%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE099+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 : n007.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 1.33s 1.76s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 27
% Syntax : Number of formulae : 161 ( 157 unt; 12 def)
% Number of atoms : 489 ( 164 equ)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 12 ( 8 ~; 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 : 118 ( 0 sgn 115 !; 3 ?; 59 :)
% 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(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
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(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
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(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2)
=> multiplication(antidomain(X2),multiplication(X0,domain(X1))) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2)
=> multiplication(antidomain(X2),multiplication(X0,domain(X1))) = zero ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1,X2] :
( addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2)
& zero != multiplication(antidomain(X2),multiplication(X0,domain(X1))) ),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
( domain(sK2) = addition(forward_diamond(sK0,domain(sK1)),domain(sK2))
& zero != multiplication(antidomain(sK2),multiplication(sK0,domain(sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f29]) ).
fof(f31,plain,
domain(sK2) = addition(forward_diamond(sK0,domain(sK1)),domain(sK2)),
inference(cnf_transformation,[],[f30]) ).
fof(f32,plain,
zero != multiplication(antidomain(sK2),multiplication(sK0,domain(sK1))),
inference(cnf_transformation,[],[f30]) ).
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,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f35,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f37,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f39,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f40,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f42,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f43,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f44,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f46,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f49,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f50,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f51,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f46,f44,f44]) ).
fof(f53,plain,
zero != multiplication(antidomain(sK2),multiplication(sK0,antidomain(antidomain(sK1)))),
inference(definition_unfolding,[],[f32,f44]) ).
fof(f54,plain,
antidomain(antidomain(sK2)) = addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(sK2))),
inference(definition_unfolding,[],[f31,f44,f52,f44,f44]) ).
tcf(c_49,negated_conjecture,
multiplication(antidomain(sK2),multiplication(sK0,antidomain(antidomain(sK1)))) != zero,
inference(cnf_transformation,[],[f53]) ).
tcf(c_50,negated_conjecture,
addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(sK2))) = antidomain(antidomain(sK2)),
inference(cnf_transformation,[],[f54]) ).
tcf(c_51,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_52,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_53,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f37]) ).
tcf(c_57,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f39]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f40]) ).
tcf(c_60,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f42]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f43]) ).
tcf(c_65,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f49]) ).
tcf(c_66,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f50]) ).
tcf(c_67,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f51]) ).
tcf(c_83,negated_conjecture,
addition(antidomain(antidomain(sK2)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1)))))))) = antidomain(antidomain(sK2)),
inference(theory_normalisation,[status(thm)],[c_50,c_54,c_55]) ).
tcf(c_85,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_65,c_54,c_55]) ).
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_83,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_49,c_142,c_143]) ).
tcf(c_247,plain,
addition(iPr_def_11,iPr_def_18) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_141,c_144]) ).
tcf(c_255,plain,
multiplication(iPr_def_11,iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_133,c_57]) ).
tcf(c_257,plain,
multiplication(iPr_def_14,iPr_def_13) = zero,
inference(superposition,[status(thm)],[c_136,c_57]) ).
tcf(c_258,plain,
multiplication(iPr_def_15,iPr_def_14) = zero,
inference(superposition,[status(thm)],[c_137,c_57]) ).
tcf(c_259,plain,
multiplication(iPr_def_17,iPr_def_16) = zero,
inference(superposition,[status(thm)],[c_139,c_57]) ).
tcf(c_265,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_11,iPr_def_10)) = X0,
inference(demodulation,[status(thm)],[c_60,c_255]) ).
tcf(c_267,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_11,iPr_def_10),X0) = multiplication(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_58,c_255]) ).
tcf(c_268,plain,
multiplication(iPr_def_11,iPr_def_10) != iPr_def_21,
inference(demodulation,[status(thm)],[c_145,c_255]) ).
tcf(c_277,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_132,c_85]) ).
tcf(c_278,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_134,c_85]) ).
tcf(c_280,plain,
addition(iPr_def_13,antidomain(iPr_def_13)) = one,
inference(superposition,[status(thm)],[c_135,c_85]) ).
tcf(c_281,plain,
addition(iPr_def_14,antidomain(iPr_def_14)) = one,
inference(superposition,[status(thm)],[c_136,c_85]) ).
tcf(c_283,plain,
addition(iPr_def_17,antidomain(iPr_def_17)) = one,
inference(superposition,[status(thm)],[c_139,c_85]) ).
tcf(c_284,plain,
addition(iPr_def_18,antidomain(iPr_def_18)) = one,
inference(superposition,[status(thm)],[c_140,c_85]) ).
tcf(c_285,plain,
addition(iPr_def_17,iPr_def_18) = one,
inference(light_normalisation,[status(thm)],[c_283,c_140]) ).
tcf(c_286,plain,
addition(iPr_def_14,iPr_def_15) = one,
inference(light_normalisation,[status(thm)],[c_281,c_137]) ).
tcf(c_287,plain,
addition(iPr_def_13,iPr_def_14) = one,
inference(light_normalisation,[status(thm)],[c_280,c_136]) ).
tcf(c_288,plain,
addition(iPr_def_12,iPr_def_13) = one,
inference(light_normalisation,[status(thm)],[c_278,c_135]) ).
tcf(c_289,plain,
addition(iPr_def_10,iPr_def_11) = one,
inference(light_normalisation,[status(thm)],[c_277,c_133]) ).
tcf(c_291,plain,
! [X0: $i] : multiplication(X0,addition(iPr_def_17,iPr_def_18)) = X0,
inference(demodulation,[status(thm)],[c_67,c_285]) ).
tcf(c_292,plain,
! [X0: $i] : multiplication(addition(iPr_def_17,iPr_def_18),X0) = X0,
inference(demodulation,[status(thm)],[c_66,c_285]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_296,plain,
! [X0: $i] : addition(iPr_def_11,addition(iPr_def_18,X0)) = addition(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_247,c_54]) ).
tcf(c_305,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(iPr_def_18,X0)) = multiplication(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_247,c_51]) ).
tcf(c_321,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_11,X0),addition(multiplication(iPr_def_18,X0),X1)) = addition(multiplication(iPr_def_11,X0),X1),
inference(superposition,[status(thm)],[c_305,c_54]) ).
tcf(c_332,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_11,X0),addition(X1,multiplication(iPr_def_18,X0))) = addition(multiplication(iPr_def_11,X0),X1),
inference(superposition,[status(thm)],[c_55,c_321]) ).
tcf(c_485,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_14,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_257,c_255]) ).
tcf(c_491,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_15,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_258,c_255]) ).
tcf(c_497,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_17,iPr_def_16),
inference(light_normalisation,[status(thm)],[c_259,c_255]) ).
tcf(c_670,plain,
addition(iPr_def_14,iPr_def_15) = addition(iPr_def_17,iPr_def_18),
inference(demodulation,[status(thm)],[c_285,c_286]) ).
tcf(c_685,plain,
addition(iPr_def_13,iPr_def_14) = addition(iPr_def_14,iPr_def_15),
inference(demodulation,[status(thm)],[c_286,c_287]) ).
tcf(c_686,plain,
addition(iPr_def_13,iPr_def_14) = addition(iPr_def_17,iPr_def_18),
inference(demodulation,[status(thm)],[c_670,c_685]) ).
tcf(c_693,plain,
addition(iPr_def_12,iPr_def_13) = addition(iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_287,c_288]) ).
tcf(c_694,plain,
addition(iPr_def_12,iPr_def_13) = addition(iPr_def_14,iPr_def_15),
inference(demodulation,[status(thm)],[c_685,c_693]) ).
tcf(c_701,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_288,c_289]) ).
tcf(c_702,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_693,c_701]) ).
tcf(c_705,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)) = multiplication(addition(iPr_def_10,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_701,c_51]) ).
tcf(c_706,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,iPr_def_13)) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_701,c_52]) ).
tcf(c_864,plain,
addition(iPr_def_18,antidomain(iPr_def_18)) = addition(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_284,c_289]) ).
tcf(c_870,plain,
addition(iPr_def_11,addition(iPr_def_10,iPr_def_11)) = addition(iPr_def_11,antidomain(iPr_def_18)),
inference(superposition,[status(thm)],[c_864,c_296]) ).
tcf(c_872,plain,
addition(iPr_def_10,addition(iPr_def_11,iPr_def_11)) = addition(iPr_def_11,antidomain(iPr_def_18)),
inference(theory_normalisation,[status(thm)],[c_870,c_54,c_55]) ).
tcf(c_892,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,iPr_def_10),X0) = X0,
inference(superposition,[status(thm)],[c_265,c_55]) ).
tcf(c_904,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,iPr_def_13)) = X0,
inference(light_normalisation,[status(thm)],[c_291,c_686,c_702,c_706]) ).
tcf(c_932,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_292,c_686,c_702,c_705]) ).
tcf(c_949,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_17,iPr_def_18),
inference(light_normalisation,[status(thm)],[c_686,c_702]) ).
tcf(c_952,plain,
! [X0: $i] : addition(multiplication(iPr_def_17,X0),multiplication(iPr_def_18,X0)) = multiplication(addition(iPr_def_10,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_949,c_51]) ).
tcf(c_965,plain,
! [X0: $i] : addition(multiplication(iPr_def_17,X0),multiplication(iPr_def_18,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_952,c_705,c_932]) ).
tcf(c_970,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_14,iPr_def_15),
inference(light_normalisation,[status(thm)],[c_694,c_701]) ).
tcf(c_973,plain,
! [X0: $i] : addition(multiplication(iPr_def_14,X0),multiplication(iPr_def_15,X0)) = multiplication(addition(iPr_def_10,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_970,c_51]) ).
tcf(c_978,plain,
! [X0: $i] : addition(multiplication(iPr_def_14,X0),multiplication(iPr_def_15,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_973,c_705,c_932]) ).
tcf(c_982,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),multiplication(X0,iPr_def_14)) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_702,c_52]) ).
tcf(c_985,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),multiplication(X0,iPr_def_14)) = X0,
inference(light_normalisation,[status(thm)],[c_982,c_706,c_904]) ).
tcf(c_1113,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_18,iPr_def_10),
inference(superposition,[status(thm)],[c_892,c_305]) ).
tcf(c_1211,plain,
! [X0: $i] : multiplication(iPr_def_11,multiplication(iPr_def_10,X0)) = multiplication(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_267,c_61]) ).
tcf(c_1214,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_11,iPr_def_21),
inference(superposition,[status(thm)],[c_143,c_1211]) ).
tcf(c_1245,plain,
addition(iPr_def_11,antidomain(iPr_def_18)) = addition(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_872,c_53]) ).
tcf(c_1248,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(antidomain(iPr_def_18),X0)) = multiplication(addition(iPr_def_10,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_1245,c_51]) ).
tcf(c_1253,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(antidomain(iPr_def_18),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1248,c_705,c_932]) ).
tcf(c_1508,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_18,iPr_def_21)) = multiplication(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_1214,c_305]) ).
tcf(c_1540,plain,
addition(iPr_def_12,addition(iPr_def_10,iPr_def_11)) = addition(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_701,c_295]) ).
tcf(c_1594,plain,
addition(iPr_def_10,addition(iPr_def_11,iPr_def_12)) = addition(iPr_def_10,iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_1540,c_54,c_55]) ).
tcf(c_1742,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_18,iPr_def_21),
inference(demodulation,[status(thm)],[c_1508,c_892]) ).
tcf(c_2174,plain,
addition(multiplication(iPr_def_17,iPr_def_10),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_1113,c_965]) ).
tcf(c_2176,plain,
addition(multiplication(iPr_def_17,iPr_def_21),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_21,
inference(superposition,[status(thm)],[c_1742,c_965]) ).
tcf(c_2189,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_17,iPr_def_21)) = iPr_def_21,
inference(theory_normalisation,[status(thm)],[c_2176,c_54,c_55]) ).
tcf(c_2190,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_17,iPr_def_10)) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_2174,c_54,c_55]) ).
tcf(c_2403,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_15,iPr_def_13)) = iPr_def_13,
inference(superposition,[status(thm)],[c_485,c_978]) ).
tcf(c_2437,plain,
addition(multiplication(iPr_def_15,iPr_def_13),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_15,
inference(superposition,[status(thm)],[c_491,c_985]) ).
tcf(c_2448,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_15,iPr_def_13)) = iPr_def_15,
inference(theory_normalisation,[status(thm)],[c_2437,c_54,c_55]) ).
tcf(c_2449,plain,
iPr_def_13 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_2448,c_2403]) ).
tcf(c_2466,plain,
multiplication(sK0,iPr_def_13) = iPr_def_16,
inference(demodulation,[status(thm)],[c_138,c_2449]) ).
tcf(c_2468,plain,
iPr_def_16 = iPr_def_20,
inference(demodulation,[status(thm)],[c_142,c_2466]) ).
tcf(c_2474,plain,
multiplication(iPr_def_10,iPr_def_16) = iPr_def_21,
inference(demodulation,[status(thm)],[c_143,c_2468]) ).
tcf(c_2970,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),X0) = X0,
inference(superposition,[status(thm)],[c_1253,c_295]) ).
tcf(c_2979,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_11,X0)) = X0,
inference(theory_normalisation,[status(thm)],[c_2970,c_54,c_55]) ).
tcf(c_3796,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(iPr_def_17,X0)) = addition(multiplication(iPr_def_11,X0),X0),
inference(superposition,[status(thm)],[c_965,c_332]) ).
tcf(c_3830,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(iPr_def_17,X0)) = addition(X0,multiplication(iPr_def_11,X0)),
inference(theory_normalisation,[status(thm)],[c_3796,c_54,c_55]) ).
tcf(c_3831,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(iPr_def_17,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3830,c_2979]) ).
tcf(c_4115,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,addition(iPr_def_11,iPr_def_12))) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_1594,c_52]) ).
tcf(c_4118,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,addition(iPr_def_11,iPr_def_12))) = X0,
inference(light_normalisation,[status(thm)],[c_4115,c_706,c_904]) ).
tcf(c_6590,plain,
multiplication(iPr_def_17,iPr_def_21) = iPr_def_21,
inference(demodulation,[status(thm)],[c_2189,c_892]) ).
tcf(c_6600,plain,
multiplication(iPr_def_17,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_2190,c_892]) ).
tcf(c_10255,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_12))) = X0,
inference(demodulation,[status(thm)],[c_4118,c_52]) ).
tcf(c_10275,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),X0) = X0,
inference(superposition,[status(thm)],[c_10255,c_295]) ).
tcf(c_10291,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_10)) = X0,
inference(theory_normalisation,[status(thm)],[c_10275,c_54,c_55]) ).
tcf(c_10371,plain,
addition(iPr_def_17,iPr_def_10) = iPr_def_17,
inference(superposition,[status(thm)],[c_6600,c_10291]) ).
tcf(c_10410,plain,
addition(iPr_def_10,iPr_def_17) = iPr_def_17,
inference(theory_normalisation,[status(thm)],[c_10371,c_54,c_55]) ).
tcf(c_10445,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_17,X0)) = multiplication(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_10410,c_51]) ).
tcf(c_16314,plain,
addition(iPr_def_21,multiplication(iPr_def_17,iPr_def_16)) = multiplication(iPr_def_17,iPr_def_16),
inference(superposition,[status(thm)],[c_2474,c_10445]) ).
tcf(c_16341,plain,
addition(iPr_def_21,multiplication(iPr_def_11,iPr_def_10)) = multiplication(iPr_def_11,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_16314,c_497]) ).
tcf(c_23368,plain,
addition(multiplication(iPr_def_11,iPr_def_21),iPr_def_21) = iPr_def_21,
inference(superposition,[status(thm)],[c_6590,c_3831]) ).
tcf(c_23399,plain,
addition(iPr_def_21,multiplication(iPr_def_11,iPr_def_21)) = iPr_def_21,
inference(theory_normalisation,[status(thm)],[c_23368,c_54,c_55]) ).
tcf(c_23400,plain,
multiplication(iPr_def_11,iPr_def_10) = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_23399,c_1214,c_16341]) ).
tcf(c_23401,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_23400,c_268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE099+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 18:54:08 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 1.33/1.76 % SZS status Started for theBenchmark.p
% 1.33/1.76 % SZS status Theorem for theBenchmark.p
% 1.33/1.76
% 1.33/1.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.33/1.76
% 1.33/1.76 % ------ iProver source info
% 1.33/1.76
% 1.33/1.76 % git: date: 2026-07-19 20:42:38 +0200
% 1.33/1.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.33/1.76 % git: non_committed_changes: false
% 1.33/1.76
% 1.33/1.76 % ------ Parsing...
% 1.33/1.76 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 1.33/1.76 %
% 1.33/1.76
% 1.33/1.76 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.33/1.76
% 1.33/1.76 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 1.33/1.76 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.33/1.76
% 1.33/1.76 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.33/1.76 % ------ Proving...
% 1.33/1.76 % ------ Problem Properties
% 1.33/1.76
% 1.33/1.76 %
% 1.33/1.76 % clauses 31
% 1.33/1.76 % conjectures 2
% 1.33/1.76 % EPR 2
% 1.33/1.76 % Horn 31
% 1.33/1.76 % unary 31
% 1.33/1.76 % binary 0
% 1.33/1.76 % lits 31
% 1.33/1.76 % lits eq 31
% 1.33/1.76 % fd_pure 0
% 1.33/1.76 % fd_pseudo 0
% 1.33/1.76 % fd_cond 0
% 1.33/1.76 % fd_pseudo_cond 0
% 1.33/1.76 % AC symbols 1
% 1.33/1.76
% 1.33/1.76 % ------ Schedule UEQ
% 1.33/1.76
% 1.33/1.76 % ------ Option_UEQ Time Limit: 10.
% 1.33/1.76
% 1.33/1.76
% 1.33/1.76 % ------
% 1.33/1.76 % Current options:
% 1.33/1.76 % ------
% 1.33/1.76
% 1.33/1.76
% 1.33/1.76 %
% 1.33/1.76
% 1.33/1.76 % ------ Proving...
% 1.33/1.76 %
% 1.33/1.76
% 1.33/1.76 % SZS status Theorem for theBenchmark.p
% 1.33/1.76
% 1.33/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.33/1.76
% 1.33/1.76
%------------------------------------------------------------------------------