1!1)),
% 5.74/5.90 inference(transitivity,[status(thm)],[642, 639, 691, 682, 680, 668, 665, 664, 661, 620])).
% 5.74/5.90 tff(693,plain,
% 5.74/5.90 (addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), one) = addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X1!1), addition(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))))))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[692, 660])).
% 5.74/5.90 tff(694,plain,
% 5.74/5.90 (addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X1!1), addition(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)))))) = addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), one)),
% 5.74/5.90 inference(symmetry,[status(thm)],[693])).
% 5.74/5.90 tff(695,plain,
% 5.74/5.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X1!1), addition(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)))))) = addition(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), addition(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))))))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(696,plain,
% 5.74/5.90 (addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X1!1), addition(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)))))) = addition(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), addition(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)))))),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[695, 202])).
% 5.74/5.90 tff(697,plain,
% 5.74/5.90 (addition(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), addition(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))))) = addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X1!1), addition(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))))))),
% 5.74/5.90 inference(symmetry,[status(thm)],[696])).
% 5.74/5.90 tff(698,plain,
% 5.74/5.90 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(X0!2, c(X0!2))),
% 5.74/5.90 inference(transitivity,[status(thm)],[85, 163, 323])).
% 5.74/5.90 tff(699,plain,
% 5.74/5.90 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X1!1) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 5.74/5.90 inference(monotonicity,[status(thm)],[698])).
% 5.74/5.90 tff(700,plain,
% 5.74/5.90 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X1!1) = addition(multiplication(X1!1, X1!1), multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(701,plain,
% 5.74/5.90 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X1!1) = addition(multiplication(X1!1, X1!1), multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[700, 129])).
% 5.74/5.90 tff(702,plain,
% 5.74/5.90 (addition(multiplication(X1!1, X1!1), multiplication(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X1!1)),
% 5.74/5.90 inference(symmetry,[status(thm)],[701])).
% 5.74/5.90 tff(703,plain,
% 5.74/5.90 (zero = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 5.74/5.90 inference(symmetry,[status(thm)],[94])).
% 5.74/5.90 tff(704,plain,
% 5.74/5.90 (addition(multiplication(X1!1, X1!1), zero) = addition(multiplication(X1!1, X1!1), multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[703])).
% 5.74/5.90 tff(705,plain,
% 5.74/5.90 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(X1!1, X1!1), zero) = multiplication(X1!1, X1!1))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(706,plain,
% 5.74/5.90 (addition(multiplication(X1!1, X1!1), zero) = multiplication(X1!1, X1!1)),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[705, 143])).
% 5.74/5.90 tff(707,plain,
% 5.74/5.90 (multiplication(X1!1, X1!1) = addition(multiplication(X1!1, X1!1), zero)),
% 5.74/5.90 inference(symmetry,[status(thm)],[706])).
% 5.74/5.90 tff(708,plain,
% 5.74/5.90 (multiplication(X1!1, X1!1) = X1!1),
% 5.74/5.90 inference(transitivity,[status(thm)],[707, 704, 702, 699, 181, 191])).
% 5.74/5.90 tff(709,plain,
% 5.74/5.90 (c(multiplication(X1!1, X1!1)) = c(X1!1)),
% 5.74/5.90 inference(monotonicity,[status(thm)],[708])).
% 5.74/5.90 tff(710,plain,
% 5.74/5.90 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(multiplication(X1!1, X1!1)) = addition(c(X1!1), c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (c(multiplication(X1!1, X1!1)) = addition(c(X1!1), c(X1!1))))),
% 5.74/5.90 inference(rewrite,[status(thm)],[])).
% 5.74/5.90 tff(711,plain,
% 5.74/5.90 (((~test(X1!1)) | (c(multiplication(X1!1, X1!1)) = addition(c(X1!1), c(X1!1))) | (~test(X1!1))) <=> ((~test(X1!1)) | (c(multiplication(X1!1, X1!1)) = addition(c(X1!1), c(X1!1))))),
% 5.74/5.90 inference(rewrite,[status(thm)],[])).
% 5.74/5.90 tff(712,plain,
% 5.74/5.90 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(multiplication(X1!1, X1!1)) = addition(c(X1!1), c(X1!1))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(multiplication(X1!1, X1!1)) = addition(c(X1!1), c(X1!1)))))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[711])).
% 5.74/5.90 tff(713,plain,
% 5.74/5.90 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(multiplication(X1!1, X1!1)) = addition(c(X1!1), c(X1!1))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (c(multiplication(X1!1, X1!1)) = addition(c(X1!1), c(X1!1))))),
% 5.74/5.90 inference(transitivity,[status(thm)],[712, 710])).
% 5.74/5.90 tff(714,plain,
% 5.74/5.90 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(multiplication(X1!1, X1!1)) = addition(c(X1!1), c(X1!1))) | (~test(X1!1)))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(715,plain,
% 5.74/5.90 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (c(multiplication(X1!1, X1!1)) = addition(c(X1!1), c(X1!1)))),
% 5.74/5.90 inference(modus_ponens,[status(thm)],[714, 713])).
% 5.74/5.90 tff(716,plain,
% 5.74/5.90 (c(multiplication(X1!1, X1!1)) = addition(c(X1!1), c(X1!1))),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[715, 242, 20])).
% 5.74/5.90 tff(717,plain,
% 5.74/5.90 (addition(c(X1!1), c(X1!1)) = c(multiplication(X1!1, X1!1))),
% 5.74/5.90 inference(symmetry,[status(thm)],[716])).
% 5.74/5.90 tff(718,plain,
% 5.74/5.90 (addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = addition(c(X1!1), c(X1!1))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[281, 281])).
% 5.74/5.90 tff(719,plain,
% 5.74/5.90 (addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = tptp_fun_X1_0(X1!1)),
% 5.74/5.90 inference(transitivity,[status(thm)],[718, 717, 709, 103])).
% 5.74/5.90 tff(720,plain,
% 5.74/5.90 (addition(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), addition(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))))) = addition(tptp_fun_X1_0(X1!1), addition(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)))))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[719])).
% 5.74/5.90 tff(721,plain,
% 5.74/5.90 (addition(tptp_fun_X1_0(X1!1), addition(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))))) = addition(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), addition(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)))))),
% 5.74/5.90 inference(symmetry,[status(thm)],[720])).
% 5.74/5.90 tff(722,plain,
% 5.74/5.90 (one = addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), one)),
% 5.74/5.90 inference(transitivity,[status(thm)],[589, 465, 659, 658, 721, 697, 694])).
% 5.74/5.90 tff(723,plain,
% 5.74/5.90 (addition(multiplication(X1!1, X0!2), X1!1) = addition(X1!1, multiplication(X1!1, X0!2))),
% 5.74/5.90 inference(symmetry,[status(thm)],[655])).
% 5.74/5.90 tff(724,plain,
% 5.74/5.90 (addition(addition(multiplication(X1!1, X0!2), X1!1), one) = addition(addition(X1!1, multiplication(X1!1, X0!2)), addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), one))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[723, 722])).
% 5.74/5.90 tff(725,plain,
% 5.74/5.90 (addition(addition(X1!1, multiplication(X1!1, X0!2)), addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), one)) = addition(addition(multiplication(X1!1, X0!2), X1!1), one)),
% 5.74/5.90 inference(symmetry,[status(thm)],[724])).
% 5.74/5.90 tff(726,plain,
% 5.74/5.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(X1!1, multiplication(X1!1, X0!2)), addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), one)) = addition(addition(addition(X1!1, multiplication(X1!1, X0!2)), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)), one))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(727,plain,
% 5.74/5.90 (addition(addition(X1!1, multiplication(X1!1, X0!2)), addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), one)) = addition(addition(addition(X1!1, multiplication(X1!1, X0!2)), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)), one)),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[726, 202])).
% 5.74/5.90 tff(728,plain,
% 5.74/5.90 (addition(addition(addition(X1!1, multiplication(X1!1, X0!2)), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)), one) = addition(addition(X1!1, multiplication(X1!1, X0!2)), addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), one))),
% 5.74/5.90 inference(symmetry,[status(thm)],[727])).
% 5.74/5.90 tff(729,plain,
% 5.74/5.90 (addition(X1!1, addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[193, 610])).
% 5.74/5.90 tff(730,plain,
% 5.74/5.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X1!1, addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))) = addition(addition(X1!1, multiplication(X1!1, X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(731,plain,
% 5.74/5.90 (addition(X1!1, addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))) = addition(addition(X1!1, multiplication(X1!1, X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[730, 202])).
% 5.74/5.90 tff(732,plain,
% 5.74/5.90 (addition(addition(X1!1, multiplication(X1!1, X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = addition(X1!1, addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 5.74/5.90 inference(symmetry,[status(thm)],[731])).
% 5.74/5.90 tff(733,plain,
% 5.74/5.90 (addition(addition(X1!1, multiplication(X1!1, X0!2)), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)) = addition(addition(X1!1, multiplication(X1!1, X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 5.74/5.90 inference(monotonicity,[status(thm)],[643])).
% 5.74/5.90 tff(734,plain,
% 5.74/5.90 (addition(addition(X1!1, multiplication(X1!1, X0!2)), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 5.74/5.90 inference(transitivity,[status(thm)],[733, 732, 729])).
% 5.74/5.90 tff(735,plain,
% 5.74/5.90 (addition(addition(addition(X1!1, multiplication(X1!1, X0!2)), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)), one) = addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), one)),
% 5.74/5.90 inference(monotonicity,[status(thm)],[734])).
% 5.74/5.90 tff(736,plain,
% 5.74/5.90 (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), one) = addition(addition(addition(X1!1, multiplication(X1!1, X0!2)), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)), one)),
% 5.74/5.90 inference(symmetry,[status(thm)],[735])).
% 5.74/5.90 tff(737,plain,
% 5.74/5.90 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), one) = addition(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 5.74/5.90 inference(quant_inst,[status(thm)],[])).
% 5.74/5.90 tff(738,plain,
% 5.74/5.90 (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), one) = addition(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 5.74/5.90 inference(unit_resolution,[status(thm)],[737, 7])).
% 5.74/5.91 tff(739,plain,
% 5.74/5.91 (addition(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), one)),
% 5.74/5.91 inference(symmetry,[status(thm)],[738])).
% 5.74/5.91 tff(740,plain,
% 5.74/5.91 (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), zero) = addition(addition(X1!1, multiplication(X0!2, X0!2)), zero)),
% 5.74/5.91 inference(monotonicity,[status(thm)],[557])).
% 5.74/5.91 tff(741,plain,
% 5.74/5.91 (addition(addition(X1!1, multiplication(X0!2, X0!2)), zero) = addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), zero)),
% 5.74/5.91 inference(symmetry,[status(thm)],[740])).
% 5.74/5.91 tff(742,plain,
% 5.74/5.91 (addition(X1!1, multiplication(X0!2, X0!2)) = addition(X1!1, addition(multiplication(X0!2, X0!2), zero))),
% 5.74/5.91 inference(symmetry,[status(thm)],[195])).
% 5.74/5.91 tff(743,plain,
% 5.74/5.91 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), zero)),
% 5.74/5.91 inference(transitivity,[status(thm)],[557, 742, 204, 741])).
% 5.74/5.91 tff(744,plain,
% 5.74/5.91 (addition(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(one, addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), zero))),
% 5.74/5.91 inference(monotonicity,[status(thm)],[743])).
% 5.74/5.91 tff(745,plain,
% 5.74/5.91 (addition(one, addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), zero)) = addition(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 5.74/5.91 inference(symmetry,[status(thm)],[744])).
% 5.74/5.91 tff(746,plain,
% 5.74/5.91 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), zero)) = addition(addition(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), zero))),
% 5.74/5.91 inference(quant_inst,[status(thm)],[])).
% 5.74/5.91 tff(747,plain,
% 5.74/5.91 (addition(one, addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), zero)) = addition(addition(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), zero)),
% 5.74/5.91 inference(unit_resolution,[status(thm)],[746, 202])).
% 5.74/5.91 tff(748,plain,
% 5.74/5.91 (addition(addition(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), zero) = addition(one, addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), zero))),
% 5.74/5.91 inference(symmetry,[status(thm)],[747])).
% 5.74/5.91 tff(749,plain,
% 5.74/5.91 (addition(addition(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), zero) = addition(addition(one, 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)))),
% 5.74/5.91 inference(monotonicity,[status(thm)],[667])).
% 5.74/5.91 tff(750,plain,
% 5.74/5.91 (addition(addition(one, 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))) = addition(addition(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), zero)),
% 5.74/5.91 inference(symmetry,[status(thm)],[749])).
% 5.74/5.91 tff(751,plain,
% 5.74/5.91 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(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)))) = addition(addition(one, 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))))),
% 5.74/5.91 inference(quant_inst,[status(thm)],[])).
% 5.74/5.91 tff(752,plain,
% 5.74/5.91 (addition(one, addition(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)))) = addition(addition(one, 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)))),
% 5.74/5.91 inference(unit_resolution,[status(thm)],[751, 202])).
% 5.74/5.91 tff(753,plain,
% 5.74/5.91 (addition(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))) = 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)))),
% 5.74/5.91 inference(monotonicity,[status(thm)],[10])).
% 5.74/5.91 tff(754,plain,
% 5.74/5.91 (addition(one, addition(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)))) = addition(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))))),
% 5.74/5.91 inference(monotonicity,[status(thm)],[753])).
% 5.74/5.91 tff(755,plain,
% 5.74/5.91 (addition(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(one, addition(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))))),
% 5.74/5.91 inference(symmetry,[status(thm)],[754])).
% 5.74/5.91 tff(756,plain,
% 5.74/5.91 (one = addition(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))))),
% 5.74/5.91 inference(transitivity,[status(thm)],[589, 465, 755, 752, 750, 748, 745, 739, 736, 728, 725, 657, 618, 615])).
% 5.74/5.91 tff(757,plain,
% 5.74/5.91 (addition(multiplication(X0!2, X0!2), tptp_fun_X1_0(X0!2)) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 5.74/5.91 inference(monotonicity,[status(thm)],[254])).
% 5.74/5.91 tff(758,plain,
% 5.74/5.91 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(multiplication(X0!2, X0!2), tptp_fun_X1_0(X0!2))),
% 5.74/5.91 inference(symmetry,[status(thm)],[757])).
% 5.74/5.91 tff(759,plain,
% 5.74/5.91 (one = addition(multiplication(X0!2, X0!2), tptp_fun_X1_0(X0!2))),
% 5.74/5.91 inference(transitivity,[status(thm)],[163, 758])).
% 5.74/5.91 tff(760,plain,
% 5.74/5.91 (addition(multiplication(c(X0!2), c(X1!1)), one) = addition(zero, addition(multiplication(X0!2, X0!2), tptp_fun_X1_0(X0!2)))),
% 5.74/5.91 inference(monotonicity,[status(thm)],[556, 759])).
% 5.74/5.91 tff(761,plain,
% 5.74/5.91 (addition(zero, addition(multiplication(X0!2, X0!2), tptp_fun_X1_0(X0!2))) = addition(multiplication(c(X0!2), c(X1!1)), one)),
% 5.74/5.91 inference(symmetry,[status(thm)],[760])).
% 5.74/5.91 tff(762,plain,
% 5.74/5.91 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(zero, addition(multiplication(X0!2, X0!2), tptp_fun_X1_0(X0!2))) = addition(addition(zero, multiplication(X0!2, X0!2)), tptp_fun_X1_0(X0!2)))),
% 5.74/5.91 inference(quant_inst,[status(thm)],[])).
% 5.74/5.91 tff(763,plain,
% 5.74/5.91 (addition(zero, addition(multiplication(X0!2, X0!2), tptp_fun_X1_0(X0!2))) = addition(addition(zero, multiplication(X0!2, X0!2)), tptp_fun_X1_0(X0!2))),
% 5.74/5.91 inference(unit_resolution,[status(thm)],[762, 202])).
% 5.74/5.91 tff(764,plain,
% 5.74/5.91 (addition(addition(zero, multiplication(X0!2, X0!2)), tptp_fun_X1_0(X0!2)) = addition(zero, addition(multiplication(X0!2, X0!2), tptp_fun_X1_0(X0!2)))),
% 5.74/5.91 inference(symmetry,[status(thm)],[763])).
% 5.74/5.91 tff(765,plain,
% 5.74/5.91 (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)),
% 5.74/5.91 inference(symmetry,[status(thm)],[686])).
% 5.74/5.91 tff(766,plain,
% 5.74/5.91 (addition(zero, multiplication(X0!2, X0!2)) = X0!2),
% 5.74/5.91 inference(transitivity,[status(thm)],[683, 765, 688, 253, 251])).
% 5.74/5.91 tff(767,plain,
% 5.74/5.91 (addition(addition(zero, multiplication(X0!2, X0!2)), tptp_fun_X1_0(X0!2)) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 5.74/5.91 inference(monotonicity,[status(thm)],[766])).
% 5.74/5.91 tff(768,plain,
% 5.74/5.91 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(addition(zero, multiplication(X0!2, X0!2)), tptp_fun_X1_0(X0!2))),
% 5.74/5.91 inference(symmetry,[status(thm)],[767])).
% 5.74/5.91 tff(769,plain,
% 5.74/5.91 (one = addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), tptp_fun_X1_0(X1!1))),
% 5.74/5.91 inference(transitivity,[status(thm)],[163, 768, 764, 761, 379, 377])).
% 5.74/5.91 tff(770,plain,
% 5.74/5.91 (addition(one, one) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), X1!1), tptp_fun_X1_0(X1!1)), addition(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)))))),
% 5.74/5.91 inference(monotonicity,[status(thm)],[769, 756])).
% 5.74/5.91 tff(771,plain,
% 5.74/5.91 (addition(one, one) = addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 5.74/5.91 inference(transitivity,[status(thm)],[770, 602, 599, 407, 594, 593, 580, 425, 569, 566, 445, 563, 439, 559, 205, 195, 194, 10])).
% 5.74/5.91 tff(772,plain,
% 5.74/5.91 ((addition(one, one) = one) <=> (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = one)),
% 5.74/5.91 inference(monotonicity,[status(thm)],[771])).
% 5.74/5.91 tff(773,plain,
% 5.74/5.91 ((addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = one) <=> (addition(one, one) = one)),
% 5.74/5.91 inference(symmetry,[status(thm)],[772])).
% 5.74/5.91 tff(774,plain,
% 5.74/5.91 ((~(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = one)) <=> (~(addition(one, one) = one))),
% 5.74/5.91 inference(monotonicity,[status(thm)],[773])).
% 5.74/5.91 tff(775,plain,
% 5.74/5.91 (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(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 5.74/5.91 inference(transitivity,[status(thm)],[559, 205, 195, 194, 10])).
% 5.74/5.91 tff(776,plain,
% 5.74/5.91 ((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) <=> (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = one)),
% 5.74/5.91 inference(monotonicity,[status(thm)],[775])).
% 5.74/5.91 tff(777,plain,
% 5.74/5.91 ((~(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)) <=> (~(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = one))),
% 5.74/5.91 inference(monotonicity,[status(thm)],[776])).
% 5.74/5.91 tff(778,plain,
% 5.74/5.91 (~(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = one)),
% 5.74/5.91 inference(modus_ponens,[status(thm)],[493, 777])).
% 5.74/5.91 tff(779,plain,
% 5.74/5.91 (~(addition(one, one) = one)),
% 5.74/5.91 inference(modus_ponens,[status(thm)],[778, 774])).
% 5.74/5.91 tff(780,plain,
% 5.74/5.91 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 5.74/5.91 inference(quant_inst,[status(thm)],[])).
% 5.74/5.91 tff(781,plain,
% 5.74/5.91 ($false),
% 5.74/5.91 inference(unit_resolution,[status(thm)],[780, 367, 779])).
% 5.74/5.91 % SZS output end Proof
% 5.74/5.92 % E exiting
%------------------------------------------------------------------------------