%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE091+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 01:52:23 PM UTC 2026
% Result : Theorem 71.98s 12.43s
% Output : CNFRefutation 71.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 23
% Syntax : Number of formulae : 128 ( 115 unt; 4 def)
% Number of atoms : 306 ( 153 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 59 ( 33 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 119 ( 0 sgn 118 !; 1 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(f17,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(f19,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(f20,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain4) ).
fof(f21,conjecture,
! [X0] : domain(codomain(X0)) = codomain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
~ ! [X0] : domain(codomain(X0)) = codomain(X0),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0] : codomain(X0) != domain(codomain(X0)),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
codomain(sK0) != domain(codomain(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f23]) ).
fof(f25,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f28,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f31,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f33,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f34,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f36,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f37,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(f38,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f39,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f42,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
inference(cnf_transformation,[],[f20]) ).
fof(f44,plain,
codomain(sK0) != domain(codomain(sK0)),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
coantidomain(coantidomain(sK0)) != antidomain(antidomain(coantidomain(coantidomain(sK0)))),
inference(definition_unfolding,[],[f44,f43,f39,f43]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f25]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f27]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f30]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f31]) ).
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,[],[f32]) ).
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,[],[f33]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f34]) ).
tcf(c_60,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f36]) ).
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,[],[f37]) ).
tcf(c_62,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f38]) ).
tcf(c_63,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[],[f40]) ).
tcf(c_65,plain,
! [X0: $i] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[],[f42]) ).
tcf(c_66,negated_conjecture,
antidomain(antidomain(coantidomain(coantidomain(sK0)))) != coantidomain(coantidomain(sK0)),
inference(cnf_transformation,[],[f45]) ).
tcf(c_82,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_83,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_65,c_50,c_49]) ).
tcf(c_128,definition,
iPr_def_10 = coantidomain(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_129,definition,
iPr_def_11 = coantidomain(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_130,definition,
iPr_def_12 = antidomain(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_131,definition,
iPr_def_13 = antidomain(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_132,negated_conjecture,
iPr_def_13 != iPr_def_11,
inference(demodulation,[status(thm)],[c_66,c_128,c_129,c_130,c_131]) ).
tcf(c_133,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_670,plain,
! [X0: $i] :
( ( iPr_def_13 = iPr_def_11 )
| ( iPr_def_13 != X0 )
| ( iPr_def_11 != X0 ) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_694,plain,
( ( iPr_def_13 = iPr_def_11 )
| ( iPr_def_13 != iPr_def_13 )
| ( iPr_def_11 != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_670]) ).
tcf(c_695,plain,
iPr_def_13 = iPr_def_13,
inference(instantiation,[status(thm)],[c_133]) ).
tcf(c_696,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_13 = X0 )
| ( iPr_def_13 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_798,plain,
! [X0: $i] :
( ( iPr_def_11 = iPr_def_13 )
| ( iPr_def_13 != X0 )
| ( iPr_def_11 != X0 ) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_844,plain,
! [X0: $i] :
( ( iPr_def_13 = X0 )
| ( iPr_def_13 != iPr_def_13 )
| ( X0 != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_696]) ).
tcf(c_895,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_11 = X0 )
| ( iPr_def_11 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_999,plain,
iPr_def_11 = iPr_def_11,
inference(instantiation,[status(thm)],[c_133]) ).
tcf(c_1430,plain,
( ( iPr_def_13 = multiplication(one,iPr_def_13) )
| ( iPr_def_13 != iPr_def_13 )
| ( multiplication(one,iPr_def_13) != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_844]) ).
tcf(c_1431,plain,
multiplication(one,iPr_def_13) = iPr_def_13,
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_2121,plain,
! [X0: $i] :
( ( iPr_def_13 = X0 )
| ( iPr_def_13 != multiplication(one,iPr_def_13) )
| ( X0 != multiplication(one,iPr_def_13) ) ),
inference(instantiation,[status(thm)],[c_696]) ).
tcf(c_2450,plain,
! [X0: $i] :
( ( iPr_def_11 = X0 )
| ( iPr_def_11 != iPr_def_11 )
| ( X0 != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_895]) ).
tcf(c_6026,plain,
( ( iPr_def_11 = addition(iPr_def_11,zero) )
| ( iPr_def_11 != iPr_def_11 )
| ( addition(iPr_def_11,zero) != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_2450]) ).
tcf(c_6027,plain,
addition(iPr_def_11,zero) = iPr_def_11,
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_15899,plain,
( ( iPr_def_11 = iPr_def_13 )
| ( iPr_def_13 != addition(iPr_def_11,zero) )
| ( iPr_def_11 != addition(iPr_def_11,zero) ) ),
inference(instantiation,[status(thm)],[c_798]) ).
tcf(c_82223,plain,
( ( iPr_def_13 = addition(iPr_def_11,zero) )
| ( iPr_def_13 != multiplication(one,iPr_def_13) )
| ( addition(iPr_def_11,zero) != multiplication(one,iPr_def_13) ) ),
inference(instantiation,[status(thm)],[c_2121]) ).
tcf(c_145226,plain,
addition(iPr_def_13,antidomain(iPr_def_13)) = one,
inference(superposition,[status(thm)],[c_131,c_82]) ).
tcf(c_145231,plain,
antidomain(one) = zero,
inference(superposition,[status(thm)],[c_60,c_54]) ).
tcf(c_145233,plain,
addition(zero,antidomain(zero)) = one,
inference(superposition,[status(thm)],[c_145231,c_82]) ).
tcf(c_145236,plain,
multiplication(iPr_def_10,iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_129,c_63]) ).
tcf(c_145239,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_145243,plain,
antidomain(zero) = one,
inference(demodulation,[status(thm)],[c_145233,c_145239]) ).
tcf(c_145250,plain,
addition(iPr_def_10,coantidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_128,c_83]) ).
tcf(c_145251,plain,
addition(iPr_def_11,coantidomain(iPr_def_11)) = one,
inference(superposition,[status(thm)],[c_129,c_83]) ).
tcf(c_145253,plain,
addition(iPr_def_10,iPr_def_11) = one,
inference(light_normalisation,[status(thm)],[c_145250,c_129]) ).
tcf(c_145257,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_145288,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_145290,plain,
! [X0: $i,X1: $i] : addition(zero,multiplication(X0,X1)) = multiplication(X0,addition(zero,X1)),
inference(superposition,[status(thm)],[c_58,c_56]) ).
tcf(c_145293,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(coantidomain(X0),X1)) = addition(zero,multiplication(X0,X1)),
inference(superposition,[status(thm)],[c_63,c_56]) ).
tcf(c_145301,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,X1),zero) = multiplication(X0,addition(X1,zero)),
inference(superposition,[status(thm)],[c_58,c_56]) ).
tcf(c_145319,plain,
! [X0: $i,X1: $i] : addition(zero,multiplication(X0,X1)) = multiplication(X0,addition(X1,zero)),
inference(theory_normalisation,[status(thm)],[c_145301,c_50,c_49]) ).
tcf(c_145333,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c_60,c_57]) ).
tcf(c_145377,plain,
! [X0: $i] : addition(iPr_def_11,addition(coantidomain(iPr_def_11),X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_145251,c_50]) ).
tcf(c_145443,plain,
! [X0: $i] : addition(antidomain(X0),one) = one,
inference(superposition,[status(thm)],[c_82,c_145257]) ).
tcf(c_145445,plain,
addition(iPr_def_13,one) = one,
inference(superposition,[status(thm)],[c_145226,c_145257]) ).
tcf(c_145447,plain,
addition(iPr_def_11,one) = one,
inference(superposition,[status(thm)],[c_145251,c_145257]) ).
tcf(c_145452,plain,
! [X0: $i] : addition(one,antidomain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_145443,c_50,c_49]) ).
tcf(c_145500,plain,
addition(antidomain(zero),antidomain(multiplication(iPr_def_10,antidomain(antidomain(iPr_def_11))))) = antidomain(multiplication(iPr_def_10,antidomain(antidomain(iPr_def_11)))),
inference(superposition,[status(thm)],[c_145236,c_61]) ).
tcf(c_145522,plain,
addition(one,antidomain(multiplication(iPr_def_10,iPr_def_13))) = antidomain(multiplication(iPr_def_10,iPr_def_13)),
inference(light_normalisation,[status(thm)],[c_145500,c_130,c_131,c_145243]) ).
tcf(c_146083,plain,
! [X0: $i] : addition(iPr_def_11,addition(X0,coantidomain(iPr_def_11))) = addition(one,X0),
inference(superposition,[status(thm)],[c_49,c_145377]) ).
tcf(c_146435,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,addition(zero,X1)),
inference(light_normalisation,[status(thm)],[c_145293,c_145290]) ).
tcf(c_146436,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,X1),
inference(demodulation,[status(thm)],[c_146435,c_145239]) ).
tcf(c_146442,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(superposition,[status(thm)],[c_49,c_146436]) ).
tcf(c_148101,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(demodulation,[status(thm)],[c_145333,c_51,c_145319]) ).
tcf(c_148108,plain,
! [X0: $i] : multiplication(antidomain(antidomain(X0)),X0) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_82,c_148101]) ).
tcf(c_148133,plain,
! [X0: $i] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(light_normalisation,[status(thm)],[c_148108,c_55]) ).
tcf(c_148142,plain,
multiplication(antidomain(iPr_def_12),iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_130,c_148133]) ).
tcf(c_148159,plain,
multiplication(iPr_def_13,iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_148142,c_131]) ).
tcf(c_148173,plain,
multiplication(iPr_def_13,addition(one,iPr_def_11)) = addition(iPr_def_13,iPr_def_11),
inference(superposition,[status(thm)],[c_148159,c_145288]) ).
tcf(c_148183,plain,
multiplication(iPr_def_13,addition(iPr_def_11,one)) = addition(iPr_def_11,iPr_def_13),
inference(theory_normalisation,[status(thm)],[c_148173,c_50,c_49]) ).
tcf(c_148184,plain,
addition(iPr_def_11,iPr_def_13) = multiplication(iPr_def_13,one),
inference(light_normalisation,[status(thm)],[c_148183,c_145447]) ).
tcf(c_148272,plain,
addition(iPr_def_11,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_148184,c_54]) ).
tcf(c_148273,plain,
! [X0: $i] : addition(iPr_def_11,addition(iPr_def_13,X0)) = addition(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_148272,c_50]) ).
tcf(c_148611,plain,
addition(iPr_def_13,coantidomain(iPr_def_11)) = addition(one,iPr_def_13),
inference(superposition,[status(thm)],[c_148273,c_146083]) ).
tcf(c_148613,plain,
addition(iPr_def_13,coantidomain(iPr_def_11)) = addition(iPr_def_13,one),
inference(theory_normalisation,[status(thm)],[c_148611,c_50,c_49]) ).
tcf(c_148614,plain,
addition(iPr_def_13,coantidomain(iPr_def_11)) = one,
inference(light_normalisation,[status(thm)],[c_148613,c_145445]) ).
tcf(c_148735,plain,
multiplication(iPr_def_11,one) = multiplication(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_148614,c_146442]) ).
tcf(c_148745,plain,
multiplication(iPr_def_11,iPr_def_13) = iPr_def_11,
inference(demodulation,[status(thm)],[c_148735,c_54]) ).
tcf(c_148751,plain,
! [X0: $i] : addition(iPr_def_11,multiplication(X0,iPr_def_13)) = multiplication(addition(iPr_def_11,X0),iPr_def_13),
inference(superposition,[status(thm)],[c_148745,c_57]) ).
tcf(c_156535,plain,
antidomain(multiplication(iPr_def_10,iPr_def_13)) = one,
inference(demodulation,[status(thm)],[c_145522,c_145452]) ).
tcf(c_156547,plain,
multiplication(one,multiplication(iPr_def_10,iPr_def_13)) = zero,
inference(superposition,[status(thm)],[c_156535,c_60]) ).
tcf(c_156565,plain,
multiplication(iPr_def_10,iPr_def_13) = zero,
inference(demodulation,[status(thm)],[c_156547,c_55]) ).
tcf(c_168737,plain,
multiplication(addition(iPr_def_11,iPr_def_10),iPr_def_13) = addition(iPr_def_11,zero),
inference(superposition,[status(thm)],[c_156565,c_148751]) ).
tcf(c_168774,plain,
multiplication(addition(iPr_def_10,iPr_def_11),iPr_def_13) = addition(iPr_def_11,zero),
inference(theory_normalisation,[status(thm)],[c_168737,c_50,c_49]) ).
tcf(c_168775,plain,
addition(iPr_def_11,zero) = multiplication(one,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_168774,c_145253]) ).
tcf(c_168965,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_168775,c_82223,c_15899,c_6027,c_6026,c_1431,c_1430,c_999,c_695,c_694,c_132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE091+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 18:54:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 71.98/12.43 % SZS status Started for theBenchmark.p
% 71.98/12.43 % SZS status Theorem for theBenchmark.p
% 71.98/12.43
% 71.98/12.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 71.98/12.43
% 71.98/12.43 % ------ iProver source info
% 71.98/12.43
% 71.98/12.43 % git: date: 2026-07-19 20:42:38 +0200
% 71.98/12.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 71.98/12.43 % git: non_committed_changes: false
% 71.98/12.43
% 71.98/12.43 % ------ Parsing...
% 71.98/12.43 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 71.98/12.43 %
% 71.98/12.43
% 71.98/12.43 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 71.98/12.43
% 71.98/12.43 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 71.98/12.43 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 71.98/12.43
% 71.98/12.43 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 71.98/12.43 % ------ Proving...
% 71.98/12.43 % ------ Problem Properties
% 71.98/12.43
% 71.98/12.43 %
% 71.98/12.43 % clauses 22
% 71.98/12.43 % conjectures 1
% 71.98/12.43 % EPR 1
% 71.98/12.43 % Horn 22
% 71.98/12.43 % unary 22
% 71.98/12.43 % binary 0
% 71.98/12.43 % lits 22
% 71.98/12.43 % lits eq 22
% 71.98/12.43 % fd_pure 0
% 71.98/12.43 % fd_pseudo 0
% 71.98/12.43 % fd_cond 0
% 71.98/12.43 % fd_pseudo_cond 0
% 71.98/12.43 % AC symbols 1
% 71.98/12.43
% 71.98/12.43 % ------ Schedule UEQ
% 71.98/12.43
% 71.98/12.43 % ------ Option_UEQ Time Limit: 10.
% 71.98/12.43
% 71.98/12.43
% 71.98/12.43 % ------
% 71.98/12.43 % Current options:
% 71.98/12.43 % ------
% 71.98/12.43
% 71.98/12.43
% 71.98/12.43 %
% 71.98/12.43
% 71.98/12.43 % ------ Proving...
% 71.98/12.43 % Proof_search_loop: time out after: 2335 full_loop iterations
% 71.98/12.43
% 71.98/12.43 % ------ Option_UEQ Time Limit: 15.
% 71.98/12.43
% 71.98/12.43
% 71.98/12.43 % ------
% 71.98/12.43 % Current options:
% 71.98/12.43 % ------
% 71.98/12.43
% 71.98/12.43
% 71.98/12.43 %
% 71.98/12.43
% 71.98/12.43 % ------ Proving...
% 71.98/12.43 %
% 71.98/12.43
% 71.98/12.43 % SZS status Theorem for theBenchmark.p
% 71.98/12.43
% 71.98/12.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 71.98/12.43
% 71.98/12.43
%------------------------------------------------------------------------------