%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE114+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 : n011.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 01:52:26 PM UTC 2026
% Result : Theorem 3.31s 16.41s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 28
% Syntax : Number of formulae : 164 ( 164 unt; 11 def)
% Number of atoms : 473 ( 163 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 14 ( 14 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 12 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 114 !; 1 ?; 53 :)
% 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(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(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
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(f21,axiom,
! [X0] : c(X0) = antidomain(domain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',complement) ).
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(f25,axiom,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_box) ).
fof(f27,conjecture,
! [X0] : forward_box(X0,one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0] : forward_box(X0,one) = one,
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0] : one != forward_box(X0,one),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
one != forward_box(sK0,one),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[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(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(f41,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f42,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
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(f50,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f52,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f54,plain,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
inference(cnf_transformation,[],[f25]) ).
fof(f56,plain,
one != forward_box(sK0,one),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
! [X0] : c(X0) = antidomain(antidomain(antidomain(X0))),
inference(definition_unfolding,[],[f50,f45]) ).
fof(f61,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f52,f45,f45]) ).
fof(f62,plain,
! [X0,X1] : forward_box(X0,X1) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X0,antidomain(antidomain(antidomain(antidomain(antidomain(X1))))))))))),
inference(definition_unfolding,[],[f54,f57,f61,f57]) ).
fof(f63,plain,
one != antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(one))))))))))),
inference(definition_unfolding,[],[f56,f62]) ).
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_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_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f41]) ).
tcf(c_60,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f42]) ).
tcf(c_62,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f44]) ).
tcf(c_66,negated_conjecture,
antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(antidomain(one))))))))))) != one,
inference(cnf_transformation,[],[f63]) ).
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_128,definition,
iPr_def_10 = antidomain(one),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_129,definition,
iPr_def_11 = antidomain(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,definition,
iPr_def_14 = antidomain(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_133,definition,
iPr_def_15 = multiplication(sK0,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_134,definition,
iPr_def_16 = antidomain(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_135,definition,
iPr_def_17 = antidomain(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_136,definition,
iPr_def_18 = antidomain(iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_137,definition,
iPr_def_19 = antidomain(iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_138,definition,
iPr_def_20 = antidomain(iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_139,negated_conjecture,
iPr_def_20 != one,
inference(demodulation,[status(thm)],[c_66,c_128,c_129,c_130,c_131,c_132,c_133,c_134,c_135,c_136,c_137,c_138]) ).
tcf(c_244,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_128,c_82]) ).
tcf(c_245,plain,
addition(iPr_def_11,antidomain(iPr_def_11)) = one,
inference(superposition,[status(thm)],[c_129,c_82]) ).
tcf(c_246,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_130,c_82]) ).
tcf(c_247,plain,
addition(iPr_def_13,antidomain(iPr_def_13)) = one,
inference(superposition,[status(thm)],[c_131,c_82]) ).
tcf(c_249,plain,
addition(iPr_def_16,antidomain(iPr_def_16)) = one,
inference(superposition,[status(thm)],[c_134,c_82]) ).
tcf(c_250,plain,
addition(iPr_def_17,antidomain(iPr_def_17)) = one,
inference(superposition,[status(thm)],[c_135,c_82]) ).
tcf(c_251,plain,
addition(iPr_def_17,iPr_def_18) = one,
inference(light_normalisation,[status(thm)],[c_250,c_136]) ).
tcf(c_252,plain,
addition(iPr_def_16,iPr_def_17) = one,
inference(light_normalisation,[status(thm)],[c_249,c_135]) ).
tcf(c_253,plain,
addition(iPr_def_13,iPr_def_14) = one,
inference(light_normalisation,[status(thm)],[c_247,c_132]) ).
tcf(c_254,plain,
addition(iPr_def_12,iPr_def_13) = one,
inference(light_normalisation,[status(thm)],[c_246,c_131]) ).
tcf(c_255,plain,
addition(iPr_def_11,iPr_def_12) = one,
inference(light_normalisation,[status(thm)],[c_245,c_130]) ).
tcf(c_256,plain,
addition(iPr_def_10,iPr_def_11) = one,
inference(light_normalisation,[status(thm)],[c_244,c_129]) ).
tcf(c_258,plain,
antidomain(addition(iPr_def_17,iPr_def_18)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_128,c_251]) ).
tcf(c_259,plain,
addition(iPr_def_17,iPr_def_18) != iPr_def_20,
inference(demodulation,[status(thm)],[c_139,c_251]) ).
tcf(c_260,plain,
! [X0: $i] : multiplication(X0,addition(iPr_def_17,iPr_def_18)) = X0,
inference(light_normalisation,[status(thm)],[c_54,c_251]) ).
tcf(c_261,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_17),multiplication(X0,iPr_def_18)) = X0,
inference(demodulation,[status(thm)],[c_260,c_56]) ).
tcf(c_262,plain,
! [X0: $i] : multiplication(addition(iPr_def_17,iPr_def_18),X0) = X0,
inference(light_normalisation,[status(thm)],[c_55,c_251]) ).
tcf(c_263,plain,
! [X0: $i] : addition(multiplication(iPr_def_17,X0),multiplication(iPr_def_18,X0)) = X0,
inference(demodulation,[status(thm)],[c_262,c_57]) ).
tcf(c_270,plain,
addition(iPr_def_16,iPr_def_17) = addition(iPr_def_17,iPr_def_18),
inference(demodulation,[status(thm)],[c_251,c_252]) ).
tcf(c_271,plain,
addition(iPr_def_16,iPr_def_17) != iPr_def_20,
inference(demodulation,[status(thm)],[c_259,c_270]) ).
tcf(c_272,plain,
addition(iPr_def_13,iPr_def_14) = addition(iPr_def_16,iPr_def_17),
inference(demodulation,[status(thm)],[c_252,c_253]) ).
tcf(c_273,plain,
addition(iPr_def_13,iPr_def_14) != iPr_def_20,
inference(demodulation,[status(thm)],[c_271,c_272]) ).
tcf(c_274,plain,
addition(iPr_def_13,iPr_def_14) = addition(iPr_def_17,iPr_def_18),
inference(demodulation,[status(thm)],[c_270,c_272]) ).
tcf(c_275,plain,
addition(iPr_def_12,iPr_def_13) = addition(iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_253,c_254]) ).
tcf(c_276,plain,
addition(iPr_def_12,iPr_def_13) != iPr_def_20,
inference(demodulation,[status(thm)],[c_273,c_275]) ).
tcf(c_277,plain,
addition(iPr_def_12,iPr_def_13) = addition(iPr_def_16,iPr_def_17),
inference(demodulation,[status(thm)],[c_272,c_275]) ).
tcf(c_279,plain,
multiplication(iPr_def_11,iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_129,c_60]) ).
tcf(c_284,plain,
multiplication(iPr_def_17,iPr_def_16) = zero,
inference(superposition,[status(thm)],[c_135,c_60]) ).
tcf(c_285,plain,
multiplication(iPr_def_18,iPr_def_17) = zero,
inference(superposition,[status(thm)],[c_136,c_60]) ).
tcf(c_295,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = multiplication(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_60,c_279]) ).
tcf(c_296,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_11,iPr_def_10),X0) = multiplication(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_59,c_279]) ).
tcf(c_297,plain,
! [X0: $i] : multiplication(X0,multiplication(iPr_def_11,iPr_def_10)) = multiplication(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_58,c_279]) ).
tcf(c_298,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_11,iPr_def_10)) = X0,
inference(demodulation,[status(thm)],[c_51,c_279]) ).
tcf(c_312,plain,
addition(iPr_def_11,iPr_def_12) = addition(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_254,c_255]) ).
tcf(c_314,plain,
addition(iPr_def_11,iPr_def_12) = addition(iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_275,c_312]) ).
tcf(c_317,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_11,iPr_def_12),
inference(demodulation,[status(thm)],[c_255,c_256]) ).
tcf(c_318,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_312,c_317]) ).
tcf(c_321,plain,
addition(iPr_def_10,iPr_def_11) != iPr_def_20,
inference(light_normalisation,[status(thm)],[c_276,c_318]) ).
tcf(c_326,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_17,iPr_def_16),
inference(light_normalisation,[status(thm)],[c_284,c_279]) ).
tcf(c_327,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_18,iPr_def_16)) = iPr_def_16,
inference(superposition,[status(thm)],[c_326,c_263]) ).
tcf(c_328,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_18,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_285,c_279]) ).
tcf(c_330,plain,
addition(multiplication(iPr_def_17,iPr_def_17),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_17,
inference(superposition,[status(thm)],[c_328,c_263]) ).
tcf(c_331,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_17,iPr_def_17)) = iPr_def_17,
inference(theory_normalisation,[status(thm)],[c_330,c_50,c_49]) ).
tcf(c_346,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_11,iPr_def_10),X0) = multiplication(iPr_def_18,multiplication(iPr_def_17,X0)),
inference(superposition,[status(thm)],[c_328,c_53]) ).
tcf(c_352,plain,
! [X0: $i] : multiplication(iPr_def_18,multiplication(iPr_def_17,X0)) = multiplication(iPr_def_11,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_346,c_296]) ).
tcf(c_365,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_12)) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_317,c_56]) ).
tcf(c_382,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(iPr_def_12,X0)) = multiplication(addition(iPr_def_10,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_317,c_57]) ).
tcf(c_438,plain,
antidomain(addition(iPr_def_10,iPr_def_11)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_258,c_274,c_314,c_317]) ).
tcf(c_446,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_17,iPr_def_18),
inference(light_normalisation,[status(thm)],[c_274,c_314,c_317]) ).
tcf(c_448,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_17),multiplication(X0,iPr_def_18)) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_446,c_56]) ).
tcf(c_449,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_446,c_57]) ).
tcf(c_451,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(iPr_def_12,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_449,c_263,c_382]) ).
tcf(c_452,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_12)) = X0,
inference(light_normalisation,[status(thm)],[c_448,c_261,c_365]) ).
tcf(c_453,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_16,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_277,c_318]) ).
tcf(c_455,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_16),multiplication(X0,iPr_def_17)) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_453,c_56]) ).
tcf(c_459,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_16),multiplication(X0,iPr_def_17)) = X0,
inference(light_normalisation,[status(thm)],[c_455,c_365,c_452]) ).
tcf(c_482,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,iPr_def_10),X0) = X0,
inference(superposition,[status(thm)],[c_298,c_49]) ).
tcf(c_593,plain,
multiplication(iPr_def_10,addition(iPr_def_10,iPr_def_11)) = multiplication(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_438,c_295]) ).
tcf(c_606,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,addition(iPr_def_10,iPr_def_11)),X0) = X0,
inference(demodulation,[status(thm)],[c_482,c_593]) ).
tcf(c_626,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_10,addition(iPr_def_10,iPr_def_11)),X0) = multiplication(iPr_def_10,addition(iPr_def_10,iPr_def_11)),
inference(light_normalisation,[status(thm)],[c_296,c_593]) ).
tcf(c_627,plain,
! [X0: $i] : multiplication(iPr_def_10,X0) = iPr_def_10,
inference(demodulation,[status(thm)],[c_626,c_53,c_365,c_382,c_451,c_452]) ).
tcf(c_643,plain,
! [X0: $i] : multiplication(X0,multiplication(iPr_def_10,addition(iPr_def_10,iPr_def_11))) = multiplication(iPr_def_10,addition(iPr_def_10,iPr_def_11)),
inference(light_normalisation,[status(thm)],[c_297,c_593]) ).
tcf(c_644,plain,
! [X0: $i] : multiplication(X0,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_643,c_627]) ).
tcf(c_728,plain,
! [X0: $i] : multiplication(iPr_def_18,multiplication(iPr_def_17,X0)) = multiplication(iPr_def_10,addition(iPr_def_10,iPr_def_11)),
inference(light_normalisation,[status(thm)],[c_352,c_593]) ).
tcf(c_729,plain,
! [X0: $i] : multiplication(iPr_def_18,multiplication(iPr_def_17,X0)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_728,c_627]) ).
tcf(c_784,plain,
addition(multiplication(iPr_def_10,addition(iPr_def_10,iPr_def_11)),multiplication(iPr_def_18,iPr_def_16)) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_327,c_593]) ).
tcf(c_785,plain,
multiplication(iPr_def_18,iPr_def_16) = iPr_def_16,
inference(demodulation,[status(thm)],[c_784,c_606]) ).
tcf(c_865,plain,
addition(multiplication(iPr_def_10,addition(iPr_def_10,iPr_def_11)),multiplication(iPr_def_17,iPr_def_17)) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_331,c_593]) ).
tcf(c_866,plain,
multiplication(iPr_def_17,iPr_def_17) = iPr_def_17,
inference(demodulation,[status(thm)],[c_865,c_606]) ).
tcf(c_873,plain,
multiplication(iPr_def_18,iPr_def_17) = iPr_def_10,
inference(superposition,[status(thm)],[c_866,c_729]) ).
tcf(c_1118,plain,
addition(multiplication(iPr_def_18,iPr_def_16),iPr_def_10) = iPr_def_18,
inference(superposition,[status(thm)],[c_873,c_459]) ).
tcf(c_1130,plain,
addition(iPr_def_10,multiplication(iPr_def_18,iPr_def_16)) = iPr_def_18,
inference(theory_normalisation,[status(thm)],[c_1118,c_50,c_49]) ).
tcf(c_1131,plain,
addition(iPr_def_10,iPr_def_16) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_1130,c_785]) ).
tcf(c_1139,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,iPr_def_16)) = multiplication(X0,iPr_def_18),
inference(superposition,[status(thm)],[c_1131,c_56]) ).
tcf(c_1142,plain,
! [X0: $i] : addition(iPr_def_10,multiplication(X0,iPr_def_16)) = multiplication(X0,iPr_def_18),
inference(light_normalisation,[status(thm)],[c_1139,c_644]) ).
tcf(c_1154,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_17),addition(iPr_def_10,multiplication(X0,iPr_def_16))) = X0,
inference(demodulation,[status(thm)],[c_261,c_1142]) ).
tcf(c_1157,plain,
! [X0: $i] : addition(iPr_def_10,addition(multiplication(X0,iPr_def_16),multiplication(X0,iPr_def_17))) = X0,
inference(theory_normalisation,[status(thm)],[c_1154,c_50,c_49]) ).
tcf(c_1158,plain,
! [X0: $i] : addition(iPr_def_10,X0) = X0,
inference(light_normalisation,[status(thm)],[c_1157,c_459]) ).
tcf(c_1166,plain,
antidomain(iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_438,c_1158]) ).
tcf(c_1168,plain,
iPr_def_11 != iPr_def_20,
inference(demodulation,[status(thm)],[c_321,c_1158]) ).
tcf(c_1171,plain,
iPr_def_16 = iPr_def_18,
inference(demodulation,[status(thm)],[c_1131,c_1158]) ).
tcf(c_1173,plain,
antidomain(iPr_def_16) = iPr_def_19,
inference(demodulation,[status(thm)],[c_137,c_1171]) ).
tcf(c_1174,plain,
antidomain(iPr_def_17) = iPr_def_16,
inference(demodulation,[status(thm)],[c_136,c_1171]) ).
tcf(c_1175,plain,
iPr_def_17 = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_1173,c_135]) ).
tcf(c_1184,plain,
antidomain(iPr_def_17) = iPr_def_20,
inference(demodulation,[status(thm)],[c_138,c_1175]) ).
tcf(c_1185,plain,
iPr_def_10 = iPr_def_12,
inference(demodulation,[status(thm)],[c_130,c_1166]) ).
tcf(c_1190,plain,
antidomain(iPr_def_10) = iPr_def_13,
inference(demodulation,[status(thm)],[c_131,c_1185]) ).
tcf(c_1191,plain,
iPr_def_11 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_1190,c_129]) ).
tcf(c_1193,plain,
antidomain(iPr_def_11) = iPr_def_14,
inference(demodulation,[status(thm)],[c_132,c_1191]) ).
tcf(c_1256,plain,
iPr_def_16 = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_1184,c_1174]) ).
tcf(c_1257,plain,
iPr_def_11 != iPr_def_16,
inference(demodulation,[status(thm)],[c_1168,c_1256]) ).
tcf(c_1258,plain,
iPr_def_10 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_1193,c_1166]) ).
tcf(c_1262,plain,
multiplication(sK0,iPr_def_10) = iPr_def_15,
inference(demodulation,[status(thm)],[c_133,c_1258]) ).
tcf(c_1361,plain,
iPr_def_10 = iPr_def_15,
inference(demodulation,[status(thm)],[c_1262,c_644]) ).
tcf(c_1363,plain,
antidomain(iPr_def_10) = iPr_def_16,
inference(demodulation,[status(thm)],[c_134,c_1361]) ).
tcf(c_1364,plain,
iPr_def_11 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_1363,c_129]) ).
tcf(c_1365,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1364,c_1257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE114+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/15.47 % CPULimit : 300
% 0.10/15.47 % WCLimit : 300
% 0.10/15.47 % DateTime : Wed Sep 23 18:59:55 UTC 2026
% 0.10/15.48 % CPUTime :
% 0.10/15.48 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.38/15.52 Running first-order theorem proving
% 0.38/15.52 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
% 0.38/15.53
% 0.38/15.53 % ======== iProver multi-core TPTP/SMT =========
% 0.38/15.53
% 0.38/15.53 % Detected problem language: tptp
% 0.38/15.55 % Proving...
% 3.31/16.41 % SZS status Started for theBenchmark.p
% 3.31/16.41 % SZS status Theorem for theBenchmark.p
% 3.31/16.41
% 3.31/16.41 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.31/16.41
% 3.31/16.41 % ------ iProver source info
% 3.31/16.41
% 3.31/16.41 % git: date: 2026-07-19 20:42:38 +0200
% 3.31/16.41 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.31/16.41 % git: non_committed_changes: false
% 3.31/16.41
% 3.31/16.41 % ------ Parsing...
% 3.31/16.41 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 3.31/16.41 %
% 3.31/16.41
% 3.31/16.41 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.31/16.41
% 3.31/16.41 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.31/16.41 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.31/16.41
% 3.31/16.41 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.31/16.41 % ------ Proving...
% 3.31/16.41 % ------ Problem Properties
% 3.31/16.41
% 3.31/16.41 %
% 3.31/16.41 % clauses 29
% 3.31/16.41 % conjectures 1
% 3.31/16.41 % EPR 1
% 3.31/16.41 % Horn 29
% 3.31/16.41 % unary 29
% 3.31/16.41 % binary 0
% 3.31/16.41 % lits 29
% 3.31/16.41 % lits eq 29
% 3.31/16.41 % fd_pure 0
% 3.31/16.41 % fd_pseudo 0
% 3.31/16.41 % fd_cond 0
% 3.31/16.41 % fd_pseudo_cond 0
% 3.31/16.41 % AC symbols 1
% 3.31/16.41
% 3.31/16.41 % ------ Schedule UEQ
% 3.31/16.41
% 3.31/16.41 % ------ Option_UEQ Time Limit: 10.
% 3.31/16.41
% 3.31/16.41
% 3.31/16.41 % ------
% 3.31/16.41 % Current options:
% 3.31/16.41 % ------
% 3.31/16.41
% 3.31/16.41
% 3.31/16.41 %
% 3.31/16.41
% 3.31/16.41 % ------ Proving...
% 3.31/16.41 %
% 3.31/16.41
% 3.31/16.41 % SZS status Theorem for theBenchmark.p
% 3.31/16.41
% 3.31/16.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.31/16.41
% 3.31/16.41
%------------------------------------------------------------------------------