TSTP Solution File: KLE081+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE081+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:24:07 EDT 2022
% Result : Theorem 42.30s 26.59s
% Output : Proof 42.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : KLE081+1 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n013.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Sep 1 08:11:31 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.15/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.31 Usage: tptp [options] [-file:]file
% 0.15/0.31 -h, -? prints this message.
% 0.15/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.31 -m, -model generate model.
% 0.15/0.31 -p, -proof generate proof.
% 0.15/0.31 -c, -core generate unsat core of named formulas.
% 0.15/0.31 -st, -statistics display statistics.
% 0.15/0.31 -t:timeout set timeout (in second).
% 0.15/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.31 -<param>:<value> configuration parameter and value.
% 0.15/0.31 -o:<output-file> file to place output in.
% 42.30/26.59 % SZS status Theorem
% 42.30/26.59 % SZS output start Proof
% 42.30/26.59 tff(zero_type, type, (
% 42.30/26.59 zero: $i)).
% 42.30/26.59 tff(multiplication_type, type, (
% 42.30/26.59 multiplication: ( $i * $i ) > $i)).
% 42.30/26.59 tff(tptp_fun_X0_0_type, type, (
% 42.30/26.59 tptp_fun_X0_0: $i)).
% 42.30/26.59 tff(antidomain_type, type, (
% 42.30/26.59 antidomain: $i > $i)).
% 42.30/26.59 tff(one_type, type, (
% 42.30/26.59 one: $i)).
% 42.30/26.59 tff(domain_type, type, (
% 42.30/26.59 domain: $i > $i)).
% 42.30/26.59 tff(addition_type, type, (
% 42.30/26.59 addition: ( $i * $i ) > $i)).
% 42.30/26.59 tff(1,plain,
% 42.30/26.59 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(2,plain,
% 42.30/26.59 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 42.30/26.59 inference(quant_intro,[status(thm)],[1])).
% 42.30/26.59 tff(3,plain,
% 42.30/26.59 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(4,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 42.30/26.59 tff(5,plain,
% 42.30/26.59 (![A: $i] : (multiplication(zero, A) = zero)),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[4, 3])).
% 42.30/26.59 tff(6,plain,(
% 42.30/26.59 ![A: $i] : (multiplication(zero, A) = zero)),
% 42.30/26.59 inference(skolemize,[status(sab)],[5])).
% 42.30/26.59 tff(7,plain,
% 42.30/26.59 (![A: $i] : (multiplication(zero, A) = zero)),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[6, 2])).
% 42.30/26.59 tff(8,plain,
% 42.30/26.59 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, X0!0) = zero)),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(9,plain,
% 42.30/26.59 (multiplication(zero, X0!0) = zero),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[8, 7])).
% 42.30/26.59 tff(10,plain,
% 42.30/26.59 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, zero) = zero)),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(11,plain,
% 42.30/26.59 (multiplication(zero, zero) = zero),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[10, 7])).
% 42.30/26.59 tff(12,plain,
% 42.30/26.59 ((domain(zero) = zero) <=> (domain(zero) = zero)),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(13,axiom,(domain(zero) = zero), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain4')).
% 42.30/26.59 tff(14,plain,
% 42.30/26.59 (domain(zero) = zero),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[13, 12])).
% 42.30/26.59 tff(15,plain,
% 42.30/26.59 (multiplication(domain(zero), zero) = multiplication(zero, zero)),
% 42.30/26.59 inference(monotonicity,[status(thm)],[14])).
% 42.30/26.59 tff(16,plain,
% 42.30/26.59 (^[X0: $i] : refl((addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(17,plain,
% 42.30/26.59 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 42.30/26.59 inference(quant_intro,[status(thm)],[16])).
% 42.30/26.59 tff(18,plain,
% 42.30/26.59 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(19,axiom,(![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain1')).
% 42.30/26.59 tff(20,plain,
% 42.30/26.59 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[19, 18])).
% 42.30/26.59 tff(21,plain,(
% 42.30/26.59 ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 42.30/26.59 inference(skolemize,[status(sab)],[20])).
% 42.30/26.59 tff(22,plain,
% 42.30/26.59 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[21, 17])).
% 42.30/26.59 tff(23,plain,
% 42.30/26.59 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(zero, multiplication(domain(zero), zero)) = multiplication(domain(zero), zero))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(24,plain,
% 42.30/26.59 (addition(zero, multiplication(domain(zero), zero)) = multiplication(domain(zero), zero)),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[23, 22])).
% 42.30/26.59 tff(25,plain,
% 42.30/26.59 (multiplication(zero, zero) = multiplication(domain(zero), zero)),
% 42.30/26.59 inference(symmetry,[status(thm)],[15])).
% 42.30/26.59 tff(26,plain,
% 42.30/26.59 (zero = multiplication(zero, zero)),
% 42.30/26.59 inference(symmetry,[status(thm)],[11])).
% 42.30/26.59 tff(27,plain,
% 42.30/26.59 (zero = multiplication(domain(zero), zero)),
% 42.30/26.59 inference(transitivity,[status(thm)],[26, 25])).
% 42.30/26.59 tff(28,plain,
% 42.30/26.59 (addition(zero, zero) = addition(zero, multiplication(domain(zero), zero))),
% 42.30/26.59 inference(monotonicity,[status(thm)],[27])).
% 42.30/26.59 tff(29,plain,
% 42.30/26.59 (^[X1: $i] : refl((~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero)))) <=> (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero)))))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(30,plain,
% 42.30/26.59 (![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero)))) <=> ![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))),
% 42.30/26.59 inference(quant_intro,[status(thm)],[29])).
% 42.30/26.59 tff(31,plain,
% 42.30/26.59 (^[X1: $i] : rewrite(((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) <=> (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero)))))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(32,plain,
% 42.30/26.59 (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) <=> ![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))),
% 42.30/26.59 inference(quant_intro,[status(thm)],[31])).
% 42.30/26.59 tff(33,plain,
% 42.30/26.59 ((![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) & (~(multiplication(antidomain(X0!0), X0!0) = zero))) <=> (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) & (~(multiplication(antidomain(X0!0), X0!0) = zero)))),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(34,plain,
% 42.30/26.59 ((~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero))) <=> (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero)))),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(35,plain,
% 42.30/26.59 ((~![X0: $i] : (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) => (multiplication(antidomain(X0), X0) = zero))) <=> (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero)))),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(36,axiom,(~![X0: $i] : (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) => (multiplication(antidomain(X0), X0) = zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 42.30/26.59 tff(37,plain,
% 42.30/26.59 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[36, 35])).
% 42.30/26.59 tff(38,plain,
% 42.30/26.59 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[37, 34])).
% 42.30/26.59 tff(39,plain,
% 42.30/26.59 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[38, 34])).
% 42.30/26.59 tff(40,plain,
% 42.30/26.59 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[39, 34])).
% 42.30/26.59 tff(41,plain,
% 42.30/26.59 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[40, 34])).
% 42.30/26.59 tff(42,plain,
% 42.30/26.59 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[41, 34])).
% 42.30/26.59 tff(43,plain,
% 42.30/26.59 (~![X0: $i] : ((~![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))) | (multiplication(antidomain(X0), X0) = zero))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[42, 34])).
% 42.30/26.59 tff(44,plain,
% 42.30/26.59 (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero)) & (~(multiplication(antidomain(X0!0), X0!0) = zero))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[43, 33])).
% 42.30/26.59 tff(45,plain,
% 42.30/26.59 (![X1: $i] : ((addition(domain(X1), antidomain(X1)) = one) & (multiplication(domain(X1), antidomain(X1)) = zero))),
% 42.30/26.59 inference(and_elim,[status(thm)],[44])).
% 42.30/26.59 tff(46,plain,
% 42.30/26.59 (![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[45, 32])).
% 42.30/26.59 tff(47,plain,
% 42.30/26.59 (![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[46, 30])).
% 42.30/26.59 tff(48,plain,
% 42.30/26.59 ((~![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))) | (~((~(addition(domain(zero), antidomain(zero)) = one)) | (~(multiplication(domain(zero), antidomain(zero)) = zero))))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(49,plain,
% 42.30/26.59 (~((~(addition(domain(zero), antidomain(zero)) = one)) | (~(multiplication(domain(zero), antidomain(zero)) = zero)))),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[48, 47])).
% 42.30/26.59 tff(50,plain,
% 42.30/26.59 (((~(addition(domain(zero), antidomain(zero)) = one)) | (~(multiplication(domain(zero), antidomain(zero)) = zero))) | (multiplication(domain(zero), antidomain(zero)) = zero)),
% 42.30/26.59 inference(tautology,[status(thm)],[])).
% 42.30/26.59 tff(51,plain,
% 42.30/26.59 (multiplication(domain(zero), antidomain(zero)) = zero),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[50, 49])).
% 42.30/26.59 tff(52,plain,
% 42.30/26.59 (zero = domain(zero)),
% 42.30/26.59 inference(symmetry,[status(thm)],[14])).
% 42.30/26.59 tff(53,plain,
% 42.30/26.59 (multiplication(zero, antidomain(zero)) = multiplication(domain(zero), antidomain(zero))),
% 42.30/26.59 inference(monotonicity,[status(thm)],[52])).
% 42.30/26.59 tff(54,plain,
% 42.30/26.59 (multiplication(zero, antidomain(zero)) = zero),
% 42.30/26.59 inference(transitivity,[status(thm)],[53, 51])).
% 42.30/26.59 tff(55,plain,
% 42.30/26.59 (addition(multiplication(zero, antidomain(zero)), multiplication(zero, zero)) = addition(zero, zero)),
% 42.30/26.59 inference(monotonicity,[status(thm)],[54, 11])).
% 42.30/26.59 tff(56,plain,
% 42.30/26.59 (^[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))))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(57,plain,
% 42.30/26.59 (![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)))),
% 42.30/26.59 inference(quant_intro,[status(thm)],[56])).
% 42.30/26.59 tff(58,plain,
% 42.30/26.59 (![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)))),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(59,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 42.30/26.59 tff(60,plain,
% 42.30/26.59 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[59, 58])).
% 42.30/26.59 tff(61,plain,(
% 42.30/26.59 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 42.30/26.59 inference(skolemize,[status(sab)],[60])).
% 42.30/26.59 tff(62,plain,
% 42.30/26.59 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[61, 57])).
% 42.30/26.59 tff(63,plain,
% 42.30/26.59 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(zero, addition(antidomain(zero), zero)) = addition(multiplication(zero, antidomain(zero)), multiplication(zero, zero)))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(64,plain,
% 42.30/26.59 (multiplication(zero, addition(antidomain(zero), zero)) = addition(multiplication(zero, antidomain(zero)), multiplication(zero, zero))),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[63, 62])).
% 42.30/26.59 tff(65,plain,
% 42.30/26.59 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(66,plain,
% 42.30/26.59 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 42.30/26.59 inference(quant_intro,[status(thm)],[65])).
% 42.30/26.59 tff(67,plain,
% 42.30/26.59 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(68,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 42.30/26.59 tff(69,plain,
% 42.30/26.59 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[68, 67])).
% 42.30/26.59 tff(70,plain,(
% 42.30/26.59 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 42.30/26.59 inference(skolemize,[status(sab)],[69])).
% 42.30/26.59 tff(71,plain,
% 42.30/26.59 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[70, 66])).
% 42.30/26.59 tff(72,plain,
% 42.30/26.59 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, antidomain(zero)) = addition(antidomain(zero), zero))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(73,plain,
% 42.30/26.59 (addition(zero, antidomain(zero)) = addition(antidomain(zero), zero)),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[72, 71])).
% 42.30/26.59 tff(74,plain,
% 42.30/26.59 (addition(zero, antidomain(zero)) = addition(domain(zero), antidomain(zero))),
% 42.30/26.59 inference(monotonicity,[status(thm)],[52])).
% 42.30/26.59 tff(75,plain,
% 42.30/26.59 (addition(domain(zero), antidomain(zero)) = addition(zero, antidomain(zero))),
% 42.30/26.59 inference(symmetry,[status(thm)],[74])).
% 42.30/26.59 tff(76,plain,
% 42.30/26.59 (((~(addition(domain(zero), antidomain(zero)) = one)) | (~(multiplication(domain(zero), antidomain(zero)) = zero))) | (addition(domain(zero), antidomain(zero)) = one)),
% 42.30/26.59 inference(tautology,[status(thm)],[])).
% 42.30/26.59 tff(77,plain,
% 42.30/26.59 (addition(domain(zero), antidomain(zero)) = one),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[76, 49])).
% 42.30/26.59 tff(78,plain,
% 42.30/26.59 (one = addition(domain(zero), antidomain(zero))),
% 42.30/26.59 inference(symmetry,[status(thm)],[77])).
% 42.30/26.59 tff(79,plain,
% 42.30/26.59 (one = addition(antidomain(zero), zero)),
% 42.30/26.59 inference(transitivity,[status(thm)],[78, 75, 73])).
% 42.30/26.59 tff(80,plain,
% 42.30/26.59 ((~![X1: $i] : (~((~(addition(domain(X1), antidomain(X1)) = one)) | (~(multiplication(domain(X1), antidomain(X1)) = zero))))) | (~((~(addition(domain(X0!0), antidomain(X0!0)) = one)) | (~(multiplication(domain(X0!0), antidomain(X0!0)) = zero))))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(81,plain,
% 42.30/26.59 (~((~(addition(domain(X0!0), antidomain(X0!0)) = one)) | (~(multiplication(domain(X0!0), antidomain(X0!0)) = zero)))),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[80, 47])).
% 42.30/26.59 tff(82,plain,
% 42.30/26.59 (((~(addition(domain(X0!0), antidomain(X0!0)) = one)) | (~(multiplication(domain(X0!0), antidomain(X0!0)) = zero))) | (multiplication(domain(X0!0), antidomain(X0!0)) = zero)),
% 42.30/26.59 inference(tautology,[status(thm)],[])).
% 42.30/26.59 tff(83,plain,
% 42.30/26.59 (multiplication(domain(X0!0), antidomain(X0!0)) = zero),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[82, 81])).
% 42.30/26.59 tff(84,plain,
% 42.30/26.59 (multiplication(multiplication(domain(X0!0), antidomain(X0!0)), one) = multiplication(zero, addition(antidomain(zero), zero))),
% 42.30/26.59 inference(monotonicity,[status(thm)],[83, 79])).
% 42.30/26.59 tff(85,plain,
% 42.30/26.59 (^[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)))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(86,plain,
% 42.30/26.59 (![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))),
% 42.30/26.59 inference(quant_intro,[status(thm)],[85])).
% 42.30/26.59 tff(87,plain,
% 42.30/26.59 (![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))),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(88,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_associativity')).
% 42.30/26.59 tff(89,plain,
% 42.30/26.59 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[88, 87])).
% 42.30/26.59 tff(90,plain,(
% 42.30/26.59 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 42.30/26.59 inference(skolemize,[status(sab)],[89])).
% 42.30/26.59 tff(91,plain,
% 42.30/26.59 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[90, 86])).
% 42.30/26.59 tff(92,plain,
% 42.30/26.59 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(domain(X0!0), multiplication(antidomain(X0!0), one)) = multiplication(multiplication(domain(X0!0), antidomain(X0!0)), one))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(93,plain,
% 42.30/26.59 (multiplication(domain(X0!0), multiplication(antidomain(X0!0), one)) = multiplication(multiplication(domain(X0!0), antidomain(X0!0)), one)),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[92, 91])).
% 42.30/26.59 tff(94,plain,
% 42.30/26.59 (multiplication(domain(X0!0), multiplication(antidomain(X0!0), one)) = zero),
% 42.30/26.59 inference(transitivity,[status(thm)],[93, 84, 64, 55, 28, 24, 15, 11])).
% 42.30/26.59 tff(95,plain,
% 42.30/26.59 (multiplication(multiplication(domain(X0!0), multiplication(antidomain(X0!0), one)), X0!0) = multiplication(zero, X0!0)),
% 42.30/26.59 inference(monotonicity,[status(thm)],[94])).
% 42.30/26.59 tff(96,plain,
% 42.30/26.59 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(domain(X0!0), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = multiplication(multiplication(domain(X0!0), multiplication(antidomain(X0!0), one)), X0!0))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(97,plain,
% 42.30/26.59 (multiplication(domain(X0!0), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = multiplication(multiplication(domain(X0!0), multiplication(antidomain(X0!0), one)), X0!0)),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[96, 91])).
% 42.30/26.59 tff(98,plain,
% 42.30/26.59 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(99,plain,
% 42.30/26.59 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 42.30/26.59 inference(quant_intro,[status(thm)],[98])).
% 42.30/26.59 tff(100,plain,
% 42.30/26.59 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(101,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 42.30/26.59 tff(102,plain,
% 42.30/26.59 (![A: $i] : (multiplication(one, A) = A)),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[101, 100])).
% 42.30/26.59 tff(103,plain,(
% 42.30/26.59 ![A: $i] : (multiplication(one, A) = A)),
% 42.30/26.59 inference(skolemize,[status(sab)],[102])).
% 42.30/26.59 tff(104,plain,
% 42.30/26.59 (![A: $i] : (multiplication(one, A) = A)),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[103, 99])).
% 42.30/26.59 tff(105,plain,
% 42.30/26.59 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, domain(X0!0)) = domain(X0!0))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(106,plain,
% 42.30/26.59 (multiplication(one, domain(X0!0)) = domain(X0!0)),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[105, 104])).
% 42.30/26.59 tff(107,plain,
% 42.30/26.59 (multiplication(multiplication(one, domain(X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = multiplication(domain(X0!0), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.59 inference(monotonicity,[status(thm)],[106])).
% 42.30/26.59 tff(108,plain,
% 42.30/26.59 (domain(X0!0) = multiplication(one, domain(X0!0))),
% 42.30/26.59 inference(symmetry,[status(thm)],[106])).
% 42.30/26.59 tff(109,plain,
% 42.30/26.59 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!0) = X0!0)),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(110,plain,
% 42.30/26.59 (multiplication(one, X0!0) = X0!0),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[109, 104])).
% 42.30/26.59 tff(111,plain,
% 42.30/26.59 (domain(multiplication(one, X0!0)) = domain(X0!0)),
% 42.30/26.59 inference(monotonicity,[status(thm)],[110])).
% 42.30/26.59 tff(112,plain,
% 42.30/26.59 (^[X0: $i, X1: $i] : refl((domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(113,plain,
% 42.30/26.59 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 42.30/26.59 inference(quant_intro,[status(thm)],[112])).
% 42.30/26.59 tff(114,plain,
% 42.30/26.59 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(115,axiom,(![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain2')).
% 42.30/26.59 tff(116,plain,
% 42.30/26.59 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[115, 114])).
% 42.30/26.59 tff(117,plain,(
% 42.30/26.59 ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 42.30/26.59 inference(skolemize,[status(sab)],[116])).
% 42.30/26.59 tff(118,plain,
% 42.30/26.59 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[117, 113])).
% 42.30/26.59 tff(119,plain,
% 42.30/26.59 ((~![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))) | (domain(multiplication(one, X0!0)) = domain(multiplication(one, domain(X0!0))))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(120,plain,
% 42.30/26.59 (domain(multiplication(one, X0!0)) = domain(multiplication(one, domain(X0!0)))),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[119, 118])).
% 42.30/26.59 tff(121,plain,
% 42.30/26.59 (domain(multiplication(one, domain(X0!0))) = domain(multiplication(one, X0!0))),
% 42.30/26.59 inference(symmetry,[status(thm)],[120])).
% 42.30/26.59 tff(122,plain,
% 42.30/26.59 (((~(addition(domain(X0!0), antidomain(X0!0)) = one)) | (~(multiplication(domain(X0!0), antidomain(X0!0)) = zero))) | (addition(domain(X0!0), antidomain(X0!0)) = one)),
% 42.30/26.59 inference(tautology,[status(thm)],[])).
% 42.30/26.59 tff(123,plain,
% 42.30/26.59 (addition(domain(X0!0), antidomain(X0!0)) = one),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[122, 81])).
% 42.30/26.59 tff(124,plain,
% 42.30/26.59 (multiplication(addition(domain(X0!0), antidomain(X0!0)), domain(X0!0)) = multiplication(one, domain(X0!0))),
% 42.30/26.59 inference(monotonicity,[status(thm)],[123])).
% 42.30/26.59 tff(125,plain,
% 42.30/26.59 (^[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))))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(126,plain,
% 42.30/26.59 (![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)))),
% 42.30/26.59 inference(quant_intro,[status(thm)],[125])).
% 42.30/26.59 tff(127,plain,
% 42.30/26.59 (![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)))),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(128,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 42.30/26.59 tff(129,plain,
% 42.30/26.59 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[128, 127])).
% 42.30/26.59 tff(130,plain,(
% 42.30/26.59 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 42.30/26.59 inference(skolemize,[status(sab)],[129])).
% 42.30/26.59 tff(131,plain,
% 42.30/26.59 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[130, 126])).
% 42.30/26.59 tff(132,plain,
% 42.30/26.59 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(domain(X0!0), antidomain(X0!0)), domain(X0!0)) = addition(multiplication(domain(X0!0), domain(X0!0)), multiplication(antidomain(X0!0), domain(X0!0))))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(133,plain,
% 42.30/26.59 (multiplication(addition(domain(X0!0), antidomain(X0!0)), domain(X0!0)) = addition(multiplication(domain(X0!0), domain(X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[132, 131])).
% 42.30/26.59 tff(134,plain,
% 42.30/26.59 (addition(multiplication(domain(X0!0), domain(X0!0)), multiplication(antidomain(X0!0), domain(X0!0))) = multiplication(addition(domain(X0!0), antidomain(X0!0)), domain(X0!0))),
% 42.30/26.59 inference(symmetry,[status(thm)],[133])).
% 42.30/26.59 tff(135,plain,
% 42.30/26.59 (multiplication(antidomain(X0!0), domain(X0!0)) = multiplication(antidomain(X0!0), multiplication(one, domain(X0!0)))),
% 42.30/26.59 inference(monotonicity,[status(thm)],[108])).
% 42.30/26.59 tff(136,plain,
% 42.30/26.59 (multiplication(antidomain(X0!0), multiplication(one, domain(X0!0))) = multiplication(antidomain(X0!0), domain(X0!0))),
% 42.30/26.59 inference(symmetry,[status(thm)],[135])).
% 42.30/26.59 tff(137,plain,
% 42.30/26.59 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(antidomain(X0!0), multiplication(one, domain(X0!0))) = multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(138,plain,
% 42.30/26.59 (multiplication(antidomain(X0!0), multiplication(one, domain(X0!0))) = multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[137, 91])).
% 42.30/26.59 tff(139,plain,
% 42.30/26.59 (multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)) = multiplication(antidomain(X0!0), multiplication(one, domain(X0!0)))),
% 42.30/26.59 inference(symmetry,[status(thm)],[138])).
% 42.30/26.59 tff(140,plain,
% 42.30/26.59 (multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)) = multiplication(antidomain(X0!0), domain(X0!0))),
% 42.30/26.59 inference(transitivity,[status(thm)],[139, 136])).
% 42.30/26.59 tff(141,plain,
% 42.30/26.59 (multiplication(domain(X0!0), domain(X0!0)) = multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0)))),
% 42.30/26.59 inference(monotonicity,[status(thm)],[108, 108])).
% 42.30/26.59 tff(142,plain,
% 42.30/26.59 (multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0))) = multiplication(domain(X0!0), domain(X0!0))),
% 42.30/26.59 inference(symmetry,[status(thm)],[141])).
% 42.30/26.59 tff(143,plain,
% 42.30/26.59 (addition(multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))) = addition(multiplication(domain(X0!0), domain(X0!0)), multiplication(antidomain(X0!0), domain(X0!0)))),
% 42.30/26.59 inference(monotonicity,[status(thm)],[142, 140])).
% 42.30/26.59 tff(144,plain,
% 42.30/26.59 (addition(multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))) = multiplication(one, domain(X0!0))),
% 42.30/26.59 inference(transitivity,[status(thm)],[143, 134, 124])).
% 42.30/26.59 tff(145,plain,
% 42.30/26.59 (domain(addition(multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))) = domain(multiplication(one, domain(X0!0)))),
% 42.30/26.59 inference(monotonicity,[status(thm)],[144])).
% 42.30/26.59 tff(146,plain,
% 42.30/26.59 (^[X0: $i, X1: $i] : refl((domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(147,plain,
% 42.30/26.59 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 42.30/26.59 inference(quant_intro,[status(thm)],[146])).
% 42.30/26.59 tff(148,plain,
% 42.30/26.59 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(149,axiom,(![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain5')).
% 42.30/26.59 tff(150,plain,
% 42.30/26.59 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[149, 148])).
% 42.30/26.59 tff(151,plain,(
% 42.30/26.59 ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 42.30/26.59 inference(skolemize,[status(sab)],[150])).
% 42.30/26.59 tff(152,plain,
% 42.30/26.59 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[151, 147])).
% 42.30/26.59 tff(153,plain,
% 42.30/26.59 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))) = addition(domain(multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0)))), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(154,plain,
% 42.30/26.59 (domain(addition(multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))) = addition(domain(multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0)))), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))))),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[153, 152])).
% 42.30/26.59 tff(155,plain,
% 42.30/26.59 (addition(domain(multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0)))), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))) = domain(addition(multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))))),
% 42.30/26.59 inference(symmetry,[status(thm)],[154])).
% 42.30/26.59 tff(156,plain,
% 42.30/26.59 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(157,plain,
% 42.30/26.59 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 42.30/26.59 inference(quant_intro,[status(thm)],[156])).
% 42.30/26.59 tff(158,plain,
% 42.30/26.59 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(159,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 42.30/26.59 tff(160,plain,
% 42.30/26.59 (![A: $i] : (addition(A, zero) = A)),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[159, 158])).
% 42.30/26.59 tff(161,plain,(
% 42.30/26.59 ![A: $i] : (addition(A, zero) = A)),
% 42.30/26.59 inference(skolemize,[status(sab)],[160])).
% 42.30/26.59 tff(162,plain,
% 42.30/26.59 (![A: $i] : (addition(A, zero) = A)),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[161, 157])).
% 42.30/26.59 tff(163,plain,
% 42.30/26.59 ((~![A: $i] : (addition(A, zero) = A)) | (addition(domain(X0!0), zero) = domain(X0!0))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(164,plain,
% 42.30/26.59 (addition(domain(X0!0), zero) = domain(X0!0)),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[163, 162])).
% 42.30/26.59 tff(165,plain,
% 42.30/26.59 (addition(domain(X0!0), zero) = multiplication(one, domain(X0!0))),
% 42.30/26.59 inference(transitivity,[status(thm)],[164, 108])).
% 42.30/26.59 tff(166,plain,
% 42.30/26.59 (multiplication(addition(domain(X0!0), zero), domain(X0!0)) = multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0)))),
% 42.30/26.59 inference(monotonicity,[status(thm)],[165, 108])).
% 42.30/26.59 tff(167,plain,
% 42.30/26.59 (multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0))) = multiplication(addition(domain(X0!0), zero), domain(X0!0))),
% 42.30/26.59 inference(symmetry,[status(thm)],[166])).
% 42.30/26.59 tff(168,plain,
% 42.30/26.59 (domain(multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0)))) = domain(multiplication(addition(domain(X0!0), zero), domain(X0!0)))),
% 42.30/26.59 inference(monotonicity,[status(thm)],[167])).
% 42.30/26.59 tff(169,plain,
% 42.30/26.59 (domain(multiplication(addition(domain(X0!0), zero), domain(X0!0))) = domain(multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0))))),
% 42.30/26.59 inference(symmetry,[status(thm)],[168])).
% 42.30/26.59 tff(170,plain,
% 42.30/26.59 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(171,plain,
% 42.30/26.59 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 42.30/26.59 inference(quant_intro,[status(thm)],[170])).
% 42.30/26.59 tff(172,plain,
% 42.30/26.59 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(173,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 42.30/26.59 tff(174,plain,
% 42.30/26.59 (![A: $i] : (multiplication(A, one) = A)),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[173, 172])).
% 42.30/26.59 tff(175,plain,(
% 42.30/26.59 ![A: $i] : (multiplication(A, one) = A)),
% 42.30/26.59 inference(skolemize,[status(sab)],[174])).
% 42.30/26.59 tff(176,plain,
% 42.30/26.59 (![A: $i] : (multiplication(A, one) = A)),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[175, 171])).
% 42.30/26.59 tff(177,plain,
% 42.30/26.59 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(addition(domain(X0!0), zero), one) = addition(domain(X0!0), zero))),
% 42.30/26.59 inference(quant_inst,[status(thm)],[])).
% 42.30/26.59 tff(178,plain,
% 42.30/26.59 (multiplication(addition(domain(X0!0), zero), one) = addition(domain(X0!0), zero)),
% 42.30/26.59 inference(unit_resolution,[status(thm)],[177, 176])).
% 42.30/26.59 tff(179,plain,
% 42.30/26.59 (^[X0: $i] : refl((addition(domain(X0), one) = one) <=> (addition(domain(X0), one) = one))),
% 42.30/26.59 inference(bind,[status(th)],[])).
% 42.30/26.59 tff(180,plain,
% 42.30/26.59 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 42.30/26.59 inference(quant_intro,[status(thm)],[179])).
% 42.30/26.59 tff(181,plain,
% 42.30/26.59 (![X0: $i] : (addition(domain(X0), one) = one) <=> ![X0: $i] : (addition(domain(X0), one) = one)),
% 42.30/26.59 inference(rewrite,[status(thm)],[])).
% 42.30/26.59 tff(182,axiom,(![X0: $i] : (addition(domain(X0), one) = one)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain3')).
% 42.30/26.59 tff(183,plain,
% 42.30/26.59 (![X0: $i] : (addition(domain(X0), one) = one)),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[182, 181])).
% 42.30/26.59 tff(184,plain,(
% 42.30/26.59 ![X0: $i] : (addition(domain(X0), one) = one)),
% 42.30/26.59 inference(skolemize,[status(sab)],[183])).
% 42.30/26.59 tff(185,plain,
% 42.30/26.59 (![X0: $i] : (addition(domain(X0), one) = one)),
% 42.30/26.59 inference(modus_ponens,[status(thm)],[184, 180])).
% 42.30/26.59 tff(186,plain,
% 42.30/26.59 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(zero), one) = one)),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(187,plain,
% 42.30/26.60 (addition(domain(zero), one) = one),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[186, 185])).
% 42.30/26.60 tff(188,plain,
% 42.30/26.60 (addition(zero, addition(domain(X0!0), antidomain(X0!0))) = addition(domain(zero), one)),
% 42.30/26.60 inference(monotonicity,[status(thm)],[52, 123])).
% 42.30/26.60 tff(189,plain,
% 42.30/26.60 (^[C: $i, B: $i, A: $i] : refl((addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> (addition(A, addition(B, C)) = addition(addition(A, B), C)))),
% 42.30/26.60 inference(bind,[status(th)],[])).
% 42.30/26.60 tff(190,plain,
% 42.30/26.60 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 42.30/26.60 inference(quant_intro,[status(thm)],[189])).
% 42.30/26.60 tff(191,plain,
% 42.30/26.60 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 42.30/26.60 inference(rewrite,[status(thm)],[])).
% 42.30/26.60 tff(192,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 42.30/26.60 tff(193,plain,
% 42.30/26.60 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 42.30/26.60 inference(modus_ponens,[status(thm)],[192, 191])).
% 42.30/26.60 tff(194,plain,(
% 42.30/26.60 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 42.30/26.60 inference(skolemize,[status(sab)],[193])).
% 42.30/26.60 tff(195,plain,
% 42.30/26.60 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 42.30/26.60 inference(modus_ponens,[status(thm)],[194, 190])).
% 42.30/26.60 tff(196,plain,
% 42.30/26.60 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(zero, addition(domain(X0!0), antidomain(X0!0))) = addition(addition(zero, domain(X0!0)), antidomain(X0!0)))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(197,plain,
% 42.30/26.60 (addition(zero, addition(domain(X0!0), antidomain(X0!0))) = addition(addition(zero, domain(X0!0)), antidomain(X0!0))),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[196, 195])).
% 42.30/26.60 tff(198,plain,
% 42.30/26.60 (addition(addition(zero, domain(X0!0)), antidomain(X0!0)) = addition(zero, addition(domain(X0!0), antidomain(X0!0)))),
% 42.30/26.60 inference(symmetry,[status(thm)],[197])).
% 42.30/26.60 tff(199,plain,
% 42.30/26.60 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(antidomain(X0!0), one) = antidomain(X0!0))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(200,plain,
% 42.30/26.60 (multiplication(antidomain(X0!0), one) = antidomain(X0!0)),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[199, 176])).
% 42.30/26.60 tff(201,plain,
% 42.30/26.60 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, domain(X0!0)) = addition(domain(X0!0), zero))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(202,plain,
% 42.30/26.60 (addition(zero, domain(X0!0)) = addition(domain(X0!0), zero)),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[201, 71])).
% 42.30/26.60 tff(203,plain,
% 42.30/26.60 (addition(domain(X0!0), zero) = addition(zero, domain(X0!0))),
% 42.30/26.60 inference(symmetry,[status(thm)],[202])).
% 42.30/26.60 tff(204,plain,
% 42.30/26.60 (addition(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), one)) = addition(addition(zero, domain(X0!0)), antidomain(X0!0))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[203, 200])).
% 42.30/26.60 tff(205,plain,
% 42.30/26.60 (addition(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), one)) = one),
% 42.30/26.60 inference(transitivity,[status(thm)],[204, 198, 188, 187])).
% 42.30/26.60 tff(206,plain,
% 42.30/26.60 (multiplication(addition(domain(X0!0), zero), addition(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), one))) = multiplication(addition(domain(X0!0), zero), one)),
% 42.30/26.60 inference(monotonicity,[status(thm)],[205])).
% 42.30/26.60 tff(207,plain,
% 42.30/26.60 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(domain(X0!0), zero), addition(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), one))) = addition(multiplication(addition(domain(X0!0), zero), addition(domain(X0!0), zero)), multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), one))))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(208,plain,
% 42.30/26.60 (multiplication(addition(domain(X0!0), zero), addition(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), one))) = addition(multiplication(addition(domain(X0!0), zero), addition(domain(X0!0), zero)), multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), one)))),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[207, 62])).
% 42.30/26.60 tff(209,plain,
% 42.30/26.60 (addition(multiplication(addition(domain(X0!0), zero), addition(domain(X0!0), zero)), multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), one))) = multiplication(addition(domain(X0!0), zero), addition(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), one)))),
% 42.30/26.60 inference(symmetry,[status(thm)],[208])).
% 42.30/26.60 tff(210,plain,
% 42.30/26.60 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, domain(X0!0)) = zero)),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(211,plain,
% 42.30/26.60 (multiplication(zero, domain(X0!0)) = zero),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[210, 7])).
% 42.30/26.60 tff(212,plain,
% 42.30/26.60 (addition(multiplication(zero, domain(X0!0)), domain(X0!0)) = addition(zero, domain(X0!0))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[211])).
% 42.30/26.60 tff(213,plain,
% 42.30/26.60 (addition(zero, domain(X0!0)) = addition(multiplication(zero, domain(X0!0)), domain(X0!0))),
% 42.30/26.60 inference(symmetry,[status(thm)],[212])).
% 42.30/26.60 tff(214,plain,
% 42.30/26.60 (addition(domain(X0!0), zero) = addition(multiplication(zero, domain(X0!0)), domain(X0!0))),
% 42.30/26.60 inference(transitivity,[status(thm)],[203, 213])).
% 42.30/26.60 tff(215,plain,
% 42.30/26.60 (multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), one)) = multiplication(addition(multiplication(zero, domain(X0!0)), domain(X0!0)), antidomain(X0!0))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[214, 200])).
% 42.30/26.60 tff(216,plain,
% 42.30/26.60 (multiplication(addition(multiplication(zero, domain(X0!0)), domain(X0!0)), antidomain(X0!0)) = multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), one))),
% 42.30/26.60 inference(symmetry,[status(thm)],[215])).
% 42.30/26.60 tff(217,plain,
% 42.30/26.60 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(zero, domain(X0!0)), domain(X0!0)), antidomain(X0!0)) = addition(multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)), multiplication(domain(X0!0), antidomain(X0!0))))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(218,plain,
% 42.30/26.60 (multiplication(addition(multiplication(zero, domain(X0!0)), domain(X0!0)), antidomain(X0!0)) = addition(multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)), multiplication(domain(X0!0), antidomain(X0!0)))),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[217, 131])).
% 42.30/26.60 tff(219,plain,
% 42.30/26.60 (addition(multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)), multiplication(domain(X0!0), antidomain(X0!0))) = multiplication(addition(multiplication(zero, domain(X0!0)), domain(X0!0)), antidomain(X0!0))),
% 42.30/26.60 inference(symmetry,[status(thm)],[218])).
% 42.30/26.60 tff(220,plain,
% 42.30/26.60 (multiplication(zero, multiplication(domain(X0!0), antidomain(X0!0))) = multiplication(domain(zero), zero)),
% 42.30/26.60 inference(monotonicity,[status(thm)],[52, 83])).
% 42.30/26.60 tff(221,plain,
% 42.30/26.60 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(zero, multiplication(domain(X0!0), antidomain(X0!0))) = multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(222,plain,
% 42.30/26.60 (multiplication(zero, multiplication(domain(X0!0), antidomain(X0!0))) = multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0))),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[221, 91])).
% 42.30/26.60 tff(223,plain,
% 42.30/26.60 (multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)) = multiplication(zero, multiplication(domain(X0!0), antidomain(X0!0)))),
% 42.30/26.60 inference(symmetry,[status(thm)],[222])).
% 42.30/26.60 tff(224,plain,
% 42.30/26.60 (multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)) = zero),
% 42.30/26.60 inference(transitivity,[status(thm)],[223, 220, 15, 11])).
% 42.30/26.60 tff(225,plain,
% 42.30/26.60 (addition(multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)), multiplication(domain(X0!0), antidomain(X0!0))) = addition(zero, zero)),
% 42.30/26.60 inference(monotonicity,[status(thm)],[224, 83])).
% 42.30/26.60 tff(226,plain,
% 42.30/26.60 (addition(zero, zero) = addition(multiplication(multiplication(zero, domain(X0!0)), antidomain(X0!0)), multiplication(domain(X0!0), antidomain(X0!0)))),
% 42.30/26.60 inference(symmetry,[status(thm)],[225])).
% 42.30/26.60 tff(227,plain,
% 42.30/26.60 (addition(zero, multiplication(domain(zero), zero)) = addition(zero, zero)),
% 42.30/26.60 inference(symmetry,[status(thm)],[28])).
% 42.30/26.60 tff(228,plain,
% 42.30/26.60 (multiplication(domain(zero), zero) = addition(zero, multiplication(domain(zero), zero))),
% 42.30/26.60 inference(symmetry,[status(thm)],[24])).
% 42.30/26.60 tff(229,plain,
% 42.30/26.60 (^[A: $i] : refl((multiplication(A, zero) = zero) <=> (multiplication(A, zero) = zero))),
% 42.30/26.60 inference(bind,[status(th)],[])).
% 42.30/26.60 tff(230,plain,
% 42.30/26.60 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 42.30/26.60 inference(quant_intro,[status(thm)],[229])).
% 42.30/26.60 tff(231,plain,
% 42.30/26.60 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 42.30/26.60 inference(rewrite,[status(thm)],[])).
% 42.30/26.60 tff(232,axiom,(![A: $i] : (multiplication(A, zero) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','right_annihilation')).
% 42.30/26.60 tff(233,plain,
% 42.30/26.60 (![A: $i] : (multiplication(A, zero) = zero)),
% 42.30/26.60 inference(modus_ponens,[status(thm)],[232, 231])).
% 42.30/26.60 tff(234,plain,(
% 42.30/26.60 ![A: $i] : (multiplication(A, zero) = zero)),
% 42.30/26.60 inference(skolemize,[status(sab)],[233])).
% 42.30/26.60 tff(235,plain,
% 42.30/26.60 (![A: $i] : (multiplication(A, zero) = zero)),
% 42.30/26.60 inference(modus_ponens,[status(thm)],[234, 230])).
% 42.30/26.60 tff(236,plain,
% 42.30/26.60 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(antidomain(zero), zero) = zero)),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(237,plain,
% 42.30/26.60 (multiplication(antidomain(zero), zero) = zero),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[236, 235])).
% 42.30/26.60 tff(238,plain,
% 42.30/26.60 (multiplication(domain(X0!0), antidomain(X0!0)) = domain(zero)),
% 42.30/26.60 inference(transitivity,[status(thm)],[83, 52])).
% 42.30/26.60 tff(239,plain,
% 42.30/26.60 (multiplication(multiplication(domain(X0!0), antidomain(X0!0)), zero) = multiplication(domain(zero), zero)),
% 42.30/26.60 inference(monotonicity,[status(thm)],[238])).
% 42.30/26.60 tff(240,plain,
% 42.30/26.60 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(domain(X0!0), multiplication(antidomain(X0!0), zero)) = multiplication(multiplication(domain(X0!0), antidomain(X0!0)), zero))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(241,plain,
% 42.30/26.60 (multiplication(domain(X0!0), multiplication(antidomain(X0!0), zero)) = multiplication(multiplication(domain(X0!0), antidomain(X0!0)), zero)),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[240, 91])).
% 42.30/26.60 tff(242,plain,
% 42.30/26.60 (multiplication(domain(X0!0), multiplication(antidomain(X0!0), zero)) = zero),
% 42.30/26.60 inference(transitivity,[status(thm)],[241, 239, 15, 11])).
% 42.30/26.60 tff(243,plain,
% 42.30/26.60 (multiplication(antidomain(zero), multiplication(domain(X0!0), multiplication(antidomain(X0!0), zero))) = multiplication(antidomain(zero), zero)),
% 42.30/26.60 inference(monotonicity,[status(thm)],[242])).
% 42.30/26.60 tff(244,plain,
% 42.30/26.60 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(antidomain(zero), multiplication(domain(X0!0), multiplication(antidomain(X0!0), zero))) = multiplication(multiplication(antidomain(zero), domain(X0!0)), multiplication(antidomain(X0!0), zero)))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(245,plain,
% 42.30/26.60 (multiplication(antidomain(zero), multiplication(domain(X0!0), multiplication(antidomain(X0!0), zero))) = multiplication(multiplication(antidomain(zero), domain(X0!0)), multiplication(antidomain(X0!0), zero))),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[244, 91])).
% 42.30/26.60 tff(246,plain,
% 42.30/26.60 (multiplication(multiplication(antidomain(zero), domain(X0!0)), multiplication(antidomain(X0!0), zero)) = multiplication(antidomain(zero), multiplication(domain(X0!0), multiplication(antidomain(X0!0), zero)))),
% 42.30/26.60 inference(symmetry,[status(thm)],[245])).
% 42.30/26.60 tff(247,plain,
% 42.30/26.60 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(antidomain(X0!0), zero) = zero)),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(248,plain,
% 42.30/26.60 (multiplication(antidomain(X0!0), zero) = zero),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[247, 235])).
% 42.30/26.60 tff(249,plain,
% 42.30/26.60 (zero = multiplication(antidomain(X0!0), zero)),
% 42.30/26.60 inference(symmetry,[status(thm)],[248])).
% 42.30/26.60 tff(250,plain,
% 42.30/26.60 (addition(antidomain(zero), zero) = addition(zero, antidomain(zero))),
% 42.30/26.60 inference(symmetry,[status(thm)],[73])).
% 42.30/26.60 tff(251,plain,
% 42.30/26.60 ((~![A: $i] : (addition(A, zero) = A)) | (addition(antidomain(zero), zero) = antidomain(zero))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(252,plain,
% 42.30/26.60 (addition(antidomain(zero), zero) = antidomain(zero)),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[251, 162])).
% 42.30/26.60 tff(253,plain,
% 42.30/26.60 (antidomain(zero) = addition(antidomain(zero), zero)),
% 42.30/26.60 inference(symmetry,[status(thm)],[252])).
% 42.30/26.60 tff(254,plain,
% 42.30/26.60 (antidomain(zero) = one),
% 42.30/26.60 inference(transitivity,[status(thm)],[253, 250, 74, 77])).
% 42.30/26.60 tff(255,plain,
% 42.30/26.60 (multiplication(antidomain(zero), domain(X0!0)) = multiplication(one, domain(X0!0))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[254])).
% 42.30/26.60 tff(256,plain,
% 42.30/26.60 (multiplication(one, domain(X0!0)) = multiplication(antidomain(zero), domain(X0!0))),
% 42.30/26.60 inference(symmetry,[status(thm)],[255])).
% 42.30/26.60 tff(257,plain,
% 42.30/26.60 (addition(domain(X0!0), zero) = multiplication(antidomain(zero), domain(X0!0))),
% 42.30/26.60 inference(transitivity,[status(thm)],[164, 108, 256])).
% 42.30/26.60 tff(258,plain,
% 42.30/26.60 (multiplication(addition(domain(X0!0), zero), zero) = multiplication(multiplication(antidomain(zero), domain(X0!0)), multiplication(antidomain(X0!0), zero))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[257, 249])).
% 42.30/26.60 tff(259,plain,
% 42.30/26.60 (multiplication(addition(domain(X0!0), zero), zero) = multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), one))),
% 42.30/26.60 inference(transitivity,[status(thm)],[258, 246, 243, 237, 26, 25, 228, 227, 226, 219, 216])).
% 42.30/26.60 tff(260,plain,
% 42.30/26.60 (addition(multiplication(addition(domain(X0!0), zero), addition(domain(X0!0), zero)), multiplication(addition(domain(X0!0), zero), zero)) = addition(multiplication(addition(domain(X0!0), zero), addition(domain(X0!0), zero)), multiplication(addition(domain(X0!0), zero), multiplication(antidomain(X0!0), one)))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[259])).
% 42.30/26.60 tff(261,plain,
% 42.30/26.60 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(domain(X0!0), zero), addition(addition(domain(X0!0), zero), zero)) = addition(multiplication(addition(domain(X0!0), zero), addition(domain(X0!0), zero)), multiplication(addition(domain(X0!0), zero), zero)))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(262,plain,
% 42.30/26.60 (multiplication(addition(domain(X0!0), zero), addition(addition(domain(X0!0), zero), zero)) = addition(multiplication(addition(domain(X0!0), zero), addition(domain(X0!0), zero)), multiplication(addition(domain(X0!0), zero), zero))),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[261, 62])).
% 42.30/26.60 tff(263,plain,
% 42.30/26.60 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, addition(domain(X0!0), zero)) = addition(addition(domain(X0!0), zero), zero))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(264,plain,
% 42.30/26.60 (addition(zero, addition(domain(X0!0), zero)) = addition(addition(domain(X0!0), zero), zero)),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[263, 71])).
% 42.30/26.60 tff(265,plain,
% 42.30/26.60 (addition(zero, addition(domain(X0!0), zero)) = addition(zero, addition(zero, domain(X0!0)))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[203])).
% 42.30/26.60 tff(266,plain,
% 42.30/26.60 (addition(zero, addition(zero, domain(X0!0))) = addition(zero, addition(domain(X0!0), zero))),
% 42.30/26.60 inference(symmetry,[status(thm)],[265])).
% 42.30/26.60 tff(267,plain,
% 42.30/26.60 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(zero, addition(zero, domain(X0!0))) = addition(addition(zero, zero), domain(X0!0)))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(268,plain,
% 42.30/26.60 (addition(zero, addition(zero, domain(X0!0))) = addition(addition(zero, zero), domain(X0!0))),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[267, 195])).
% 42.30/26.60 tff(269,plain,
% 42.30/26.60 (addition(addition(zero, zero), domain(X0!0)) = addition(zero, addition(zero, domain(X0!0)))),
% 42.30/26.60 inference(symmetry,[status(thm)],[268])).
% 42.30/26.60 tff(270,plain,
% 42.30/26.60 (addition(zero, zero) = zero),
% 42.30/26.60 inference(transitivity,[status(thm)],[28, 24, 15, 11])).
% 42.30/26.60 tff(271,plain,
% 42.30/26.60 (addition(addition(zero, zero), domain(X0!0)) = addition(zero, domain(X0!0))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[270])).
% 42.30/26.60 tff(272,plain,
% 42.30/26.60 (addition(zero, domain(X0!0)) = addition(addition(zero, zero), domain(X0!0))),
% 42.30/26.60 inference(symmetry,[status(thm)],[271])).
% 42.30/26.60 tff(273,plain,
% 42.30/26.60 (domain(X0!0) = addition(domain(X0!0), zero)),
% 42.30/26.60 inference(symmetry,[status(thm)],[164])).
% 42.30/26.60 tff(274,plain,
% 42.30/26.60 (multiplication(one, domain(X0!0)) = addition(addition(domain(X0!0), zero), zero)),
% 42.30/26.60 inference(transitivity,[status(thm)],[106, 273, 203, 272, 269, 266, 264])).
% 42.30/26.60 tff(275,plain,
% 42.30/26.60 (multiplication(one, domain(X0!0)) = addition(domain(X0!0), zero)),
% 42.30/26.60 inference(transitivity,[status(thm)],[106, 273])).
% 42.30/26.60 tff(276,plain,
% 42.30/26.60 (multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0))) = multiplication(addition(domain(X0!0), zero), addition(addition(domain(X0!0), zero), zero))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[275, 274])).
% 42.30/26.60 tff(277,plain,
% 42.30/26.60 (multiplication(addition(domain(X0!0), zero), domain(X0!0)) = multiplication(one, domain(X0!0))),
% 42.30/26.60 inference(transitivity,[status(thm)],[166, 276, 262, 260, 209, 206, 178, 164, 108])).
% 42.30/26.60 tff(278,plain,
% 42.30/26.60 (domain(multiplication(addition(domain(X0!0), zero), domain(X0!0))) = domain(multiplication(one, domain(X0!0)))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[277])).
% 42.30/26.60 tff(279,plain,
% 42.30/26.60 (domain(multiplication(one, domain(X0!0))) = domain(multiplication(addition(domain(X0!0), zero), domain(X0!0)))),
% 42.30/26.60 inference(symmetry,[status(thm)],[278])).
% 42.30/26.60 tff(280,plain,
% 42.30/26.60 (domain(X0!0) = domain(multiplication(one, X0!0))),
% 42.30/26.60 inference(symmetry,[status(thm)],[111])).
% 42.30/26.60 tff(281,plain,
% 42.30/26.60 (addition(domain(X0!0), zero) = domain(multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0))))),
% 42.30/26.60 inference(transitivity,[status(thm)],[164, 280, 120, 279, 169])).
% 42.30/26.60 tff(282,plain,
% 42.30/26.60 (addition(addition(domain(X0!0), zero), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))) = addition(domain(multiplication(multiplication(one, domain(X0!0)), multiplication(one, domain(X0!0)))), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[281])).
% 42.30/26.60 tff(283,plain,
% 42.30/26.60 (addition(addition(domain(X0!0), zero), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))) = multiplication(one, domain(X0!0))),
% 42.30/26.60 inference(transitivity,[status(thm)],[282, 155, 145, 121, 111, 108])).
% 42.30/26.60 tff(284,plain,
% 42.30/26.60 (multiplication(addition(addition(domain(X0!0), zero), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = multiplication(multiplication(one, domain(X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[283])).
% 42.30/26.60 tff(285,plain,
% 42.30/26.60 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(domain(X0!0), zero), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = addition(multiplication(addition(domain(X0!0), zero), multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), X0!0))))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(286,plain,
% 42.30/26.60 (multiplication(addition(addition(domain(X0!0), zero), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = addition(multiplication(addition(domain(X0!0), zero), multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), X0!0)))),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[285, 131])).
% 42.30/26.60 tff(287,plain,
% 42.30/26.60 (addition(multiplication(addition(domain(X0!0), zero), multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), X0!0))) = multiplication(addition(addition(domain(X0!0), zero), domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(symmetry,[status(thm)],[286])).
% 42.30/26.60 tff(288,plain,
% 42.30/26.60 ((~![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))) | (domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)) = domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(289,plain,
% 42.30/26.60 (domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)) = domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0)))),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[288, 118])).
% 42.30/26.60 tff(290,plain,
% 42.30/26.60 (domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))) = domain(multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(symmetry,[status(thm)],[289])).
% 42.30/26.60 tff(291,plain,
% 42.30/26.60 (multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[290])).
% 42.30/26.60 tff(292,plain,
% 42.30/26.60 (multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(symmetry,[status(thm)],[291])).
% 42.30/26.60 tff(293,plain,
% 42.30/26.60 (multiplication(addition(domain(X0!0), zero), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = multiplication(multiplication(one, domain(X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[165])).
% 42.30/26.60 tff(294,plain,
% 42.30/26.60 (multiplication(multiplication(one, domain(X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = multiplication(addition(domain(X0!0), zero), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(symmetry,[status(thm)],[293])).
% 42.30/26.60 tff(295,plain,
% 42.30/26.60 (multiplication(domain(X0!0), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = multiplication(multiplication(one, domain(X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(symmetry,[status(thm)],[107])).
% 42.30/26.60 tff(296,plain,
% 42.30/26.60 (multiplication(multiplication(domain(X0!0), multiplication(antidomain(X0!0), one)), X0!0) = multiplication(domain(X0!0), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(symmetry,[status(thm)],[97])).
% 42.30/26.60 tff(297,plain,
% 42.30/26.60 (multiplication(zero, X0!0) = multiplication(multiplication(domain(X0!0), multiplication(antidomain(X0!0), one)), X0!0)),
% 42.30/26.60 inference(symmetry,[status(thm)],[95])).
% 42.30/26.60 tff(298,plain,
% 42.30/26.60 (zero = multiplication(zero, X0!0)),
% 42.30/26.60 inference(symmetry,[status(thm)],[9])).
% 42.30/26.60 tff(299,plain,
% 42.30/26.60 (zero = multiplication(addition(domain(X0!0), zero), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(transitivity,[status(thm)],[298, 297, 296, 295, 294])).
% 42.30/26.60 tff(300,plain,
% 42.30/26.60 (addition(zero, multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))) = addition(multiplication(addition(domain(X0!0), zero), multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), X0!0)))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[299, 292])).
% 42.30/26.60 tff(301,plain,
% 42.30/26.60 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(multiplication(multiplication(antidomain(X0!0), one), X0!0), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))) = multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(302,plain,
% 42.30/26.60 (addition(multiplication(multiplication(antidomain(X0!0), one), X0!0), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))) = multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[301, 22])).
% 42.30/26.60 tff(303,plain,
% 42.30/26.60 (addition(zero, addition(multiplication(multiplication(antidomain(X0!0), one), X0!0), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)))) = addition(zero, multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[302])).
% 42.30/26.60 tff(304,plain,
% 42.30/26.60 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(zero, addition(multiplication(multiplication(antidomain(X0!0), one), X0!0), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)))) = addition(addition(zero, multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(305,plain,
% 42.30/26.60 (addition(zero, addition(multiplication(multiplication(antidomain(X0!0), one), X0!0), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)))) = addition(addition(zero, multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)))),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[304, 195])).
% 42.30/26.60 tff(306,plain,
% 42.30/26.60 (addition(addition(zero, multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))) = addition(zero, addition(multiplication(multiplication(antidomain(X0!0), one), X0!0), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))))),
% 42.30/26.60 inference(symmetry,[status(thm)],[305])).
% 42.30/26.60 tff(307,plain,
% 42.30/26.60 (addition(zero, multiplication(multiplication(antidomain(X0!0), one), X0!0)) = addition(multiplication(zero, X0!0), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[298])).
% 42.30/26.60 tff(308,plain,
% 42.30/26.60 (addition(multiplication(zero, X0!0), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = addition(zero, multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(symmetry,[status(thm)],[307])).
% 42.30/26.60 tff(309,plain,
% 42.30/26.60 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(zero, multiplication(antidomain(X0!0), one)), X0!0) = addition(multiplication(zero, X0!0), multiplication(multiplication(antidomain(X0!0), one), X0!0)))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(310,plain,
% 42.30/26.60 (multiplication(addition(zero, multiplication(antidomain(X0!0), one)), X0!0) = addition(multiplication(zero, X0!0), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[309, 131])).
% 42.30/26.60 tff(311,plain,
% 42.30/26.60 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(antidomain(X0!0), one), zero) = multiplication(antidomain(X0!0), one))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(312,plain,
% 42.30/26.60 (addition(multiplication(antidomain(X0!0), one), zero) = multiplication(antidomain(X0!0), one)),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[311, 162])).
% 42.30/26.60 tff(313,plain,
% 42.30/26.60 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, multiplication(antidomain(X0!0), one)) = addition(multiplication(antidomain(X0!0), one), zero))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(314,plain,
% 42.30/26.60 (addition(zero, multiplication(antidomain(X0!0), one)) = addition(multiplication(antidomain(X0!0), one), zero)),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[313, 71])).
% 42.30/26.60 tff(315,plain,
% 42.30/26.60 (addition(zero, multiplication(antidomain(X0!0), one)) = multiplication(antidomain(X0!0), one)),
% 42.30/26.60 inference(transitivity,[status(thm)],[314, 312])).
% 42.30/26.60 tff(316,plain,
% 42.30/26.60 (multiplication(addition(zero, multiplication(antidomain(X0!0), one)), X0!0) = multiplication(multiplication(antidomain(X0!0), one), X0!0)),
% 42.30/26.60 inference(monotonicity,[status(thm)],[315])).
% 42.30/26.60 tff(317,plain,
% 42.30/26.60 (multiplication(multiplication(antidomain(X0!0), one), X0!0) = multiplication(addition(zero, multiplication(antidomain(X0!0), one)), X0!0)),
% 42.30/26.60 inference(symmetry,[status(thm)],[316])).
% 42.30/26.60 tff(318,plain,
% 42.30/26.60 (multiplication(multiplication(antidomain(X0!0), one), X0!0) = addition(zero, multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(transitivity,[status(thm)],[317, 310, 308])).
% 42.30/26.60 tff(319,plain,
% 42.30/26.60 (addition(multiplication(multiplication(antidomain(X0!0), one), X0!0), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))) = addition(addition(zero, multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)))),
% 42.30/26.60 inference(monotonicity,[status(thm)],[318])).
% 42.30/26.60 tff(320,plain,
% 42.30/26.60 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(multiplication(antidomain(X0!0), one), X0!0), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))) = addition(multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)))),
% 42.30/26.60 inference(quant_inst,[status(thm)],[])).
% 42.30/26.60 tff(321,plain,
% 42.30/26.60 (addition(multiplication(multiplication(antidomain(X0!0), one), X0!0), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))) = addition(multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.60 inference(unit_resolution,[status(thm)],[320, 71])).
% 42.30/26.61 tff(322,plain,
% 42.30/26.61 (addition(multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = addition(multiplication(multiplication(antidomain(X0!0), one), X0!0), multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)))),
% 42.30/26.61 inference(symmetry,[status(thm)],[321])).
% 42.30/26.61 tff(323,plain,
% 42.30/26.61 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, multiplication(multiplication(antidomain(X0!0), one), X0!0)) = multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.61 inference(quant_inst,[status(thm)],[])).
% 42.30/26.61 tff(324,plain,
% 42.30/26.61 (multiplication(one, multiplication(multiplication(antidomain(X0!0), one), X0!0)) = multiplication(multiplication(antidomain(X0!0), one), X0!0)),
% 42.30/26.61 inference(unit_resolution,[status(thm)],[323, 104])).
% 42.30/26.61 tff(325,plain,
% 42.30/26.61 (addition(multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(one, multiplication(multiplication(antidomain(X0!0), one), X0!0))) = addition(multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.61 inference(monotonicity,[status(thm)],[291, 324])).
% 42.30/26.61 tff(326,plain,
% 42.30/26.61 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), one), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = addition(multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(one, multiplication(multiplication(antidomain(X0!0), one), X0!0))))),
% 42.30/26.61 inference(quant_inst,[status(thm)],[])).
% 42.30/26.61 tff(327,plain,
% 42.30/26.61 (multiplication(addition(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), one), multiplication(multiplication(antidomain(X0!0), one), X0!0)) = addition(multiplication(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), multiplication(multiplication(antidomain(X0!0), one), X0!0)), multiplication(one, multiplication(multiplication(antidomain(X0!0), one), X0!0)))),
% 42.30/26.61 inference(unit_resolution,[status(thm)],[326, 131])).
% 42.30/26.61 tff(328,plain,
% 42.30/26.61 ((~![X0: $i] : (addition(domain(X0), one) = one)) | (addition(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), one) = one)),
% 42.30/26.61 inference(quant_inst,[status(thm)],[])).
% 42.30/26.61 tff(329,plain,
% 42.30/26.61 (addition(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), one) = one),
% 42.30/26.61 inference(unit_resolution,[status(thm)],[328, 185])).
% 42.30/26.61 tff(330,plain,
% 42.30/26.61 (one = addition(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), one)),
% 42.30/26.61 inference(symmetry,[status(thm)],[329])).
% 42.30/26.61 tff(331,plain,
% 42.30/26.61 (multiplication(one, multiplication(multiplication(antidomain(X0!0), one), X0!0)) = multiplication(addition(domain(multiplication(multiplication(antidomain(X0!0), one), domain(X0!0))), one), multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.61 inference(monotonicity,[status(thm)],[330])).
% 42.30/26.61 tff(332,plain,
% 42.30/26.61 (multiplication(multiplication(antidomain(X0!0), one), X0!0) = multiplication(one, multiplication(multiplication(antidomain(X0!0), one), X0!0))),
% 42.30/26.61 inference(symmetry,[status(thm)],[324])).
% 42.30/26.61 tff(333,plain,
% 42.30/26.61 (antidomain(X0!0) = multiplication(antidomain(X0!0), one)),
% 42.30/26.61 inference(symmetry,[status(thm)],[200])).
% 42.30/26.61 tff(334,plain,
% 42.30/26.61 (multiplication(antidomain(X0!0), X0!0) = multiplication(multiplication(antidomain(X0!0), one), X0!0)),
% 42.30/26.61 inference(monotonicity,[status(thm)],[333])).
% 42.30/26.61 tff(335,plain,
% 42.30/26.61 (multiplication(antidomain(X0!0), X0!0) = zero),
% 42.30/26.61 inference(transitivity,[status(thm)],[334, 332, 331, 327, 325, 322, 319, 306, 303, 300, 287, 284, 107, 97, 95, 9])).
% 42.30/26.61 tff(336,plain,
% 42.30/26.61 (~(multiplication(antidomain(X0!0), X0!0) = zero)),
% 42.30/26.61 inference(and_elim,[status(thm)],[44])).
% 42.30/26.61 tff(337,plain,
% 42.30/26.61 ($false),
% 42.30/26.61 inference(unit_resolution,[status(thm)],[336, 335])).
% 42.30/26.61 % SZS output end Proof
%------------------------------------------------------------------------------