%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE098+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 : n019.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 29.59s 6.70s
% Output : CNFRefutation 29.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 27
% Syntax : Number of formulae : 144 ( 140 unt; 13 def)
% Number of atoms : 400 ( 147 equ)
% Maximal formula atoms : 2 ( 2 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 : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 103 !; 3 ?; 49 :)
% 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(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)
=> addition(multiplication(X0,domain(X1)),multiplication(domain(X2),X0)) = multiplication(domain(X2),X0) ),
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)
=> addition(multiplication(X0,domain(X1)),multiplication(domain(X2),X0)) = multiplication(domain(X2),X0) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1,X2] :
( addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2)
& multiplication(domain(X2),X0) != addition(multiplication(X0,domain(X1)),multiplication(domain(X2),X0)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
( domain(sK2) = addition(forward_diamond(sK0,domain(sK1)),domain(sK2))
& multiplication(domain(sK2),sK0) != addition(multiplication(sK0,domain(sK1)),multiplication(domain(sK2),sK0)) ),
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,
multiplication(domain(sK2),sK0) != addition(multiplication(sK0,domain(sK1)),multiplication(domain(sK2),sK0)),
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(f38,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f43,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f45,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f46,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f50,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f52,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f40,f39,f39]) ).
fof(f53,plain,
multiplication(antidomain(antidomain(sK2)),sK0) != addition(multiplication(sK0,antidomain(antidomain(sK1))),multiplication(antidomain(antidomain(sK2)),sK0)),
inference(definition_unfolding,[],[f32,f39,f39,f39]) ).
fof(f54,plain,
antidomain(antidomain(sK2)) = addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(sK2))),
inference(definition_unfolding,[],[f31,f39,f52,f39,f39]) ).
tcf(c_49,negated_conjecture,
addition(multiplication(sK0,antidomain(antidomain(sK1))),multiplication(antidomain(antidomain(sK2)),sK0)) != multiplication(antidomain(antidomain(sK2)),sK0),
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_56,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f41]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f43]) ).
tcf(c_61,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f45]) ).
tcf(c_62,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f46]) ).
tcf(c_66,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f50]) ).
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_84,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_57,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_11,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_144,definition,
iPr_def_22 = addition(iPr_def_20,iPr_def_21),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_145,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_146,negated_conjecture,
iPr_def_22 != iPr_def_21,
inference(demodulation,[status(thm)],[c_49,c_143,c_142,c_144]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_54,c_55]) ).
tcf(c_256,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_132,c_84]) ).
tcf(c_257,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_134,c_84]) ).
tcf(c_259,plain,
addition(iPr_def_13,antidomain(iPr_def_13)) = one,
inference(superposition,[status(thm)],[c_135,c_84]) ).
tcf(c_260,plain,
addition(iPr_def_14,antidomain(iPr_def_14)) = one,
inference(superposition,[status(thm)],[c_136,c_84]) ).
tcf(c_262,plain,
addition(iPr_def_14,iPr_def_15) = one,
inference(light_normalisation,[status(thm)],[c_260,c_137]) ).
tcf(c_263,plain,
addition(iPr_def_13,iPr_def_14) = one,
inference(light_normalisation,[status(thm)],[c_259,c_136]) ).
tcf(c_264,plain,
addition(iPr_def_12,iPr_def_13) = one,
inference(light_normalisation,[status(thm)],[c_257,c_135]) ).
tcf(c_265,plain,
addition(iPr_def_10,iPr_def_11) = one,
inference(light_normalisation,[status(thm)],[c_256,c_133]) ).
tcf(c_266,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = addition(iPr_def_14,iPr_def_15),
inference(demodulation,[status(thm)],[c_84,c_262]) ).
tcf(c_267,plain,
! [X0: $i] : multiplication(addition(iPr_def_14,iPr_def_15),X0) = X0,
inference(light_normalisation,[status(thm)],[c_61,c_262]) ).
tcf(c_268,plain,
! [X0: $i] : addition(multiplication(iPr_def_14,X0),multiplication(iPr_def_15,X0)) = X0,
inference(demodulation,[status(thm)],[c_267,c_51]) ).
tcf(c_269,plain,
! [X0: $i] : multiplication(X0,addition(iPr_def_14,iPr_def_15)) = X0,
inference(light_normalisation,[status(thm)],[c_62,c_262]) ).
tcf(c_270,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_14),multiplication(X0,iPr_def_15)) = X0,
inference(demodulation,[status(thm)],[c_269,c_52]) ).
tcf(c_277,plain,
addition(multiplication(sK0,iPr_def_14),iPr_def_16) = sK0,
inference(superposition,[status(thm)],[c_138,c_270]) ).
tcf(c_278,plain,
addition(iPr_def_16,multiplication(sK0,iPr_def_14)) = sK0,
inference(theory_normalisation,[status(thm)],[c_277,c_54,c_55]) ).
tcf(c_279,plain,
addition(iPr_def_11,iPr_def_18) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_141,c_145]) ).
tcf(c_280,plain,
addition(iPr_def_13,iPr_def_14) = addition(iPr_def_14,iPr_def_15),
inference(demodulation,[status(thm)],[c_262,c_263]) ).
tcf(c_281,plain,
addition(iPr_def_12,iPr_def_13) = addition(iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_263,c_264]) ).
tcf(c_282,plain,
addition(iPr_def_12,iPr_def_13) = addition(iPr_def_14,iPr_def_15),
inference(demodulation,[status(thm)],[c_280,c_281]) ).
tcf(c_283,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_264,c_265]) ).
tcf(c_284,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_281,c_283]) ).
tcf(c_288,plain,
multiplication(iPr_def_11,iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_133,c_59]) ).
tcf(c_290,plain,
multiplication(iPr_def_14,iPr_def_13) = zero,
inference(superposition,[status(thm)],[c_136,c_59]) ).
tcf(c_291,plain,
multiplication(iPr_def_15,iPr_def_14) = zero,
inference(superposition,[status(thm)],[c_137,c_59]) ).
tcf(c_292,plain,
multiplication(iPr_def_17,iPr_def_16) = zero,
inference(superposition,[status(thm)],[c_139,c_59]) ).
tcf(c_294,plain,
addition(zero,multiplication(antidomain(iPr_def_14),iPr_def_15)) = antidomain(iPr_def_14),
inference(superposition,[status(thm)],[c_59,c_270]) ).
tcf(c_297,plain,
addition(zero,multiplication(iPr_def_15,iPr_def_15)) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_294,c_137]) ).
tcf(c_298,plain,
addition(multiplication(iPr_def_15,iPr_def_15),zero) = iPr_def_15,
inference(theory_normalisation,[status(thm)],[c_297,c_54,c_55]) ).
tcf(c_300,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_11,iPr_def_10)) = X0,
inference(demodulation,[status(thm)],[c_66,c_288]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_460,plain,
! [X0: $i] : multiplication(sK0,multiplication(iPr_def_15,X0)) = multiplication(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_138,c_56]) ).
tcf(c_478,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(iPr_def_18,X0)) = multiplication(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_279,c_51]) ).
tcf(c_481,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_283,c_51]) ).
tcf(c_506,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_283,c_52]) ).
tcf(c_564,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_14,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_290,c_288]) ).
tcf(c_567,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_15,iPr_def_13)) = iPr_def_13,
inference(superposition,[status(thm)],[c_564,c_268]) ).
tcf(c_570,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_15,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_291,c_288]) ).
tcf(c_578,plain,
multiplication(iPr_def_11,iPr_def_10) = multiplication(iPr_def_17,iPr_def_16),
inference(light_normalisation,[status(thm)],[c_292,c_288]) ).
tcf(c_610,plain,
addition(iPr_def_21,multiplication(iPr_def_18,sK0)) = iPr_def_21,
inference(superposition,[status(thm)],[c_143,c_478]) ).
tcf(c_617,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_11,X0),addition(X1,multiplication(iPr_def_18,X0))) = addition(X1,multiplication(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_478,c_249]) ).
tcf(c_865,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = addition(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_266,c_282,c_283]) ).
tcf(c_880,plain,
addition(iPr_def_17,antidomain(iPr_def_17)) = addition(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_139,c_865]) ).
tcf(c_887,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_17,iPr_def_18),
inference(light_normalisation,[status(thm)],[c_880,c_140]) ).
tcf(c_899,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_14,iPr_def_15),
inference(light_normalisation,[status(thm)],[c_282,c_283]) ).
tcf(c_901,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_899,c_51]) ).
tcf(c_903,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_14),multiplication(X0,iPr_def_15)) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_899,c_52]) ).
tcf(c_906,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,iPr_def_13)) = X0,
inference(light_normalisation,[status(thm)],[c_903,c_270,c_506]) ).
tcf(c_907,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_901,c_268,c_481]) ).
tcf(c_911,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_284,c_52]) ).
tcf(c_914,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),multiplication(X0,iPr_def_14)) = X0,
inference(light_normalisation,[status(thm)],[c_911,c_506,c_906]) ).
tcf(c_916,plain,
addition(multiplication(iPr_def_15,iPr_def_15),multiplication(iPr_def_11,iPr_def_10)) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_298,c_288]) ).
tcf(c_917,plain,
multiplication(iPr_def_15,iPr_def_15) = iPr_def_15,
inference(demodulation,[status(thm)],[c_916,c_300]) ).
tcf(c_936,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,iPr_def_10),X0) = X0,
inference(superposition,[status(thm)],[c_300,c_55]) ).
tcf(c_949,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_887,c_51]) ).
tcf(c_964,plain,
! [X0: $i] : addition(multiplication(iPr_def_17,X0),multiplication(iPr_def_18,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_949,c_481,c_907]) ).
tcf(c_1439,plain,
addition(iPr_def_16,sK0) = sK0,
inference(superposition,[status(thm)],[c_278,c_308]) ).
tcf(c_1601,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_16),multiplication(X0,sK0)) = multiplication(X0,sK0),
inference(superposition,[status(thm)],[c_1439,c_52]) ).
tcf(c_1887,plain,
multiplication(sK0,iPr_def_15) = multiplication(iPr_def_16,iPr_def_15),
inference(superposition,[status(thm)],[c_917,c_460]) ).
tcf(c_1895,plain,
multiplication(iPr_def_16,iPr_def_15) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_1887,c_138]) ).
tcf(c_2186,plain,
multiplication(iPr_def_15,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_567,c_936]) ).
tcf(c_2190,plain,
multiplication(sK0,iPr_def_13) = multiplication(iPr_def_16,iPr_def_13),
inference(superposition,[status(thm)],[c_2186,c_460]) ).
tcf(c_2194,plain,
multiplication(iPr_def_16,iPr_def_13) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_2190,c_142]) ).
tcf(c_3190,plain,
addition(iPr_def_13,multiplication(iPr_def_15,iPr_def_14)) = iPr_def_15,
inference(superposition,[status(thm)],[c_2186,c_914]) ).
tcf(c_3211,plain,
addition(iPr_def_13,multiplication(iPr_def_11,iPr_def_10)) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_3190,c_570]) ).
tcf(c_3526,plain,
addition(multiplication(iPr_def_11,iPr_def_10),multiplication(iPr_def_18,iPr_def_16)) = iPr_def_16,
inference(superposition,[status(thm)],[c_578,c_964]) ).
tcf(c_3721,plain,
iPr_def_13 = iPr_def_15,
inference(demodulation,[status(thm)],[c_3211,c_300]) ).
tcf(c_3748,plain,
multiplication(iPr_def_16,iPr_def_13) = iPr_def_16,
inference(demodulation,[status(thm)],[c_1895,c_3721]) ).
tcf(c_3771,plain,
iPr_def_16 = iPr_def_20,
inference(demodulation,[status(thm)],[c_2194,c_3748]) ).
tcf(c_3784,plain,
addition(iPr_def_16,iPr_def_21) = iPr_def_22,
inference(demodulation,[status(thm)],[c_144,c_3771]) ).
tcf(c_8754,plain,
addition(multiplication(iPr_def_11,sK0),multiplication(iPr_def_18,sK0)) = addition(multiplication(iPr_def_18,iPr_def_16),multiplication(iPr_def_11,sK0)),
inference(superposition,[status(thm)],[c_1601,c_617]) ).
tcf(c_8758,plain,
addition(multiplication(iPr_def_18,iPr_def_16),iPr_def_21) = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_8754,c_143,c_610]) ).
tcf(c_8759,plain,
addition(iPr_def_21,multiplication(iPr_def_18,iPr_def_16)) = iPr_def_21,
inference(theory_normalisation,[status(thm)],[c_8758,c_54,c_55]) ).
tcf(c_42448,plain,
multiplication(iPr_def_18,iPr_def_16) = iPr_def_16,
inference(demodulation,[status(thm)],[c_3526,c_936]) ).
tcf(c_42451,plain,
addition(iPr_def_21,iPr_def_16) = iPr_def_21,
inference(demodulation,[status(thm)],[c_8759,c_42448]) ).
tcf(c_42452,plain,
addition(iPr_def_16,iPr_def_21) = iPr_def_21,
inference(theory_normalisation,[status(thm)],[c_42451,c_54,c_55]) ).
tcf(c_42454,plain,
iPr_def_21 = iPr_def_22,
inference(demodulation,[status(thm)],[c_3784,c_42452]) ).
tcf(c_42461,plain,
iPr_def_21 != iPr_def_21,
inference(demodulation,[status(thm)],[c_146,c_42454]) ).
tcf(c_42462,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_42461]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE098+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n019.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 18:56:34 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...
% 29.59/6.70 % SZS status Started for theBenchmark.p
% 29.59/6.70 % SZS status Theorem for theBenchmark.p
% 29.59/6.70
% 29.59/6.70 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 29.59/6.70
% 29.59/6.70 % ------ iProver source info
% 29.59/6.70
% 29.59/6.70 % git: date: 2026-07-19 20:42:38 +0200
% 29.59/6.70 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 29.59/6.70 % git: non_committed_changes: false
% 29.59/6.70
% 29.59/6.70 % ------ Parsing...
% 29.59/6.70 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 29.59/6.70 %
% 29.59/6.70
% 29.59/6.70 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 29.59/6.70
% 29.59/6.70 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 29.59/6.70 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 29.59/6.70
% 29.59/6.70 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 29.59/6.70 % ------ Proving...
% 29.59/6.70 % ------ Problem Properties
% 29.59/6.70
% 29.59/6.70 %
% 29.59/6.70 % clauses 32
% 29.59/6.70 % conjectures 2
% 29.59/6.70 % EPR 2
% 29.59/6.70 % Horn 32
% 29.59/6.70 % unary 32
% 29.59/6.70 % binary 0
% 29.59/6.70 % lits 32
% 29.59/6.70 % lits eq 32
% 29.59/6.70 % fd_pure 0
% 29.59/6.70 % fd_pseudo 0
% 29.59/6.70 % fd_cond 0
% 29.59/6.70 % fd_pseudo_cond 0
% 29.59/6.70 % AC symbols 1
% 29.59/6.70
% 29.59/6.70 % ------ Schedule UEQ
% 29.59/6.70
% 29.59/6.70 % ------ Option_UEQ Time Limit: 10.
% 29.59/6.70
% 29.59/6.70
% 29.59/6.70 % ------
% 29.59/6.70 % Current options:
% 29.59/6.70 % ------
% 29.59/6.70
% 29.59/6.70
% 29.59/6.70 %
% 29.59/6.70
% 29.59/6.70 % ------ Proving...
% 29.59/6.70 %
% 29.59/6.70
% 29.59/6.70 % SZS status Theorem for theBenchmark.p
% 29.59/6.70
% 29.59/6.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 29.59/6.71
% 29.59/6.71
%------------------------------------------------------------------------------