%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE100+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:52:24 PM UTC 2026
% Result : Theorem 80.72s 15.50s
% Output : CNFRefutation 110.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 28
% Syntax : Number of formulae : 184 ( 180 unt; 12 def)
% Number of atoms : 466 ( 187 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 13 ( 9 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 155 ( 0 sgn 152 !; 3 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(f14,axiom,
! [X0,X1] : 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) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( multiplication(antidomain(X2),multiplication(X0,domain(X1))) = zero
=> addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( multiplication(antidomain(X2),multiplication(X0,domain(X1))) = zero
=> addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1,X2] :
( multiplication(antidomain(X2),multiplication(X0,domain(X1))) = zero
& domain(X2) != addition(forward_diamond(X0,domain(X1)),domain(X2)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
( zero = multiplication(antidomain(sK2),multiplication(sK0,domain(sK1)))
& domain(sK2) != addition(forward_diamond(sK0,domain(sK1)),domain(sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f29]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f40,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f42,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f43,plain,
! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(cnf_transformation,[],[f14]) ).
fof(f44,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f52,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f56,plain,
zero = multiplication(antidomain(sK2),multiplication(sK0,domain(sK1))),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
domain(sK2) != addition(forward_diamond(sK0,domain(sK1)),domain(sK2)),
inference(cnf_transformation,[],[f30]) ).
fof(f62,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f52,f45,f45]) ).
fof(f64,plain,
antidomain(antidomain(sK2)) != addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(sK2))),
inference(definition_unfolding,[],[f57,f45,f62,f45,f45]) ).
fof(f65,plain,
zero = multiplication(antidomain(sK2),multiplication(sK0,antidomain(antidomain(sK1)))),
inference(definition_unfolding,[],[f56,f45]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f34]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f37]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f39]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f40]) ).
tcf(c_60,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f42]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(cnf_transformation,[],[f43]) ).
tcf(c_62,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f44]) ).
tcf(c_66,negated_conjecture,
addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(sK2))) != antidomain(antidomain(sK2)),
inference(cnf_transformation,[],[f64]) ).
tcf(c_67,negated_conjecture,
multiplication(antidomain(sK2),multiplication(sK0,antidomain(antidomain(sK1)))) = zero,
inference(cnf_transformation,[],[f65]) ).
tcf(c_83,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_85,negated_conjecture,
addition(antidomain(antidomain(sK2)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1)))))))) != antidomain(antidomain(sK2)),
inference(theory_normalisation,[status(thm)],[c_66,c_50,c_49]) ).
tcf(c_132,definition,
iPr_def_10 = antidomain(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_133,definition,
iPr_def_11 = antidomain(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_134,definition,
iPr_def_12 = antidomain(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_135,definition,
iPr_def_13 = antidomain(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_136,definition,
iPr_def_14 = antidomain(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_137,definition,
iPr_def_15 = antidomain(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_138,definition,
iPr_def_16 = multiplication(sK0,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_139,definition,
iPr_def_17 = antidomain(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_140,definition,
iPr_def_18 = antidomain(iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_141,definition,
iPr_def_19 = addition(iPr_def_11,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_142,definition,
iPr_def_20 = multiplication(sK0,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_143,definition,
iPr_def_21 = multiplication(iPr_def_10,iPr_def_20),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_144,negated_conjecture,
iPr_def_19 != iPr_def_11,
inference(demodulation,[status(thm)],[c_85,c_134,c_135,c_136,c_137,c_138,c_139,c_140,c_132,c_133,c_141]) ).
tcf(c_145,negated_conjecture,
iPr_def_21 = zero,
inference(demodulation,[status(thm)],[c_67,c_142,c_143]) ).
tcf(c_93731,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_93736,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_132,c_83]) ).
tcf(c_93738,plain,
addition(iPr_def_10,iPr_def_11) = one,
inference(light_normalisation,[status(thm)],[c_93736,c_133]) ).
tcf(c_93744,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_134,c_83]) ).
tcf(c_93749,plain,
addition(iPr_def_12,iPr_def_13) = one,
inference(light_normalisation,[status(thm)],[c_93744,c_135]) ).
tcf(c_93750,plain,
addition(iPr_def_13,antidomain(iPr_def_13)) = one,
inference(superposition,[status(thm)],[c_135,c_83]) ).
tcf(c_93755,plain,
addition(iPr_def_13,iPr_def_14) = one,
inference(light_normalisation,[status(thm)],[c_93750,c_136]) ).
tcf(c_93762,plain,
addition(iPr_def_15,antidomain(iPr_def_15)) = one,
inference(superposition,[status(thm)],[c_137,c_83]) ).
tcf(c_93767,plain,
addition(iPr_def_17,antidomain(iPr_def_17)) = one,
inference(superposition,[status(thm)],[c_139,c_83]) ).
tcf(c_93772,plain,
addition(iPr_def_17,iPr_def_18) = one,
inference(light_normalisation,[status(thm)],[c_93767,c_140]) ).
tcf(c_93773,plain,
addition(iPr_def_18,antidomain(iPr_def_18)) = one,
inference(superposition,[status(thm)],[c_140,c_83]) ).
tcf(c_93778,plain,
! [X0: $i] : addition(X0,iPr_def_21) = X0,
inference(light_normalisation,[status(thm)],[c_51,c_145]) ).
tcf(c_93779,plain,
! [X0: $i] : multiplication(X0,iPr_def_21) = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_58,c_145]) ).
tcf(c_93794,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_60,c_145]) ).
tcf(c_93796,plain,
multiplication(iPr_def_10,sK2) = iPr_def_21,
inference(superposition,[status(thm)],[c_132,c_93794]) ).
tcf(c_93797,plain,
multiplication(iPr_def_12,sK1) = iPr_def_21,
inference(superposition,[status(thm)],[c_134,c_93794]) ).
tcf(c_93804,plain,
antidomain(one) = iPr_def_21,
inference(superposition,[status(thm)],[c_93794,c_54]) ).
tcf(c_93808,plain,
! [X0: $i] : addition(iPr_def_21,X0) = X0,
inference(superposition,[status(thm)],[c_93778,c_49]) ).
tcf(c_93814,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_93822,plain,
addition(iPr_def_21,antidomain(iPr_def_21)) = one,
inference(superposition,[status(thm)],[c_93804,c_83]) ).
tcf(c_93826,plain,
! [X0: $i] : addition(iPr_def_12,addition(iPr_def_13,X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_93749,c_50]) ).
tcf(c_93841,plain,
! [X0: $i] : addition(iPr_def_10,addition(X0,iPr_def_11)) = addition(X0,one),
inference(superposition,[status(thm)],[c_93738,c_93731]) ).
tcf(c_93884,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(one,X1)),
inference(superposition,[status(thm)],[c_54,c_56]) ).
tcf(c_93886,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X0,X1)) = addition(iPr_def_21,multiplication(antidomain(X0),X1)),
inference(superposition,[status(thm)],[c_93794,c_56]) ).
tcf(c_93893,plain,
! [X0: $i] : addition(iPr_def_21,multiplication(iPr_def_10,X0)) = multiplication(iPr_def_10,addition(sK2,X0)),
inference(superposition,[status(thm)],[c_93796,c_56]) ).
tcf(c_93894,plain,
! [X0: $i] : addition(iPr_def_21,multiplication(iPr_def_12,X0)) = multiplication(iPr_def_12,addition(sK1,X0)),
inference(superposition,[status(thm)],[c_93797,c_56]) ).
tcf(c_93909,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,X1),iPr_def_21) = multiplication(X0,addition(X1,iPr_def_21)),
inference(superposition,[status(thm)],[c_93779,c_56]) ).
tcf(c_93935,plain,
! [X0: $i,X1: $i] : addition(iPr_def_21,multiplication(X0,X1)) = multiplication(X0,addition(X1,iPr_def_21)),
inference(theory_normalisation,[status(thm)],[c_93909,c_50,c_49]) ).
tcf(c_93949,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_93950,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = addition(iPr_def_21,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c_93794,c_57]) ).
tcf(c_94013,plain,
! [X0: $i,X1: $i,X2: $i] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(multiplication(X0,X1),antidomain(antidomain(X2))))) = antidomain(multiplication(multiplication(X0,X1),antidomain(antidomain(X2)))),
inference(superposition,[status(thm)],[c_53,c_61]) ).
tcf(c_94016,plain,
! [X0: $i] : addition(antidomain(iPr_def_21),antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0))))) = antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0)))),
inference(superposition,[status(thm)],[c_93794,c_61]) ).
tcf(c_94232,plain,
antidomain(iPr_def_21) = one,
inference(demodulation,[status(thm)],[c_93822,c_93808]) ).
tcf(c_94627,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(demodulation,[status(thm)],[c_93950,c_93778,c_93935]) ).
tcf(c_94633,plain,
! [X0: $i] : multiplication(antidomain(antidomain(X0)),X0) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_83,c_94627]) ).
tcf(c_94641,plain,
! [X0: $i] : multiplication(addition(iPr_def_15,X0),iPr_def_14) = multiplication(X0,iPr_def_14),
inference(superposition,[status(thm)],[c_137,c_94627]) ).
tcf(c_94662,plain,
! [X0: $i] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(light_normalisation,[status(thm)],[c_94633,c_55]) ).
tcf(c_94674,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(demodulation,[status(thm)],[c_93886,c_93778,c_93935]) ).
tcf(c_94675,plain,
! [X0: $i] : multiplication(iPr_def_10,addition(sK2,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_132,c_94674]) ).
tcf(c_94676,plain,
! [X0: $i] : multiplication(iPr_def_12,addition(sK1,X0)) = multiplication(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_134,c_94674]) ).
tcf(c_94682,plain,
! [X0: $i] : multiplication(iPr_def_18,addition(iPr_def_17,X0)) = multiplication(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_140,c_94674]) ).
tcf(c_94779,plain,
! [X0: $i] : addition(antidomain(X0),one) = one,
inference(superposition,[status(thm)],[c_83,c_93814]) ).
tcf(c_94784,plain,
addition(iPr_def_15,one) = one,
inference(superposition,[status(thm)],[c_93762,c_93814]) ).
tcf(c_94786,plain,
addition(iPr_def_13,one) = one,
inference(superposition,[status(thm)],[c_93755,c_93814]) ).
tcf(c_94788,plain,
addition(iPr_def_10,one) = one,
inference(superposition,[status(thm)],[c_93738,c_93814]) ).
tcf(c_94791,plain,
addition(iPr_def_18,one) = one,
inference(superposition,[status(thm)],[c_93773,c_93814]) ).
tcf(c_94792,plain,
addition(iPr_def_17,one) = one,
inference(superposition,[status(thm)],[c_93772,c_93814]) ).
tcf(c_94798,plain,
! [X0: $i] : addition(one,antidomain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_94779,c_50,c_49]) ).
tcf(c_94909,plain,
! [X0: $i] : addition(one,antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0))))) = antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0)))),
inference(light_normalisation,[status(thm)],[c_94016,c_94232]) ).
tcf(c_94910,plain,
! [X0: $i] : antidomain(multiplication(antidomain(X0),antidomain(antidomain(X0)))) = one,
inference(demodulation,[status(thm)],[c_94909,c_94798]) ).
tcf(c_94938,plain,
! [X0: $i] : multiplication(one,multiplication(antidomain(X0),antidomain(antidomain(X0)))) = iPr_def_21,
inference(superposition,[status(thm)],[c_94910,c_93794]) ).
tcf(c_94955,plain,
! [X0: $i] : multiplication(antidomain(X0),antidomain(antidomain(X0))) = iPr_def_21,
inference(demodulation,[status(thm)],[c_94938,c_55]) ).
tcf(c_94967,plain,
multiplication(iPr_def_10,antidomain(iPr_def_10)) = iPr_def_21,
inference(superposition,[status(thm)],[c_132,c_94955]) ).
tcf(c_94968,plain,
multiplication(iPr_def_12,antidomain(iPr_def_12)) = iPr_def_21,
inference(superposition,[status(thm)],[c_134,c_94955]) ).
tcf(c_94992,plain,
multiplication(iPr_def_12,iPr_def_13) = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_94968,c_135]) ).
tcf(c_94993,plain,
multiplication(iPr_def_10,iPr_def_11) = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_94967,c_133]) ).
tcf(c_95220,plain,
! [X0: $i] : addition(iPr_def_21,multiplication(iPr_def_12,X0)) = multiplication(iPr_def_12,addition(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_94992,c_56]) ).
tcf(c_95482,plain,
! [X0: $i] : addition(iPr_def_21,multiplication(iPr_def_10,X0)) = multiplication(iPr_def_10,addition(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_94993,c_56]) ).
tcf(c_95633,plain,
multiplication(antidomain(iPr_def_14),iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_136,c_94662]) ).
tcf(c_95654,plain,
multiplication(iPr_def_15,iPr_def_13) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_95633,c_137]) ).
tcf(c_96942,plain,
! [X0: $i] : multiplication(addition(X0,iPr_def_15),iPr_def_14) = multiplication(X0,iPr_def_14),
inference(superposition,[status(thm)],[c_49,c_94641]) ).
tcf(c_98350,plain,
! [X0: $i] : multiplication(iPr_def_18,addition(X0,iPr_def_17)) = multiplication(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_49,c_94682]) ).
tcf(c_99378,plain,
multiplication(iPr_def_15,addition(one,iPr_def_13)) = addition(iPr_def_15,iPr_def_13),
inference(superposition,[status(thm)],[c_95654,c_93884]) ).
tcf(c_99621,plain,
multiplication(iPr_def_15,addition(iPr_def_13,one)) = addition(iPr_def_13,iPr_def_15),
inference(theory_normalisation,[status(thm)],[c_99378,c_50,c_49]) ).
tcf(c_99622,plain,
addition(iPr_def_13,iPr_def_15) = multiplication(iPr_def_15,one),
inference(light_normalisation,[status(thm)],[c_99621,c_94786]) ).
tcf(c_101066,plain,
! [X0: $i] : multiplication(iPr_def_10,addition(iPr_def_11,X0)) = multiplication(iPr_def_10,X0),
inference(light_normalisation,[status(thm)],[c_93893,c_94675,c_95482]) ).
tcf(c_101210,plain,
addition(iPr_def_13,iPr_def_15) = iPr_def_15,
inference(demodulation,[status(thm)],[c_99622,c_54]) ).
tcf(c_101214,plain,
addition(one,iPr_def_15) = addition(iPr_def_12,iPr_def_15),
inference(superposition,[status(thm)],[c_101210,c_93826]) ).
tcf(c_101215,plain,
addition(iPr_def_12,iPr_def_15) = addition(iPr_def_15,one),
inference(theory_normalisation,[status(thm)],[c_101214,c_50,c_49]) ).
tcf(c_101216,plain,
addition(iPr_def_12,iPr_def_15) = one,
inference(light_normalisation,[status(thm)],[c_101215,c_94784]) ).
tcf(c_101524,plain,
! [X0: $i] : multiplication(iPr_def_12,addition(iPr_def_13,X0)) = multiplication(iPr_def_12,X0),
inference(light_normalisation,[status(thm)],[c_93894,c_94676,c_95220]) ).
tcf(c_101530,plain,
multiplication(iPr_def_12,one) = multiplication(iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_93755,c_101524]) ).
tcf(c_102441,plain,
multiplication(iPr_def_12,iPr_def_14) = iPr_def_12,
inference(demodulation,[status(thm)],[c_101530,c_54]) ).
tcf(c_102732,plain,
multiplication(one,iPr_def_14) = multiplication(iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_101216,c_96942]) ).
tcf(c_102744,plain,
multiplication(one,iPr_def_14) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_102732,c_102441]) ).
tcf(c_102777,plain,
iPr_def_12 = iPr_def_14,
inference(demodulation,[status(thm)],[c_102744,c_55]) ).
tcf(c_102830,plain,
antidomain(iPr_def_12) = iPr_def_15,
inference(demodulation,[status(thm)],[c_137,c_102777]) ).
tcf(c_102832,plain,
iPr_def_13 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_102830,c_135]) ).
tcf(c_102878,plain,
multiplication(sK0,iPr_def_13) = iPr_def_16,
inference(demodulation,[status(thm)],[c_138,c_102832]) ).
tcf(c_102879,plain,
iPr_def_16 = iPr_def_20,
inference(demodulation,[status(thm)],[c_142,c_102878]) ).
tcf(c_102914,plain,
multiplication(iPr_def_10,iPr_def_16) = iPr_def_21,
inference(demodulation,[status(thm)],[c_143,c_102879]) ).
tcf(c_103514,plain,
! [X0: $i] : addition(iPr_def_21,multiplication(iPr_def_10,X0)) = multiplication(iPr_def_10,addition(iPr_def_16,X0)),
inference(superposition,[status(thm)],[c_102914,c_56]) ).
tcf(c_103516,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),iPr_def_21) = multiplication(iPr_def_10,addition(X0,iPr_def_16)),
inference(superposition,[status(thm)],[c_102914,c_56]) ).
tcf(c_103525,plain,
! [X0: $i] : addition(iPr_def_21,multiplication(iPr_def_10,X0)) = multiplication(iPr_def_10,addition(X0,iPr_def_16)),
inference(theory_normalisation,[status(thm)],[c_103516,c_50,c_49]) ).
tcf(c_103526,plain,
! [X0: $i] : multiplication(iPr_def_10,addition(iPr_def_16,X0)) = multiplication(iPr_def_10,X0),
inference(light_normalisation,[status(thm)],[c_103514,c_95482,c_101066]) ).
tcf(c_107576,plain,
! [X0: $i] : multiplication(iPr_def_10,addition(X0,iPr_def_16)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_49,c_103526]) ).
tcf(c_126393,plain,
! [X0: $i,X1: $i,X2: $i] : addition(antidomain(multiplication(X0,multiplication(X1,X2))),antidomain(multiplication(X0,multiplication(X1,antidomain(antidomain(X2)))))) = antidomain(multiplication(X0,multiplication(X1,antidomain(antidomain(X2))))),
inference(demodulation,[status(thm)],[c_94013,c_53]) ).
tcf(c_126570,plain,
! [X0: $i] : addition(antidomain(multiplication(X0,iPr_def_21)),antidomain(multiplication(X0,multiplication(iPr_def_10,antidomain(antidomain(iPr_def_16)))))) = antidomain(multiplication(X0,multiplication(iPr_def_10,antidomain(antidomain(iPr_def_16))))),
inference(superposition,[status(thm)],[c_102914,c_126393]) ).
tcf(c_127124,plain,
! [X0: $i] : addition(one,antidomain(multiplication(X0,multiplication(iPr_def_10,iPr_def_18)))) = antidomain(multiplication(X0,multiplication(iPr_def_10,iPr_def_18))),
inference(light_normalisation,[status(thm)],[c_126570,c_139,c_140,c_93779,c_94232]) ).
tcf(c_128164,plain,
! [X0: $i] : antidomain(multiplication(X0,multiplication(iPr_def_10,iPr_def_18))) = one,
inference(demodulation,[status(thm)],[c_127124,c_94798]) ).
tcf(c_128195,plain,
! [X0: $i] : multiplication(one,multiplication(X0,multiplication(iPr_def_10,iPr_def_18))) = iPr_def_21,
inference(superposition,[status(thm)],[c_128164,c_93794]) ).
tcf(c_128232,plain,
! [X0: $i] : multiplication(X0,multiplication(iPr_def_10,iPr_def_18)) = iPr_def_21,
inference(demodulation,[status(thm)],[c_128195,c_55]) ).
tcf(c_128353,plain,
multiplication(iPr_def_10,iPr_def_18) = iPr_def_21,
inference(superposition,[status(thm)],[c_128232,c_94662]) ).
tcf(c_128506,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),iPr_def_21) = multiplication(iPr_def_10,addition(X0,iPr_def_18)),
inference(superposition,[status(thm)],[c_128353,c_56]) ).
tcf(c_128529,plain,
! [X0: $i] : addition(iPr_def_21,multiplication(iPr_def_10,X0)) = multiplication(iPr_def_10,addition(X0,iPr_def_18)),
inference(theory_normalisation,[status(thm)],[c_128506,c_50,c_49]) ).
tcf(c_128530,plain,
! [X0: $i] : multiplication(iPr_def_10,addition(X0,iPr_def_18)) = multiplication(iPr_def_10,X0),
inference(light_normalisation,[status(thm)],[c_128529,c_103525,c_107576]) ).
tcf(c_129184,plain,
multiplication(iPr_def_10,one) = multiplication(iPr_def_10,iPr_def_17),
inference(superposition,[status(thm)],[c_93772,c_128530]) ).
tcf(c_129470,plain,
multiplication(iPr_def_10,iPr_def_17) = iPr_def_10,
inference(demodulation,[status(thm)],[c_129184,c_54]) ).
tcf(c_129499,plain,
multiplication(addition(one,iPr_def_10),iPr_def_17) = addition(iPr_def_17,iPr_def_10),
inference(superposition,[status(thm)],[c_129470,c_93949]) ).
tcf(c_129510,plain,
multiplication(addition(iPr_def_10,one),iPr_def_17) = addition(iPr_def_10,iPr_def_17),
inference(theory_normalisation,[status(thm)],[c_129499,c_50,c_49]) ).
tcf(c_129511,plain,
addition(iPr_def_10,iPr_def_17) = multiplication(one,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_129510,c_94788]) ).
tcf(c_130103,plain,
addition(iPr_def_10,iPr_def_17) = iPr_def_17,
inference(demodulation,[status(thm)],[c_129511,c_55]) ).
tcf(c_130106,plain,
! [X0: $i] : addition(iPr_def_10,addition(iPr_def_17,X0)) = addition(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_130103,c_50]) ).
tcf(c_131222,plain,
addition(iPr_def_17,one) = addition(iPr_def_17,iPr_def_11),
inference(superposition,[status(thm)],[c_130106,c_93841]) ).
tcf(c_131223,plain,
addition(iPr_def_11,iPr_def_17) = addition(iPr_def_17,one),
inference(theory_normalisation,[status(thm)],[c_131222,c_50,c_49]) ).
tcf(c_131224,plain,
addition(iPr_def_11,iPr_def_17) = one,
inference(light_normalisation,[status(thm)],[c_131223,c_94792]) ).
tcf(c_131265,plain,
multiplication(iPr_def_18,one) = multiplication(iPr_def_18,iPr_def_11),
inference(superposition,[status(thm)],[c_131224,c_98350]) ).
tcf(c_133062,plain,
multiplication(iPr_def_18,iPr_def_11) = iPr_def_18,
inference(demodulation,[status(thm)],[c_131265,c_54]) ).
tcf(c_133089,plain,
multiplication(addition(one,iPr_def_18),iPr_def_11) = addition(iPr_def_11,iPr_def_18),
inference(superposition,[status(thm)],[c_133062,c_93949]) ).
tcf(c_133105,plain,
multiplication(addition(iPr_def_18,one),iPr_def_11) = addition(iPr_def_11,iPr_def_18),
inference(theory_normalisation,[status(thm)],[c_133089,c_50,c_49]) ).
tcf(c_133106,plain,
multiplication(one,iPr_def_11) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_133105,c_141,c_94791]) ).
tcf(c_133178,plain,
iPr_def_11 = iPr_def_19,
inference(demodulation,[status(thm)],[c_133106,c_55]) ).
tcf(c_133276,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_144,c_133178]) ).
tcf(c_133277,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_133276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE100+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 19:00:44 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.45 % Proving...
% 80.72/15.50 % SZS status Started for theBenchmark.p
% 80.72/15.50 % SZS status Theorem for theBenchmark.p
% 80.72/15.50
% 80.72/15.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 80.72/15.50
% 80.72/15.50 % ------ iProver source info
% 80.72/15.50
% 80.72/15.50 % git: date: 2026-07-19 20:42:38 +0200
% 80.72/15.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 80.72/15.50 % git: non_committed_changes: false
% 80.72/15.50
% 80.72/15.50 % ------ Parsing...
% 80.72/15.50 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 80.72/15.50 %
% 80.72/15.50
% 80.72/15.50 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 80.72/15.50
% 80.72/15.50 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 80.72/15.50 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 80.72/15.50
% 80.72/15.50 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 80.72/15.50 % ------ Proving...
% 80.72/15.50 % ------ Problem Properties
% 80.72/15.50
% 80.72/15.50 %
% 80.72/15.50 % clauses 31
% 80.72/15.50 % conjectures 2
% 80.72/15.50 % EPR 2
% 80.72/15.50 % Horn 31
% 80.72/15.50 % unary 31
% 80.72/15.50 % binary 0
% 80.72/15.50 % lits 31
% 80.72/15.50 % lits eq 31
% 80.72/15.50 % fd_pure 0
% 80.72/15.50 % fd_pseudo 0
% 80.72/15.50 % fd_cond 0
% 80.72/15.50 % fd_pseudo_cond 0
% 80.72/15.50 % AC symbols 1
% 80.72/15.50
% 80.72/15.50 % ------ Schedule UEQ
% 80.72/15.50
% 80.72/15.50 % ------ Option_UEQ Time Limit: 10.
% 80.72/15.50
% 80.72/15.50
% 80.72/15.50 % ------
% 80.72/15.50 % Current options:
% 80.72/15.50 % ------
% 80.72/15.50
% 80.72/15.50
% 80.72/15.50 %
% 80.72/15.50
% 80.72/15.50 % ------ Proving...
% 80.72/15.50 % Proof_search_loop: time out after: 1642 full_loop iterations
% 80.72/15.50
% 80.72/15.50 % ------ Option_UEQ Time Limit: 15.
% 80.72/15.50
% 80.72/15.50
% 80.72/15.50 % ------
% 80.72/15.50 % Current options:
% 80.72/15.50 % ------
% 80.72/15.50
% 80.72/15.50
% 80.72/15.50 %
% 80.72/15.50
% 80.72/15.50 % ------ Proving...
% 80.72/15.50 %
% 80.72/15.50
% 80.72/15.50 % SZS status Theorem for theBenchmark.p
% 80.72/15.50
% 80.72/15.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 110.47/15.50
% 110.47/15.50
%------------------------------------------------------------------------------