TSTP Solution File: KLE128+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE128+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 17:24:15 EDT 2022
% Result : Timeout 294.60s 186.70s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : KLE128+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Sep 1 09:00:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 294.60/186.70 % SZS status Theorem
% 294.60/186.70 % SZS output start Proof
% 294.60/186.70 tff(addition_type, type, (
% 294.60/186.70 addition: ( $i * $i ) > $i)).
% 294.60/186.70 tff(domain_type, type, (
% 294.60/186.70 domain: $i > $i)).
% 294.60/186.70 tff(zero_type, type, (
% 294.60/186.70 zero: $i)).
% 294.60/186.70 tff(forward_diamond_type, type, (
% 294.60/186.70 forward_diamond: ( $i * $i ) > $i)).
% 294.60/186.70 tff(tptp_fun_X1_1_type, type, (
% 294.60/186.70 tptp_fun_X1_1: $i)).
% 294.60/186.70 tff(tptp_fun_X0_0_type, type, (
% 294.60/186.70 tptp_fun_X0_0: $i)).
% 294.60/186.70 tff(divergence_type, type, (
% 294.60/186.70 divergence: $i > $i)).
% 294.60/186.70 tff(multiplication_type, type, (
% 294.60/186.70 multiplication: ( $i * $i ) > $i)).
% 294.60/186.70 tff(antidomain_type, type, (
% 294.60/186.70 antidomain: $i > $i)).
% 294.60/186.70 tff(one_type, type, (
% 294.60/186.70 one: $i)).
% 294.60/186.70 tff(star_type, type, (
% 294.60/186.70 star: $i > $i)).
% 294.60/186.70 tff(1,plain,
% 294.60/186.70 (((~(~(divergence(X0!0) = zero))) & (~((~(addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1))) = forward_diamond(X0!0, domain(X1!1)))) | (domain(X1!1) = zero)))) <=> ((divergence(X0!0) = zero) & (~((~(addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1))) = forward_diamond(X0!0, domain(X1!1)))) | (domain(X1!1) = zero))))),
% 294.60/186.70 inference(rewrite,[status(thm)],[])).
% 294.60/186.70 tff(2,plain,
% 294.60/186.70 ((~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero)))) <=> (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))))),
% 294.60/186.70 inference(rewrite,[status(thm)],[])).
% 294.60/186.70 tff(3,plain,
% 294.60/186.70 ((~![X0: $i] : ((divergence(X0) = zero) => ![X1: $i] : ((addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1))) => (domain(X1) = zero)))) <=> (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))))),
% 294.60/186.70 inference(rewrite,[status(thm)],[])).
% 294.60/186.70 tff(4,axiom,(~![X0: $i] : ((divergence(X0) = zero) => ![X1: $i] : ((addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1))) => (domain(X1) = zero)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 294.60/186.70 tff(5,plain,
% 294.60/186.70 (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero)))),
% 294.60/186.70 inference(modus_ponens,[status(thm)],[4, 3])).
% 294.60/186.70 tff(6,plain,
% 294.60/186.70 (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero)))),
% 294.60/186.70 inference(modus_ponens,[status(thm)],[5, 2])).
% 294.60/186.70 tff(7,plain,
% 294.60/186.70 (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero)))),
% 294.60/186.70 inference(modus_ponens,[status(thm)],[6, 2])).
% 294.60/186.70 tff(8,plain,
% 294.60/186.70 (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero)))),
% 294.60/186.70 inference(modus_ponens,[status(thm)],[7, 2])).
% 294.60/186.70 tff(9,plain,
% 294.60/186.70 (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero)))),
% 294.60/186.70 inference(modus_ponens,[status(thm)],[8, 2])).
% 294.60/186.70 tff(10,plain,
% 294.60/186.70 (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero)))),
% 294.60/186.70 inference(modus_ponens,[status(thm)],[9, 2])).
% 294.60/186.70 tff(11,plain,
% 294.60/186.70 (~![X0: $i] : ((~(divergence(X0) = zero)) | ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero)))),
% 294.60/186.70 inference(modus_ponens,[status(thm)],[10, 2])).
% 294.60/186.70 tff(12,plain,
% 294.60/186.70 ((divergence(X0!0) = zero) & (~((~(addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1))) = forward_diamond(X0!0, domain(X1!1)))) | (domain(X1!1) = zero)))),
% 294.60/186.70 inference(modus_ponens,[status(thm)],[11, 1])).
% 294.60/186.70 tff(13,plain,
% 294.60/186.70 (divergence(X0!0) = zero),
% 294.60/186.71 inference(and_elim,[status(thm)],[12])).
% 294.60/186.71 tff(14,plain,
% 294.60/186.71 (^[X0: $i] : refl((forward_diamond(X0, divergence(X0)) = divergence(X0)) <=> (forward_diamond(X0, divergence(X0)) = divergence(X0)))),
% 294.60/186.71 inference(bind,[status(th)],[])).
% 294.60/186.71 tff(15,plain,
% 294.60/186.71 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0)) <=> ![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 294.60/186.71 inference(quant_intro,[status(thm)],[14])).
% 294.60/186.71 tff(16,plain,
% 294.60/186.71 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0)) <=> ![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 294.60/186.71 inference(rewrite,[status(thm)],[])).
% 294.60/186.71 tff(17,axiom,(![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+7.ax','divergence1')).
% 294.60/186.71 tff(18,plain,
% 294.60/186.71 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[17, 16])).
% 294.60/186.71 tff(19,plain,(
% 294.60/186.71 ![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 294.60/186.71 inference(skolemize,[status(sab)],[18])).
% 294.60/186.71 tff(20,plain,
% 294.60/186.71 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[19, 15])).
% 294.60/186.71 tff(21,plain,
% 294.60/186.71 ((~![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))) | (forward_diamond(X0!0, divergence(X0!0)) = divergence(X0!0))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(22,plain,
% 294.60/186.71 (forward_diamond(X0!0, divergence(X0!0)) = divergence(X0!0)),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[21, 20])).
% 294.60/186.71 tff(23,plain,
% 294.60/186.71 (zero = divergence(X0!0)),
% 294.60/186.71 inference(symmetry,[status(thm)],[13])).
% 294.60/186.71 tff(24,plain,
% 294.60/186.71 (forward_diamond(X0!0, zero) = forward_diamond(X0!0, divergence(X0!0))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[23])).
% 294.60/186.71 tff(25,plain,
% 294.60/186.71 (^[X0: $i, X1: $i] : refl((forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))))),
% 294.60/186.71 inference(bind,[status(th)],[])).
% 294.60/186.71 tff(26,plain,
% 294.60/186.71 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 294.60/186.71 inference(quant_intro,[status(thm)],[25])).
% 294.60/186.71 tff(27,plain,
% 294.60/186.71 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 294.60/186.71 inference(rewrite,[status(thm)],[])).
% 294.60/186.71 tff(28,axiom,(![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax','forward_diamond')).
% 294.60/186.71 tff(29,plain,
% 294.60/186.71 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[28, 27])).
% 294.60/186.71 tff(30,plain,(
% 294.60/186.71 ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 294.60/186.71 inference(skolemize,[status(sab)],[29])).
% 294.60/186.71 tff(31,plain,
% 294.60/186.71 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[30, 26])).
% 294.60/186.71 tff(32,plain,
% 294.60/186.71 ((~![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))) | (forward_diamond(X0!0, zero) = domain(multiplication(X0!0, domain(zero))))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(33,plain,
% 294.60/186.71 (forward_diamond(X0!0, zero) = domain(multiplication(X0!0, domain(zero)))),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[32, 31])).
% 294.60/186.71 tff(34,plain,
% 294.60/186.71 (domain(multiplication(X0!0, domain(zero))) = forward_diamond(X0!0, zero)),
% 294.60/186.71 inference(symmetry,[status(thm)],[33])).
% 294.60/186.71 tff(35,plain,
% 294.60/186.71 (^[X0: $i] : refl((domain(X0) = antidomain(antidomain(X0))) <=> (domain(X0) = antidomain(antidomain(X0))))),
% 294.60/186.71 inference(bind,[status(th)],[])).
% 294.60/186.71 tff(36,plain,
% 294.60/186.71 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 294.60/186.71 inference(quant_intro,[status(thm)],[35])).
% 294.60/186.71 tff(37,plain,
% 294.60/186.71 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 294.60/186.71 inference(rewrite,[status(thm)],[])).
% 294.60/186.71 tff(38,axiom,(![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax','domain4')).
% 294.60/186.71 tff(39,plain,
% 294.60/186.71 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[38, 37])).
% 294.60/186.71 tff(40,plain,(
% 294.60/186.71 ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 294.60/186.71 inference(skolemize,[status(sab)],[39])).
% 294.60/186.71 tff(41,plain,
% 294.60/186.71 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[40, 36])).
% 294.60/186.71 tff(42,plain,
% 294.60/186.71 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(multiplication(X0!0, domain(zero))) = antidomain(antidomain(multiplication(X0!0, domain(zero)))))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(43,plain,
% 294.60/186.71 (domain(multiplication(X0!0, domain(zero))) = antidomain(antidomain(multiplication(X0!0, domain(zero))))),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[42, 41])).
% 294.60/186.71 tff(44,plain,
% 294.60/186.71 (antidomain(antidomain(multiplication(X0!0, domain(zero)))) = domain(multiplication(X0!0, domain(zero)))),
% 294.60/186.71 inference(symmetry,[status(thm)],[43])).
% 294.60/186.71 tff(45,plain,
% 294.60/186.71 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(zero) = antidomain(antidomain(zero)))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(46,plain,
% 294.60/186.71 (domain(zero) = antidomain(antidomain(zero))),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[45, 41])).
% 294.60/186.71 tff(47,plain,
% 294.60/186.71 (antidomain(antidomain(zero)) = domain(zero)),
% 294.60/186.71 inference(symmetry,[status(thm)],[46])).
% 294.60/186.71 tff(48,plain,
% 294.60/186.71 (multiplication(X0!0, antidomain(antidomain(zero))) = multiplication(X0!0, domain(zero))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[47])).
% 294.60/186.71 tff(49,plain,
% 294.60/186.71 (multiplication(X0!0, domain(zero)) = multiplication(X0!0, antidomain(antidomain(zero)))),
% 294.60/186.71 inference(symmetry,[status(thm)],[48])).
% 294.60/186.71 tff(50,plain,
% 294.60/186.71 (antidomain(multiplication(X0!0, domain(zero))) = antidomain(multiplication(X0!0, antidomain(antidomain(zero))))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[49])).
% 294.60/186.71 tff(51,plain,
% 294.60/186.71 (antidomain(multiplication(X0!0, antidomain(antidomain(zero)))) = antidomain(multiplication(X0!0, domain(zero)))),
% 294.60/186.71 inference(symmetry,[status(thm)],[50])).
% 294.60/186.71 tff(52,plain,
% 294.60/186.71 (^[X0: $i, X1: $i] : refl((addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1))))) <=> (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1))))))),
% 294.60/186.71 inference(bind,[status(th)],[])).
% 294.60/186.71 tff(53,plain,
% 294.60/186.71 (![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1))))) <=> ![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))),
% 294.60/186.71 inference(quant_intro,[status(thm)],[52])).
% 294.60/186.71 tff(54,plain,
% 294.60/186.71 (![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1))))) <=> ![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))),
% 294.60/186.71 inference(rewrite,[status(thm)],[])).
% 294.60/186.71 tff(55,axiom,(![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax','domain2')).
% 294.60/186.71 tff(56,plain,
% 294.60/186.71 (![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[55, 54])).
% 294.60/186.71 tff(57,plain,(
% 294.60/186.71 ![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))),
% 294.60/186.71 inference(skolemize,[status(sab)],[56])).
% 294.60/186.71 tff(58,plain,
% 294.60/186.71 (![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[57, 53])).
% 294.60/186.71 tff(59,plain,
% 294.60/186.71 ((~![X0: $i, X1: $i] : (addition(antidomain(multiplication(X0, X1)), antidomain(multiplication(X0, antidomain(antidomain(X1))))) = antidomain(multiplication(X0, antidomain(antidomain(X1)))))) | (addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(60,plain,
% 294.60/186.71 (addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = antidomain(multiplication(X0!0, antidomain(antidomain(zero))))),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[59, 58])).
% 294.60/186.71 tff(61,plain,
% 294.60/186.71 (forward_diamond(X0!0, divergence(X0!0)) = forward_diamond(X0!0, zero)),
% 294.60/186.71 inference(symmetry,[status(thm)],[24])).
% 294.60/186.71 tff(62,plain,
% 294.60/186.71 (divergence(X0!0) = forward_diamond(X0!0, divergence(X0!0))),
% 294.60/186.71 inference(symmetry,[status(thm)],[22])).
% 294.60/186.71 tff(63,plain,
% 294.60/186.71 (^[A: $i] : refl((multiplication(A, zero) = zero) <=> (multiplication(A, zero) = zero))),
% 294.60/186.71 inference(bind,[status(th)],[])).
% 294.60/186.71 tff(64,plain,
% 294.60/186.71 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 294.60/186.71 inference(quant_intro,[status(thm)],[63])).
% 294.60/186.71 tff(65,plain,
% 294.60/186.71 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 294.60/186.71 inference(rewrite,[status(thm)],[])).
% 294.60/186.71 tff(66,axiom,(![A: $i] : (multiplication(A, zero) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','right_annihilation')).
% 294.60/186.71 tff(67,plain,
% 294.60/186.71 (![A: $i] : (multiplication(A, zero) = zero)),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[66, 65])).
% 294.60/186.71 tff(68,plain,(
% 294.60/186.71 ![A: $i] : (multiplication(A, zero) = zero)),
% 294.60/186.71 inference(skolemize,[status(sab)],[67])).
% 294.60/186.71 tff(69,plain,
% 294.60/186.71 (![A: $i] : (multiplication(A, zero) = zero)),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[68, 64])).
% 294.60/186.71 tff(70,plain,
% 294.60/186.71 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(X0!0, zero) = zero)),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(71,plain,
% 294.60/186.71 (multiplication(X0!0, zero) = zero),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[70, 69])).
% 294.60/186.71 tff(72,plain,
% 294.60/186.71 (multiplication(X0!0, zero) = domain(multiplication(X0!0, domain(zero)))),
% 294.60/186.71 inference(transitivity,[status(thm)],[71, 23, 62, 61, 33])).
% 294.60/186.71 tff(73,plain,
% 294.60/186.71 (antidomain(multiplication(X0!0, zero)) = antidomain(domain(multiplication(X0!0, domain(zero))))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[72])).
% 294.60/186.71 tff(74,plain,
% 294.60/186.71 (addition(zero, antidomain(multiplication(X0!0, zero))) = addition(zero, antidomain(domain(multiplication(X0!0, domain(zero)))))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[73])).
% 294.60/186.71 tff(75,plain,
% 294.60/186.71 (addition(zero, antidomain(domain(multiplication(X0!0, domain(zero))))) = addition(zero, antidomain(multiplication(X0!0, zero)))),
% 294.60/186.71 inference(symmetry,[status(thm)],[74])).
% 294.60/186.71 tff(76,plain,
% 294.60/186.71 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 294.60/186.71 inference(bind,[status(th)],[])).
% 294.60/186.71 tff(77,plain,
% 294.60/186.71 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 294.60/186.71 inference(quant_intro,[status(thm)],[76])).
% 294.60/186.71 tff(78,plain,
% 294.60/186.71 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 294.60/186.71 inference(rewrite,[status(thm)],[])).
% 294.60/186.71 tff(79,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 294.60/186.71 tff(80,plain,
% 294.60/186.71 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[79, 78])).
% 294.60/186.71 tff(81,plain,(
% 294.60/186.71 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 294.60/186.71 inference(skolemize,[status(sab)],[80])).
% 294.60/186.71 tff(82,plain,
% 294.60/186.71 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[81, 77])).
% 294.60/186.71 tff(83,plain,
% 294.60/186.71 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(antidomain(domain(multiplication(X0!0, domain(zero)))), zero) = addition(zero, antidomain(domain(multiplication(X0!0, domain(zero))))))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(84,plain,
% 294.60/186.71 (addition(antidomain(domain(multiplication(X0!0, domain(zero)))), zero) = addition(zero, antidomain(domain(multiplication(X0!0, domain(zero)))))),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[83, 82])).
% 294.60/186.71 tff(85,plain,
% 294.60/186.71 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 294.60/186.71 inference(bind,[status(th)],[])).
% 294.60/186.71 tff(86,plain,
% 294.60/186.71 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 294.60/186.71 inference(quant_intro,[status(thm)],[85])).
% 294.60/186.71 tff(87,plain,
% 294.60/186.71 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 294.60/186.71 inference(rewrite,[status(thm)],[])).
% 294.60/186.71 tff(88,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 294.60/186.71 tff(89,plain,
% 294.60/186.71 (![A: $i] : (addition(A, zero) = A)),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[88, 87])).
% 294.60/186.71 tff(90,plain,(
% 294.60/186.71 ![A: $i] : (addition(A, zero) = A)),
% 294.60/186.71 inference(skolemize,[status(sab)],[89])).
% 294.60/186.71 tff(91,plain,
% 294.60/186.71 (![A: $i] : (addition(A, zero) = A)),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[90, 86])).
% 294.60/186.71 tff(92,plain,
% 294.60/186.71 ((~![A: $i] : (addition(A, zero) = A)) | (addition(antidomain(domain(multiplication(X0!0, domain(zero)))), zero) = antidomain(domain(multiplication(X0!0, domain(zero)))))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(93,plain,
% 294.60/186.71 (addition(antidomain(domain(multiplication(X0!0, domain(zero)))), zero) = antidomain(domain(multiplication(X0!0, domain(zero))))),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[92, 91])).
% 294.60/186.71 tff(94,plain,
% 294.60/186.71 (antidomain(domain(multiplication(X0!0, domain(zero)))) = addition(antidomain(domain(multiplication(X0!0, domain(zero)))), zero)),
% 294.60/186.71 inference(symmetry,[status(thm)],[93])).
% 294.60/186.71 tff(95,plain,
% 294.60/186.71 (antidomain(multiplication(X0!0, zero)) = addition(zero, antidomain(multiplication(X0!0, zero)))),
% 294.60/186.71 inference(transitivity,[status(thm)],[73, 94, 84, 75])).
% 294.60/186.71 tff(96,plain,
% 294.60/186.71 (addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = addition(addition(zero, antidomain(multiplication(X0!0, zero))), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[95])).
% 294.60/186.71 tff(97,plain,
% 294.60/186.71 (addition(addition(zero, antidomain(multiplication(X0!0, zero))), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 294.60/186.71 inference(symmetry,[status(thm)],[96])).
% 294.60/186.71 tff(98,plain,
% 294.60/186.71 (^[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)))),
% 294.60/186.71 inference(bind,[status(th)],[])).
% 294.60/186.71 tff(99,plain,
% 294.60/186.71 (![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))),
% 294.60/186.71 inference(quant_intro,[status(thm)],[98])).
% 294.60/186.71 tff(100,plain,
% 294.60/186.71 (![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))),
% 294.60/186.71 inference(rewrite,[status(thm)],[])).
% 294.60/186.71 tff(101,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')).
% 294.60/186.71 tff(102,plain,
% 294.60/186.71 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[101, 100])).
% 294.60/186.71 tff(103,plain,(
% 294.60/186.71 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 294.60/186.71 inference(skolemize,[status(sab)],[102])).
% 294.60/186.71 tff(104,plain,
% 294.60/186.71 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[103, 99])).
% 294.60/186.71 tff(105,plain,
% 294.60/186.71 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(zero, addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))) = addition(addition(zero, antidomain(multiplication(X0!0, zero))), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(106,plain,
% 294.60/186.71 (addition(zero, addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))) = addition(addition(zero, antidomain(multiplication(X0!0, zero))), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[105, 104])).
% 294.60/186.71 tff(107,plain,
% 294.60/186.71 (addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = antidomain(multiplication(X0!0, domain(zero)))),
% 294.60/186.71 inference(transitivity,[status(thm)],[60, 51])).
% 294.60/186.71 tff(108,plain,
% 294.60/186.71 (zero = antidomain(antidomain(multiplication(X0!0, domain(zero))))),
% 294.60/186.71 inference(transitivity,[status(thm)],[23, 62, 61, 33, 43])).
% 294.60/186.71 tff(109,plain,
% 294.60/186.71 (addition(zero, addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))) = addition(antidomain(antidomain(multiplication(X0!0, domain(zero)))), antidomain(multiplication(X0!0, domain(zero))))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[108, 107])).
% 294.60/186.71 tff(110,plain,
% 294.60/186.71 (addition(antidomain(antidomain(multiplication(X0!0, domain(zero)))), antidomain(multiplication(X0!0, domain(zero)))) = addition(zero, addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))))),
% 294.60/186.71 inference(symmetry,[status(thm)],[109])).
% 294.60/186.71 tff(111,plain,
% 294.60/186.71 (^[X0: $i] : refl((addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> (addition(antidomain(antidomain(X0)), antidomain(X0)) = one))),
% 294.60/186.71 inference(bind,[status(th)],[])).
% 294.60/186.71 tff(112,plain,
% 294.60/186.71 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 294.60/186.71 inference(quant_intro,[status(thm)],[111])).
% 294.60/186.71 tff(113,plain,
% 294.60/186.71 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 294.60/186.71 inference(rewrite,[status(thm)],[])).
% 294.60/186.71 tff(114,axiom,(![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax','domain3')).
% 294.60/186.71 tff(115,plain,
% 294.60/186.71 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[114, 113])).
% 294.60/186.71 tff(116,plain,(
% 294.60/186.71 ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 294.60/186.71 inference(skolemize,[status(sab)],[115])).
% 294.60/186.71 tff(117,plain,
% 294.60/186.71 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[116, 112])).
% 294.60/186.71 tff(118,plain,
% 294.60/186.71 ((~![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)) | (addition(antidomain(antidomain(multiplication(X0!0, domain(zero)))), antidomain(multiplication(X0!0, domain(zero)))) = one)),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(119,plain,
% 294.60/186.71 (addition(antidomain(antidomain(multiplication(X0!0, domain(zero)))), antidomain(multiplication(X0!0, domain(zero)))) = one),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[118, 117])).
% 294.60/186.71 tff(120,plain,
% 294.60/186.71 (one = addition(antidomain(antidomain(multiplication(X0!0, domain(zero)))), antidomain(multiplication(X0!0, domain(zero))))),
% 294.60/186.71 inference(symmetry,[status(thm)],[119])).
% 294.60/186.71 tff(121,plain,
% 294.60/186.71 ((~![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)) | (addition(antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero))))), antidomain(antidomain(multiplication(X0!0, domain(zero))))) = one)),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(122,plain,
% 294.60/186.71 (addition(antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero))))), antidomain(antidomain(multiplication(X0!0, domain(zero))))) = one),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[121, 117])).
% 294.60/186.71 tff(123,plain,
% 294.60/186.71 (antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero))))) = antidomain(domain(multiplication(X0!0, domain(zero))))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[44])).
% 294.60/186.71 tff(124,plain,
% 294.60/186.71 (antidomain(domain(multiplication(X0!0, domain(zero)))) = antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero)))))),
% 294.60/186.71 inference(symmetry,[status(thm)],[123])).
% 294.60/186.71 tff(125,plain,
% 294.60/186.71 (addition(antidomain(domain(multiplication(X0!0, domain(zero)))), zero) = addition(antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero))))), antidomain(antidomain(multiplication(X0!0, domain(zero)))))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[124, 108])).
% 294.60/186.71 tff(126,plain,
% 294.60/186.71 (zero = domain(multiplication(X0!0, domain(zero)))),
% 294.60/186.71 inference(transitivity,[status(thm)],[23, 62, 61, 33])).
% 294.60/186.71 tff(127,plain,
% 294.60/186.71 (antidomain(zero) = antidomain(domain(multiplication(X0!0, domain(zero))))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[126])).
% 294.60/186.71 tff(128,plain,
% 294.60/186.71 (antidomain(zero) = antidomain(multiplication(X0!0, domain(zero)))),
% 294.60/186.71 inference(transitivity,[status(thm)],[127, 94, 125, 122, 120, 110, 106, 97, 60, 51])).
% 294.60/186.71 tff(129,plain,
% 294.60/186.71 (antidomain(antidomain(zero)) = antidomain(antidomain(multiplication(X0!0, domain(zero))))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[128])).
% 294.60/186.71 tff(130,plain,
% 294.60/186.71 (domain(zero) = zero),
% 294.60/186.71 inference(transitivity,[status(thm)],[46, 129, 44, 34, 24, 22, 13])).
% 294.60/186.71 tff(131,plain,
% 294.60/186.71 (addition(forward_diamond(X0!0, domain(X1!1)), domain(zero)) = addition(forward_diamond(X0!0, domain(X1!1)), zero)),
% 294.60/186.71 inference(monotonicity,[status(thm)],[130])).
% 294.60/186.71 tff(132,plain,
% 294.60/186.71 (addition(forward_diamond(X0!0, domain(X1!1)), zero) = addition(forward_diamond(X0!0, domain(X1!1)), domain(zero))),
% 294.60/186.71 inference(symmetry,[status(thm)],[131])).
% 294.60/186.71 tff(133,plain,
% 294.60/186.71 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(X1!1) = antidomain(antidomain(X1!1)))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(134,plain,
% 294.60/186.71 (domain(X1!1) = antidomain(antidomain(X1!1))),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[133, 41])).
% 294.60/186.71 tff(135,plain,
% 294.60/186.71 (antidomain(antidomain(X1!1)) = domain(X1!1)),
% 294.60/186.71 inference(symmetry,[status(thm)],[134])).
% 294.60/186.71 tff(136,plain,
% 294.60/186.71 (addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[135])).
% 294.60/186.71 tff(137,plain,
% 294.60/186.71 (addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1)) = addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1)))),
% 294.60/186.71 inference(symmetry,[status(thm)],[136])).
% 294.60/186.71 tff(138,plain,
% 294.60/186.71 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1)))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(139,plain,
% 294.60/186.71 (addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1))),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[138, 82])).
% 294.60/186.71 tff(140,plain,
% 294.60/186.71 (~((~(addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1))) = forward_diamond(X0!0, domain(X1!1)))) | (domain(X1!1) = zero))),
% 294.60/186.71 inference(and_elim,[status(thm)],[12])).
% 294.60/186.71 tff(141,plain,
% 294.60/186.71 (addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1))) = forward_diamond(X0!0, domain(X1!1))),
% 294.60/186.71 inference(or_elim,[status(thm)],[140])).
% 294.60/186.71 tff(142,plain,
% 294.60/186.71 (forward_diamond(X0!0, domain(X1!1)) = addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1)))),
% 294.60/186.71 inference(symmetry,[status(thm)],[141])).
% 294.60/186.71 tff(143,plain,
% 294.60/186.71 (forward_diamond(X0!0, domain(X1!1)) = addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1)))),
% 294.60/186.71 inference(transitivity,[status(thm)],[142, 139, 137])).
% 294.60/186.71 tff(144,plain,
% 294.60/186.71 (addition(forward_diamond(X0!0, domain(X1!1)), zero) = addition(addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1))), zero)),
% 294.60/186.71 inference(monotonicity,[status(thm)],[143])).
% 294.60/186.71 tff(145,plain,
% 294.60/186.71 (addition(addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1))), zero) = addition(forward_diamond(X0!0, domain(X1!1)), zero)),
% 294.60/186.71 inference(symmetry,[status(thm)],[144])).
% 294.60/186.71 tff(146,plain,
% 294.60/186.71 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(forward_diamond(X0!0, domain(X1!1)), addition(antidomain(antidomain(X1!1)), zero)) = addition(addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1))), zero))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(147,plain,
% 294.60/186.71 (addition(forward_diamond(X0!0, domain(X1!1)), addition(antidomain(antidomain(X1!1)), zero)) = addition(addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1))), zero)),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[146, 104])).
% 294.60/186.71 tff(148,plain,
% 294.60/186.71 ((~![A: $i] : (addition(A, zero) = A)) | (addition(antidomain(antidomain(X1!1)), zero) = antidomain(antidomain(X1!1)))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(149,plain,
% 294.60/186.71 (addition(antidomain(antidomain(X1!1)), zero) = antidomain(antidomain(X1!1))),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[148, 91])).
% 294.60/186.71 tff(150,plain,
% 294.60/186.71 (addition(antidomain(antidomain(X1!1)), zero) = domain(X1!1)),
% 294.60/186.71 inference(transitivity,[status(thm)],[149, 135])).
% 294.60/186.71 tff(151,plain,
% 294.60/186.71 (addition(forward_diamond(X0!0, domain(X1!1)), addition(antidomain(antidomain(X1!1)), zero)) = addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[150])).
% 294.60/186.71 tff(152,plain,
% 294.60/186.71 (addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1)) = addition(forward_diamond(X0!0, domain(X1!1)), addition(antidomain(antidomain(X1!1)), zero))),
% 294.60/186.71 inference(symmetry,[status(thm)],[151])).
% 294.60/186.71 tff(153,plain,
% 294.60/186.71 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 294.60/186.71 inference(bind,[status(th)],[])).
% 294.60/186.71 tff(154,plain,
% 294.60/186.71 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 294.60/186.71 inference(quant_intro,[status(thm)],[153])).
% 294.60/186.71 tff(155,plain,
% 294.60/186.71 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 294.60/186.71 inference(rewrite,[status(thm)],[])).
% 294.60/186.71 tff(156,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 294.60/186.71 tff(157,plain,
% 294.60/186.71 (![A: $i] : (multiplication(one, A) = A)),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[156, 155])).
% 294.60/186.71 tff(158,plain,(
% 294.60/186.71 ![A: $i] : (multiplication(one, A) = A)),
% 294.60/186.71 inference(skolemize,[status(sab)],[157])).
% 294.60/186.71 tff(159,plain,
% 294.60/186.71 (![A: $i] : (multiplication(one, A) = A)),
% 294.60/186.71 inference(modus_ponens,[status(thm)],[158, 154])).
% 294.60/186.71 tff(160,plain,
% 294.60/186.71 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, antidomain(antidomain(X1!1))) = antidomain(antidomain(X1!1)))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(161,plain,
% 294.60/186.71 (multiplication(one, antidomain(antidomain(X1!1))) = antidomain(antidomain(X1!1))),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[160, 159])).
% 294.60/186.71 tff(162,plain,
% 294.60/186.71 (addition(antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero))))), antidomain(antidomain(multiplication(X0!0, domain(zero))))) = addition(antidomain(domain(multiplication(X0!0, domain(zero)))), zero)),
% 294.60/186.71 inference(symmetry,[status(thm)],[125])).
% 294.60/186.71 tff(163,plain,
% 294.60/186.71 (one = addition(antidomain(antidomain(antidomain(multiplication(X0!0, domain(zero))))), antidomain(antidomain(multiplication(X0!0, domain(zero)))))),
% 294.60/186.71 inference(symmetry,[status(thm)],[122])).
% 294.60/186.71 tff(164,plain,
% 294.60/186.71 (one = antidomain(domain(multiplication(X0!0, domain(zero))))),
% 294.60/186.71 inference(transitivity,[status(thm)],[163, 162, 93])).
% 294.60/186.71 tff(165,plain,
% 294.60/186.71 (multiplication(one, antidomain(antidomain(X1!1))) = multiplication(antidomain(domain(multiplication(X0!0, domain(zero)))), antidomain(antidomain(X1!1)))),
% 294.60/186.71 inference(monotonicity,[status(thm)],[164])).
% 294.60/186.71 tff(166,plain,
% 294.60/186.71 (multiplication(antidomain(domain(multiplication(X0!0, domain(zero)))), antidomain(antidomain(X1!1))) = multiplication(one, antidomain(antidomain(X1!1)))),
% 294.60/186.71 inference(symmetry,[status(thm)],[165])).
% 294.60/186.71 tff(167,plain,
% 294.60/186.71 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))) = addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1))))))),
% 294.60/186.71 inference(quant_inst,[status(thm)],[])).
% 294.60/186.71 tff(168,plain,
% 294.60/186.71 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))) = addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1)))))),
% 294.60/186.71 inference(unit_resolution,[status(thm)],[167, 82])).
% 294.60/186.72 tff(169,plain,
% 294.60/186.72 (antidomain(antidomain(antidomain(X1!1))) = antidomain(domain(X1!1))),
% 294.60/186.72 inference(monotonicity,[status(thm)],[135])).
% 294.60/186.72 tff(170,plain,
% 294.60/186.72 (antidomain(domain(X1!1)) = antidomain(antidomain(antidomain(X1!1)))),
% 294.60/186.72 inference(symmetry,[status(thm)],[169])).
% 294.60/186.72 tff(171,plain,
% 294.60/186.72 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))) = addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(antidomain(X1!1))))),
% 294.60/186.72 inference(monotonicity,[status(thm)],[170])).
% 294.60/186.72 tff(172,plain,
% 294.60/186.72 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(antidomain(X1!1)))) = addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1)))),
% 294.60/186.72 inference(symmetry,[status(thm)],[171])).
% 294.60/186.72 tff(173,plain,
% 294.60/186.72 ((~![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)) | (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(antidomain(X1!1)))) = one)),
% 294.60/186.72 inference(quant_inst,[status(thm)],[])).
% 294.60/186.72 tff(174,plain,
% 294.60/186.72 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(antidomain(X1!1)))) = one),
% 294.60/186.72 inference(unit_resolution,[status(thm)],[173, 117])).
% 294.60/186.72 tff(175,plain,
% 294.60/186.72 (one = addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(antidomain(X1!1))))),
% 294.60/186.72 inference(symmetry,[status(thm)],[174])).
% 294.60/186.72 tff(176,plain,
% 294.60/186.72 (antidomain(domain(multiplication(X0!0, domain(zero)))) = addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1)))))),
% 294.60/186.72 inference(transitivity,[status(thm)],[94, 125, 122, 175, 172, 168])).
% 294.60/186.72 tff(177,plain,
% 294.60/186.72 (multiplication(antidomain(domain(multiplication(X0!0, domain(zero)))), antidomain(antidomain(X1!1))) = multiplication(addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1))))), antidomain(antidomain(X1!1)))),
% 294.60/186.72 inference(monotonicity,[status(thm)],[176])).
% 294.60/186.72 tff(178,plain,
% 294.60/186.72 (multiplication(addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1))))), antidomain(antidomain(X1!1))) = multiplication(antidomain(domain(multiplication(X0!0, domain(zero)))), antidomain(antidomain(X1!1)))),
% 294.60/186.72 inference(symmetry,[status(thm)],[177])).
% 294.60/186.72 tff(179,plain,
% 294.60/186.72 (^[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))))),
% 294.60/186.72 inference(bind,[status(th)],[])).
% 294.60/186.72 tff(180,plain,
% 294.60/186.72 (![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)))),
% 294.60/186.72 inference(quant_intro,[status(thm)],[179])).
% 294.60/186.72 tff(181,plain,
% 294.60/186.72 (![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)))),
% 294.71/186.72 inference(rewrite,[status(thm)],[])).
% 294.71/186.72 tff(182,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')).
% 294.71/186.72 tff(183,plain,
% 294.71/186.72 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 294.71/186.72 inference(modus_ponens,[status(thm)],[182, 181])).
% 294.71/186.72 tff(184,plain,(
% 294.71/186.72 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 294.71/186.72 inference(skolemize,[status(sab)],[183])).
% 294.71/186.72 tff(185,plain,
% 294.71/186.72 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 294.71/186.72 inference(modus_ponens,[status(thm)],[184, 180])).
% 294.71/186.72 tff(186,plain,
% 294.71/186.72 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1))))), antidomain(antidomain(X1!1))) = addition(multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1)))))),
% 294.71/186.72 inference(quant_inst,[status(thm)],[])).
% 294.71/186.72 tff(187,plain,
% 294.71/186.72 (multiplication(addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1))))), antidomain(antidomain(X1!1))) = addition(multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1))))),
% 294.71/186.72 inference(unit_resolution,[status(thm)],[186, 185])).
% 294.71/186.72 tff(188,plain,
% 294.71/186.72 (addition(multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1)))) = multiplication(addition(antidomain(domain(X1!1)), antidomain(antidomain(antidomain(antidomain(X1!1))))), antidomain(antidomain(X1!1)))),
% 294.71/186.72 inference(symmetry,[status(thm)],[187])).
% 294.71/186.72 tff(189,plain,
% 294.71/186.72 (antidomain(antidomain(domain(X1!1))) = antidomain(antidomain(antidomain(antidomain(X1!1))))),
% 294.71/186.72 inference(monotonicity,[status(thm)],[170])).
% 294.71/186.72 tff(190,plain,
% 294.71/186.72 (antidomain(antidomain(antidomain(antidomain(X1!1)))) = antidomain(antidomain(domain(X1!1)))),
% 294.71/186.72 inference(symmetry,[status(thm)],[189])).
% 294.71/186.72 tff(191,plain,
% 294.71/186.72 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))) = multiplication(antidomain(antidomain(domain(X1!1))), antidomain(domain(X1!1)))),
% 294.71/186.72 inference(monotonicity,[status(thm)],[190])).
% 294.71/186.72 tff(192,plain,
% 294.71/186.72 (multiplication(antidomain(antidomain(domain(X1!1))), antidomain(domain(X1!1))) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1)))),
% 294.71/186.72 inference(symmetry,[status(thm)],[191])).
% 294.71/186.72 tff(193,plain,
% 294.71/186.72 (^[X0: $i] : refl((multiplication(antidomain(X0), X0) = zero) <=> (multiplication(antidomain(X0), X0) = zero))),
% 294.71/186.72 inference(bind,[status(th)],[])).
% 294.71/186.72 tff(194,plain,
% 294.71/186.72 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 294.71/186.72 inference(quant_intro,[status(thm)],[193])).
% 294.71/186.72 tff(195,plain,
% 294.71/186.72 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 294.71/186.72 inference(rewrite,[status(thm)],[])).
% 294.71/186.72 tff(196,axiom,(![X0: $i] : (multiplication(antidomain(X0), X0) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax','domain1')).
% 294.71/186.72 tff(197,plain,
% 294.71/186.72 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 294.71/186.72 inference(modus_ponens,[status(thm)],[196, 195])).
% 294.71/186.72 tff(198,plain,(
% 294.71/186.72 ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 294.71/186.72 inference(skolemize,[status(sab)],[197])).
% 294.71/186.72 tff(199,plain,
% 294.71/186.72 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 294.71/186.72 inference(modus_ponens,[status(thm)],[198, 194])).
% 294.71/186.72 tff(200,plain,
% 294.71/186.72 ((~![X0: $i] : (multiplication(antidomain(X0), X0) = zero)) | (multiplication(antidomain(antidomain(domain(X1!1))), antidomain(domain(X1!1))) = zero)),
% 294.71/186.72 inference(quant_inst,[status(thm)],[])).
% 294.71/186.72 tff(201,plain,
% 294.71/186.72 (multiplication(antidomain(antidomain(domain(X1!1))), antidomain(domain(X1!1))) = zero),
% 294.71/186.72 inference(unit_resolution,[status(thm)],[200, 199])).
% 294.71/186.72 tff(202,plain,
% 294.71/186.72 (zero = multiplication(antidomain(antidomain(domain(X1!1))), antidomain(domain(X1!1)))),
% 294.71/186.72 inference(symmetry,[status(thm)],[201])).
% 294.71/186.72 tff(203,plain,
% 294.71/186.72 ((~![X0: $i] : (multiplication(antidomain(X0), X0) = zero)) | (multiplication(antidomain(antidomain(antidomain(X1!1))), antidomain(antidomain(X1!1))) = zero)),
% 294.71/186.72 inference(quant_inst,[status(thm)],[])).
% 294.71/186.72 tff(204,plain,
% 294.71/186.72 (multiplication(antidomain(antidomain(antidomain(X1!1))), antidomain(antidomain(X1!1))) = zero),
% 294.71/186.72 inference(unit_resolution,[status(thm)],[203, 199])).
% 294.71/186.72 tff(205,plain,
% 294.71/186.72 (multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))) = multiplication(antidomain(antidomain(antidomain(X1!1))), antidomain(antidomain(X1!1)))),
% 294.71/186.72 inference(monotonicity,[status(thm)],[170])).
% 294.71/186.72 tff(206,plain,
% 294.71/186.72 (multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1)))),
% 294.71/186.72 inference(transitivity,[status(thm)],[205, 204, 202, 192])).
% 294.71/186.72 tff(207,plain,
% 294.71/186.72 (addition(multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1)))) = addition(multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1))))),
% 294.71/186.72 inference(monotonicity,[status(thm)],[206])).
% 294.71/186.72 tff(208,plain,
% 294.71/186.72 (addition(multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1)))) = addition(multiplication(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1))))),
% 294.71/186.72 inference(symmetry,[status(thm)],[207])).
% 294.71/186.72 tff(209,plain,
% 294.71/186.72 (^[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))))),
% 294.71/186.72 inference(bind,[status(th)],[])).
% 294.71/186.72 tff(210,plain,
% 294.71/186.72 (![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)))),
% 294.71/186.72 inference(quant_intro,[status(thm)],[209])).
% 294.71/186.72 tff(211,plain,
% 294.71/186.72 (![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)))),
% 294.71/186.72 inference(rewrite,[status(thm)],[])).
% 294.71/186.72 tff(212,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')).
% 294.71/186.72 tff(213,plain,
% 294.71/186.72 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 294.71/186.72 inference(modus_ponens,[status(thm)],[212, 211])).
% 294.71/186.72 tff(214,plain,(
% 294.71/186.72 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 294.71/186.72 inference(skolemize,[status(sab)],[213])).
% 294.71/186.72 tff(215,plain,
% 294.71/186.72 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 294.71/186.72 inference(modus_ponens,[status(thm)],[214, 210])).
% 294.71/186.72 tff(216,plain,
% 294.71/186.72 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), addition(antidomain(domain(X1!1)), antidomain(antidomain(X1!1)))) = addition(multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1)))))),
% 294.71/186.72 inference(quant_inst,[status(thm)],[])).
% 294.71/186.72 tff(217,plain,
% 294.71/186.72 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), addition(antidomain(domain(X1!1)), antidomain(antidomain(X1!1)))) = addition(multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1))))),
% 294.71/186.72 inference(unit_resolution,[status(thm)],[216, 215])).
% 294.71/186.72 tff(218,plain,
% 294.71/186.72 ((~![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)) | (addition(antidomain(antidomain(antidomain(X1!1))), antidomain(antidomain(X1!1))) = one)),
% 294.71/186.72 inference(quant_inst,[status(thm)],[])).
% 294.71/186.72 tff(219,plain,
% 294.71/186.72 (addition(antidomain(antidomain(antidomain(X1!1))), antidomain(antidomain(X1!1))) = one),
% 294.71/186.72 inference(unit_resolution,[status(thm)],[218, 117])).
% 294.71/186.72 tff(220,plain,
% 294.71/186.72 (addition(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))) = addition(antidomain(antidomain(antidomain(X1!1))), antidomain(antidomain(X1!1)))),
% 294.71/186.72 inference(monotonicity,[status(thm)],[170])).
% 294.71/186.72 tff(221,plain,
% 294.71/186.72 (addition(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))) = antidomain(multiplication(X0!0, antidomain(antidomain(zero))))),
% 294.71/186.72 inference(transitivity,[status(thm)],[220, 219, 120, 110, 106, 97, 60])).
% 294.71/186.72 tff(222,plain,
% 294.71/186.72 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), addition(antidomain(domain(X1!1)), antidomain(antidomain(X1!1)))) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 294.71/186.72 inference(monotonicity,[status(thm)],[221])).
% 294.71/186.72 tff(223,plain,
% 294.71/186.72 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), addition(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))))),
% 294.71/186.72 inference(symmetry,[status(thm)],[222])).
% 294.71/186.72 tff(224,plain,
% 294.71/186.72 (addition(addition(zero, antidomain(multiplication(X0!0, zero))), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = addition(zero, addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))))),
% 294.71/186.72 inference(symmetry,[status(thm)],[106])).
% 294.71/186.72 tff(225,plain,
% 294.71/186.72 (antidomain(multiplication(X0!0, antidomain(antidomain(zero)))) = addition(antidomain(multiplication(X0!0, zero)), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 294.71/186.72 inference(symmetry,[status(thm)],[60])).
% 294.71/186.72 tff(226,plain,
% 294.71/186.72 (antidomain(multiplication(X0!0, antidomain(antidomain(zero)))) = one),
% 294.71/186.72 inference(transitivity,[status(thm)],[225, 96, 224, 109, 119])).
% 294.71/186.72 tff(227,plain,
% 294.71/186.72 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(multiplication(X0!0, antidomain(antidomain(zero))))) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), one)),
% 294.71/186.72 inference(monotonicity,[status(thm)],[226])).
% 294.71/186.72 tff(228,plain,
% 294.71/186.72 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), one) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(multiplication(X0!0, antidomain(antidomain(zero)))))),
% 294.71/186.72 inference(symmetry,[status(thm)],[227])).
% 294.71/186.72 tff(229,plain,
% 294.71/186.72 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 294.71/186.72 inference(bind,[status(th)],[])).
% 294.71/186.72 tff(230,plain,
% 294.71/186.72 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 294.71/186.72 inference(quant_intro,[status(thm)],[229])).
% 294.71/186.72 tff(231,plain,
% 294.71/186.72 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 294.71/186.72 inference(rewrite,[status(thm)],[])).
% 294.71/186.72 tff(232,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 294.71/186.72 tff(233,plain,
% 294.71/186.72 (![A: $i] : (multiplication(A, one) = A)),
% 294.71/186.72 inference(modus_ponens,[status(thm)],[232, 231])).
% 294.71/186.72 tff(234,plain,(
% 294.71/186.72 ![A: $i] : (multiplication(A, one) = A)),
% 294.71/186.72 inference(skolemize,[status(sab)],[233])).
% 294.71/186.72 tff(235,plain,
% 294.71/186.72 (![A: $i] : (multiplication(A, one) = A)),
% 294.71/186.72 inference(modus_ponens,[status(thm)],[234, 230])).
% 294.71/186.72 tff(236,plain,
% 294.71/186.72 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), one) = antidomain(antidomain(antidomain(antidomain(X1!1)))))),
% 294.71/186.72 inference(quant_inst,[status(thm)],[])).
% 294.71/186.72 tff(237,plain,
% 294.71/186.72 (multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), one) = antidomain(antidomain(antidomain(antidomain(X1!1))))),
% 294.71/186.72 inference(unit_resolution,[status(thm)],[236, 235])).
% 294.71/186.72 tff(238,plain,
% 294.71/186.72 (antidomain(antidomain(antidomain(antidomain(X1!1)))) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), one)),
% 294.71/186.72 inference(symmetry,[status(thm)],[237])).
% 294.71/186.72 tff(239,plain,
% 294.71/186.72 (antidomain(antidomain(antidomain(antidomain(X1!1)))) = domain(X1!1)),
% 294.71/186.72 inference(transitivity,[status(thm)],[238, 228, 223, 217, 208, 188, 178, 166, 161, 135])).
% 294.71/186.72 tff(240,plain,
% 294.71/186.72 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), forward_diamond(X0!0, domain(X1!1))) = addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1)))),
% 294.71/186.72 inference(monotonicity,[status(thm)],[239])).
% 294.71/186.72 tff(241,plain,
% 294.71/186.72 (addition(forward_diamond(X0!0, domain(X1!1)), domain(X1!1)) = addition(domain(X1!1), forward_diamond(X0!0, domain(X1!1)))),
% 294.71/186.72 inference(symmetry,[status(thm)],[139])).
% 294.71/186.72 tff(242,plain,
% 294.71/186.72 (addition(addition(forward_diamond(X0!0, domain(X1!1)), antidomain(antidomain(X1!1))), zero) = addition(forward_diamond(X0!0, domain(X1!1)), addition(antidomain(antidomain(X1!1)), zero))),
% 294.71/186.72 inference(symmetry,[status(thm)],[147])).
% 294.71/186.72 tff(243,plain,
% 294.71/186.72 (addition(forward_diamond(X0!0, domain(X1!1)), domain(zero)) = forward_diamond(X0!0, domain(X1!1))),
% 294.71/186.72 inference(transitivity,[status(thm)],[131, 144, 242, 151, 241, 141])).
% 294.71/186.72 tff(244,plain,
% 294.71/186.72 (addition(multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(domain(X1!1))), multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), antidomain(antidomain(X1!1)))) = multiplication(antidomain(antidomain(antidomain(antidomain(X1!1)))), addition(antidomain(domain(X1!1)), antidomain(antidomain(X1!1))))),
% 294.71/186.72 inference(symmetry,[status(thm)],[217])).
% 294.71/186.72 tff(245,plain,
% 294.71/186.72 (antidomain(antidomain(X1!1)) = multiplication(one, antidomain(antidomain(X1!1)))),
% 294.71/186.72 inference(symmetry,[status(thm)],[161])).
% 294.71/186.72 tff(246,plain,
% 294.71/186.72 (domain(X1!1) = antidomain(antidomain(antidomain(antidomain(X1!1))))),
% 294.71/186.72 inference(transitivity,[status(thm)],[134, 245, 165, 177, 187, 207, 244, 222, 227, 237])).
% 294.71/186.72 tff(247,plain,
% 294.71/186.72 (addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(zero))) = addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), forward_diamond(X0!0, domain(X1!1)))),
% 294.71/186.72 inference(monotonicity,[status(thm)],[246, 243])).
% 294.71/186.72 tff(248,plain,
% 294.71/186.72 (addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(zero))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(zero))),
% 294.71/186.72 inference(transitivity,[status(thm)],[247, 240, 139, 152, 147, 145, 132])).
% 294.71/186.72 tff(249,plain,
% 294.71/186.72 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(star(X0!0), zero) = zero)),
% 294.71/186.72 inference(quant_inst,[status(thm)],[])).
% 294.71/186.72 tff(250,plain,
% 294.71/186.72 (multiplication(star(X0!0), zero) = zero),
% 294.71/186.72 inference(unit_resolution,[status(thm)],[249, 69])).
% 294.71/186.72 tff(251,plain,
% 294.71/186.72 (multiplication(star(X0!0), domain(zero)) = multiplication(star(X0!0), zero)),
% 294.71/186.72 inference(monotonicity,[status(thm)],[130])).
% 294.71/186.72 tff(252,plain,
% 294.71/186.72 (multiplication(star(X0!0), domain(zero)) = zero),
% 294.71/186.72 inference(transitivity,[status(thm)],[251, 250])).
% 294.71/186.72 tff(253,plain,
% 294.71/186.72 (domain(multiplication(star(X0!0), domain(zero))) = domain(zero)),
% 294.71/186.72 inference(monotonicity,[status(thm)],[252])).
% 294.71/186.72 tff(254,plain,
% 294.71/186.72 ((~![A: $i] : (addition(A, zero) = A)) | (addition(domain(multiplication(star(X0!0), domain(zero))), zero) = domain(multiplication(star(X0!0), domain(zero))))),
% 294.71/186.72 inference(quant_inst,[status(thm)],[])).
% 294.71/186.72 tff(255,plain,
% 294.71/186.72 (addition(domain(multiplication(star(X0!0), domain(zero))), zero) = domain(multiplication(star(X0!0), domain(zero)))),
% 294.71/186.72 inference(unit_resolution,[status(thm)],[254, 91])).
% 294.71/186.72 tff(256,plain,
% 294.71/186.72 ((~![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))) | (forward_diamond(star(X0!0), zero) = domain(multiplication(star(X0!0), domain(zero))))),
% 294.71/186.72 inference(quant_inst,[status(thm)],[])).
% 294.71/186.72 tff(257,plain,
% 294.71/186.72 (forward_diamond(star(X0!0), zero) = domain(multiplication(star(X0!0), domain(zero)))),
% 294.71/186.72 inference(unit_resolution,[status(thm)],[256, 31])).
% 294.71/186.72 tff(258,plain,
% 294.71/186.72 (domain(multiplication(X0!0, domain(zero))) = zero),
% 294.71/186.72 inference(transitivity,[status(thm)],[34, 24, 22, 13])).
% 294.71/186.72 tff(259,plain,
% 294.71/186.72 (forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))) = forward_diamond(star(X0!0), zero)),
% 294.71/186.72 inference(monotonicity,[status(thm)],[258])).
% 294.71/186.72 tff(260,plain,
% 294.71/186.72 (forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))) = domain(multiplication(star(X0!0), domain(zero)))),
% 294.71/186.72 inference(transitivity,[status(thm)],[259, 257])).
% 294.71/186.72 tff(261,plain,
% 294.71/186.72 (addition(forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))), zero) = addition(domain(multiplication(star(X0!0), domain(zero))), zero)),
% 294.71/186.72 inference(monotonicity,[status(thm)],[260])).
% 294.71/186.72 tff(262,plain,
% 294.71/186.72 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))), zero))),
% 294.71/186.72 inference(quant_inst,[status(thm)],[])).
% 294.71/186.72 tff(263,plain,
% 294.71/186.72 (addition(zero, forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))), zero)),
% 294.71/186.72 inference(unit_resolution,[status(thm)],[262, 82])).
% 294.71/186.72 tff(264,plain,
% 294.71/186.72 (addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))) = addition(zero, forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))),
% 294.71/186.72 inference(monotonicity,[status(thm)],[13])).
% 294.71/186.72 tff(265,plain,
% 294.71/186.72 ((~![X0: $i] : (multiplication(antidomain(X0), X0) = zero)) | (multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1)) = zero)),
% 294.71/186.72 inference(quant_inst,[status(thm)],[])).
% 294.71/186.72 tff(266,plain,
% 294.71/186.72 (multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1)) = zero),
% 294.71/186.72 inference(unit_resolution,[status(thm)],[265, 199])).
% 294.71/186.72 tff(267,plain,
% 294.71/186.72 (zero = multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1))),
% 294.71/186.72 inference(symmetry,[status(thm)],[266])).
% 294.71/186.72 tff(268,plain,
% 294.71/186.72 (domain(multiplication(X0!0, domain(zero))) = multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1))),
% 294.71/186.72 inference(transitivity,[status(thm)],[34, 24, 22, 13, 267])).
% 294.71/186.72 tff(269,plain,
% 294.71/186.72 (domain(multiplication(X0!0, domain(zero))) = divergence(X0!0)),
% 294.71/186.72 inference(transitivity,[status(thm)],[34, 24, 22])).
% 294.71/186.72 tff(270,plain,
% 294.71/186.72 (forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))) = forward_diamond(X0!0, divergence(X0!0))),
% 294.71/186.72 inference(monotonicity,[status(thm)],[269])).
% 294.71/186.72 tff(271,plain,
% 294.71/186.72 (forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))) = multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1))),
% 294.71/186.72 inference(transitivity,[status(thm)],[270, 22, 13, 267])).
% 294.71/186.72 tff(272,plain,
% 294.71/186.72 (addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero)))) = addition(multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1)), multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1)))),
% 294.71/186.72 inference(monotonicity,[status(thm)],[271, 268])).
% 294.71/186.72 tff(273,plain,
% 294.71/186.72 (addition(multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1)), multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1))) = addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero))))),
% 294.71/186.72 inference(symmetry,[status(thm)],[272])).
% 294.71/186.72 tff(274,plain,
% 294.71/186.72 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 294.71/186.72 inference(bind,[status(th)],[])).
% 294.71/186.72 tff(275,plain,
% 294.71/186.72 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 294.71/186.72 inference(quant_intro,[status(thm)],[274])).
% 294.71/186.72 tff(276,plain,
% 294.71/186.72 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 294.71/186.72 inference(rewrite,[status(thm)],[])).
% 294.71/186.72 tff(277,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 294.71/186.72 tff(278,plain,
% 294.71/186.72 (![A: $i] : (addition(A, A) = A)),
% 294.71/186.72 inference(modus_ponens,[status(thm)],[277, 276])).
% 294.71/186.72 tff(279,plain,(
% 294.71/186.72 ![A: $i] : (addition(A, A) = A)),
% 294.71/186.72 inference(skolemize,[status(sab)],[278])).
% 294.71/186.72 tff(280,plain,
% 294.71/186.72 (![A: $i] : (addition(A, A) = A)),
% 294.71/186.72 inference(modus_ponens,[status(thm)],[279, 275])).
% 294.71/186.72 tff(281,plain,
% 294.71/186.72 ((~![A: $i] : (addition(A, A) = A)) | (addition(antidomain(antidomain(X1!1)), antidomain(antidomain(X1!1))) = antidomain(antidomain(X1!1)))),
% 294.71/186.72 inference(quant_inst,[status(thm)],[])).
% 294.71/186.72 tff(282,plain,
% 294.71/186.72 (addition(antidomain(antidomain(X1!1)), antidomain(antidomain(X1!1))) = antidomain(antidomain(X1!1))),
% 294.71/186.72 inference(unit_resolution,[status(thm)],[281, 280])).
% 294.71/186.72 tff(283,plain,
% 294.71/186.72 (multiplication(addition(antidomain(antidomain(X1!1)), antidomain(antidomain(X1!1))), antidomain(X1!1)) = multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1))),
% 294.71/186.72 inference(monotonicity,[status(thm)],[282])).
% 294.71/186.72 tff(284,plain,
% 294.71/186.72 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(antidomain(antidomain(X1!1)), antidomain(antidomain(X1!1))), antidomain(X1!1)) = addition(multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1)), multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1))))),
% 294.71/186.72 inference(quant_inst,[status(thm)],[])).
% 294.71/186.72 tff(285,plain,
% 294.71/186.72 (multiplication(addition(antidomain(antidomain(X1!1)), antidomain(antidomain(X1!1))), antidomain(X1!1)) = addition(multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1)), multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1)))),
% 294.71/186.72 inference(unit_resolution,[status(thm)],[284, 185])).
% 294.71/186.72 tff(286,plain,
% 294.71/186.72 (addition(multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1)), multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1))) = multiplication(addition(antidomain(antidomain(X1!1)), antidomain(antidomain(X1!1))), antidomain(X1!1))),
% 294.71/186.72 inference(symmetry,[status(thm)],[285])).
% 294.71/186.72 tff(287,plain,
% 294.71/186.72 (addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero)))) = multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1))),
% 294.71/186.72 inference(transitivity,[status(thm)],[272, 286, 283])).
% 294.71/186.72 tff(288,plain,
% 294.71/186.72 (addition(domain(multiplication(X0!0, domain(zero))), addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero))))) = addition(multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1)), multiplication(antidomain(antidomain(X1!1)), antidomain(X1!1)))),
% 294.71/186.72 inference(monotonicity,[status(thm)],[268, 287])).
% 294.71/186.72 tff(289,plain,
% 294.71/186.72 (addition(domain(multiplication(X0!0, domain(zero))), addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero))))),
% 294.71/186.72 inference(transitivity,[status(thm)],[288, 273])).
% 294.71/186.72 tff(290,plain,
% 294.71/186.72 (^[X0: $i, X1: $i, X2: $i] : refl(((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))) <=> ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))))),
% 294.71/186.72 inference(bind,[status(th)],[])).
% 294.71/186.72 tff(291,plain,
% 294.71/186.72 (![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))) <=> ![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 294.71/186.72 inference(quant_intro,[status(thm)],[290])).
% 294.71/186.72 tff(292,plain,
% 294.71/186.72 (![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))) <=> ![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 294.71/186.72 inference(rewrite,[status(thm)],[])).
% 294.71/186.72 tff(293,plain,
% 294.71/186.72 (^[X0: $i, X1: $i, X2: $i] : rewrite(((addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2))) => (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))) <=> ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))))),
% 294.71/186.72 inference(bind,[status(th)],[])).
% 294.71/186.72 tff(294,plain,
% 294.71/186.72 (![X0: $i, X1: $i, X2: $i] : ((addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2))) => (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2))))) <=> ![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 294.71/186.72 inference(quant_intro,[status(thm)],[293])).
% 294.71/186.72 tff(295,axiom,(![X0: $i, X1: $i, X2: $i] : ((addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2))) => (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+7.ax','divergence2')).
% 294.71/186.72 tff(296,plain,
% 294.71/186.72 (![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 294.71/186.72 inference(modus_ponens,[status(thm)],[295, 294])).
% 294.71/186.73 tff(297,plain,
% 294.71/186.73 (![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 294.71/186.73 inference(modus_ponens,[status(thm)],[296, 292])).
% 294.71/186.73 tff(298,plain,(
% 294.71/186.73 ![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 294.71/186.73 inference(skolemize,[status(sab)],[297])).
% 294.71/186.73 tff(299,plain,
% 294.71/186.73 (![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))),
% 294.71/186.73 inference(modus_ponens,[status(thm)],[298, 291])).
% 294.71/186.73 tff(300,plain,
% 294.71/186.73 (((~![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))) | ((~(addition(domain(multiplication(X0!0, domain(zero))), addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero)))))) | (addition(domain(multiplication(X0!0, domain(zero))), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))) | (~(addition(domain(multiplication(X0!0, domain(zero))), addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero)))))) | (addition(domain(multiplication(X0!0, domain(zero))), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))))),
% 294.71/186.73 inference(rewrite,[status(thm)],[])).
% 294.71/186.73 tff(301,plain,
% 294.71/186.73 ((~![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))) | ((~(addition(domain(multiplication(X0!0, domain(zero))), addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero)))))) | (addition(domain(multiplication(X0!0, domain(zero))), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))))),
% 294.71/186.73 inference(quant_inst,[status(thm)],[])).
% 294.71/186.73 tff(302,plain,
% 294.71/186.73 ((~![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))) | (~(addition(domain(multiplication(X0!0, domain(zero))), addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero)))))) | (addition(domain(multiplication(X0!0, domain(zero))), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))))),
% 294.71/186.73 inference(modus_ponens,[status(thm)],[301, 300])).
% 294.71/186.73 tff(303,plain,
% 294.71/186.73 ((~(addition(domain(multiplication(X0!0, domain(zero))), addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero))))) = addition(forward_diamond(X0!0, domain(multiplication(X0!0, domain(zero)))), domain(multiplication(X0!0, domain(zero)))))) | (addition(domain(multiplication(X0!0, domain(zero))), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))))),
% 294.71/186.73 inference(unit_resolution,[status(thm)],[302, 299])).
% 294.71/186.73 tff(304,plain,
% 294.71/186.73 (addition(domain(multiplication(X0!0, domain(zero))), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))),
% 294.71/186.73 inference(unit_resolution,[status(thm)],[303, 289])).
% 294.71/186.73 tff(305,plain,
% 294.71/186.73 (addition(zero, forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))),
% 294.71/186.73 inference(symmetry,[status(thm)],[264])).
% 294.71/186.73 tff(306,plain,
% 294.71/186.73 (addition(forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))), zero) = addition(zero, forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))),
% 294.71/186.73 inference(symmetry,[status(thm)],[263])).
% 294.71/186.73 tff(307,plain,
% 294.71/186.73 (addition(domain(multiplication(star(X0!0), domain(zero))), zero) = addition(forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))), zero)),
% 294.71/186.73 inference(symmetry,[status(thm)],[261])).
% 294.71/186.73 tff(308,plain,
% 294.71/186.73 (domain(multiplication(star(X0!0), domain(zero))) = addition(domain(multiplication(star(X0!0), domain(zero))), zero)),
% 294.71/186.73 inference(symmetry,[status(thm)],[255])).
% 294.71/186.73 tff(309,plain,
% 294.71/186.73 (domain(zero) = domain(multiplication(X0!0, domain(zero)))),
% 294.71/186.73 inference(transitivity,[status(thm)],[46, 129, 44])).
% 294.71/186.73 tff(310,plain,
% 294.71/186.73 (forward_diamond(star(X0!0), domain(zero)) = forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))),
% 294.71/186.73 inference(monotonicity,[status(thm)],[309])).
% 294.71/186.73 tff(311,plain,
% 294.71/186.73 (forward_diamond(star(X0!0), domain(zero)) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero)))))),
% 294.71/186.73 inference(transitivity,[status(thm)],[310, 259, 257, 308, 307, 306, 305])).
% 294.71/186.73 tff(312,plain,
% 294.71/186.73 (divergence(X0!0) = domain(multiplication(X0!0, domain(zero)))),
% 294.71/186.73 inference(transitivity,[status(thm)],[62, 61, 33])).
% 294.71/186.73 tff(313,plain,
% 294.71/186.73 (addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero))) = addition(domain(multiplication(X0!0, domain(zero))), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(multiplication(X0!0, domain(zero))))))),
% 294.71/186.73 inference(monotonicity,[status(thm)],[312, 311])).
% 294.71/186.73 tff(314,plain,
% 294.71/186.73 (addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero))) = zero),
% 294.71/186.73 inference(transitivity,[status(thm)],[313, 304, 264, 263, 261, 255, 253, 46, 129, 44, 34, 24, 22, 13])).
% 294.71/186.73 tff(315,plain,
% 294.71/186.73 (addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))) = addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero)),
% 294.71/186.73 inference(monotonicity,[status(thm)],[246, 314])).
% 294.71/186.73 tff(316,plain,
% 294.71/186.73 ((addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))) <=> (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = zero)),
% 294.71/186.73 inference(monotonicity,[status(thm)],[315, 314])).
% 294.71/186.73 tff(317,plain,
% 294.71/186.73 ((addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = zero) <=> (addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero))))),
% 294.71/186.73 inference(symmetry,[status(thm)],[316])).
% 294.71/186.73 tff(318,plain,
% 294.71/186.73 ((~(addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = zero)) <=> (~(addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))))),
% 294.71/186.73 inference(monotonicity,[status(thm)],[317])).
% 294.71/186.73 tff(319,plain,
% 294.71/186.73 ((~![A: $i] : (addition(A, zero) = A)) | (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = antidomain(antidomain(antidomain(antidomain(X1!1)))))),
% 294.71/186.73 inference(quant_inst,[status(thm)],[])).
% 294.71/186.73 tff(320,plain,
% 294.71/186.73 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = antidomain(antidomain(antidomain(antidomain(X1!1))))),
% 294.71/186.73 inference(unit_resolution,[status(thm)],[319, 91])).
% 294.71/186.73 tff(321,plain,
% 294.71/186.73 (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = domain(X1!1)),
% 294.71/186.73 inference(transitivity,[status(thm)],[320, 238, 228, 223, 217, 208, 188, 178, 166, 161, 135])).
% 294.71/186.73 tff(322,plain,
% 294.71/186.73 ((addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = zero) <=> (domain(X1!1) = zero)),
% 294.71/186.73 inference(monotonicity,[status(thm)],[321])).
% 294.71/186.73 tff(323,plain,
% 294.71/186.73 ((domain(X1!1) = zero) <=> (addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = zero)),
% 294.71/186.73 inference(symmetry,[status(thm)],[322])).
% 294.71/186.73 tff(324,plain,
% 294.71/186.73 ((~(domain(X1!1) = zero)) <=> (~(addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = zero))),
% 294.71/186.73 inference(monotonicity,[status(thm)],[323])).
% 294.71/186.73 tff(325,plain,
% 294.71/186.73 (~(domain(X1!1) = zero)),
% 294.71/186.73 inference(or_elim,[status(thm)],[140])).
% 294.71/186.73 tff(326,plain,
% 294.71/186.73 (~(addition(antidomain(antidomain(antidomain(antidomain(X1!1)))), zero) = zero)),
% 294.71/186.73 inference(modus_ponens,[status(thm)],[325, 324])).
% 294.71/186.73 tff(327,plain,
% 294.71/186.73 (~(addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero))))),
% 294.71/186.73 inference(modus_ponens,[status(thm)],[326, 318])).
% 294.71/186.73 tff(328,plain,
% 294.71/186.73 (((~![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))) | ((~(addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(zero))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(zero)))) | (addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))))) <=> ((~![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))) | (~(addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(zero))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(zero)))) | (addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))))),
% 294.76/186.84 inference(rewrite,[status(thm)],[])).
% 294.76/186.84 tff(329,plain,
% 294.76/186.84 ((~![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))) | ((~(addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(zero))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(zero)))) | (addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))))),
% 294.76/186.84 inference(quant_inst,[status(thm)],[])).
% 294.76/186.84 tff(330,plain,
% 294.76/186.84 ((~![X0: $i, X1: $i, X2: $i] : ((~(addition(domain(X0), addition(forward_diamond(X1, domain(X0)), domain(X2))) = addition(forward_diamond(X1, domain(X0)), domain(X2)))) | (addition(domain(X0), addition(divergence(X1), forward_diamond(star(X1), domain(X2)))) = addition(divergence(X1), forward_diamond(star(X1), domain(X2)))))) | (~(addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(zero))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(zero)))) | (addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero))))),
% 294.76/186.84 inference(modus_ponens,[status(thm)],[329, 328])).
% 294.76/186.84 tff(331,plain,
% 294.76/186.84 ((~(addition(domain(X1!1), addition(forward_diamond(X0!0, domain(X1!1)), domain(zero))) = addition(forward_diamond(X0!0, domain(X1!1)), domain(zero)))) | (addition(domain(X1!1), addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero)))) = addition(divergence(X0!0), forward_diamond(star(X0!0), domain(zero))))),
% 294.76/186.84 inference(unit_resolution,[status(thm)],[330, 299])).
% 294.76/186.84 tff(332,plain,
% 294.76/186.84 ($false),
% 294.76/186.84 inference(unit_resolution,[status(thm)],[331, 327, 248])).
% 294.76/186.84 % SZS output end Proof
%------------------------------------------------------------------------------