%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE088+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 : n004.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 01:52:22 PM UTC 2026
% Result : Theorem 6.24s 2.18s
% Output : CNFRefutation 6.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 22
% Syntax : Number of formulae : 138 ( 134 unt; 5 def)
% Number of atoms : 338 ( 141 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 13 ( 9 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 136 ( 0 sgn 134 !; 2 ?; 78 :)
% 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(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(f21,conjecture,
! [X0,X1] :
( multiplication(domain(X0),X1) = zero
=> addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
~ ! [X0,X1] :
( multiplication(domain(X0),X1) = zero
=> addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0,X1] :
( multiplication(domain(X0),X1) = zero
& antidomain(X1) != addition(domain(X0),antidomain(X1)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
( zero = multiplication(domain(sK0),sK1)
& antidomain(sK1) != addition(domain(sK0),antidomain(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f23]) ).
fof(f25,plain,
zero = multiplication(domain(sK0),sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f26,plain,
antidomain(sK1) != addition(domain(sK0),antidomain(sK1)),
inference(cnf_transformation,[],[f24]) ).
fof(f27,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f28,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f29,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f34,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f36,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f37,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f38,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f39,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(f40,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f41,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f44,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f45,plain,
antidomain(sK1) != addition(antidomain(antidomain(sK0)),antidomain(sK1)),
inference(definition_unfolding,[],[f26,f40]) ).
fof(f46,plain,
zero = multiplication(antidomain(antidomain(sK0)),sK1),
inference(definition_unfolding,[],[f25,f40]) ).
tcf(c_49,negated_conjecture,
addition(antidomain(antidomain(sK0)),antidomain(sK1)) != antidomain(sK1),
inference(cnf_transformation,[],[f45]) ).
tcf(c_50,negated_conjecture,
multiplication(antidomain(antidomain(sK0)),sK1) = zero,
inference(cnf_transformation,[],[f46]) ).
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,[],[f27]) ).
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,[],[f28]) ).
tcf(c_53,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f29]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_56,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[],[f32]) ).
tcf(c_57,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f33]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f34]) ).
tcf(c_60,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
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,X1: $i] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(cnf_transformation,[],[f39]) ).
tcf(c_64,plain,
! [X0: $i] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[],[f41]) ).
tcf(c_66,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f43]) ).
tcf(c_67,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f44]) ).
tcf(c_83,negated_conjecture,
addition(antidomain(sK1),antidomain(antidomain(sK0))) != antidomain(sK1),
inference(theory_normalisation,[status(thm)],[c_49,c_54,c_55]) ).
tcf(c_84,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_54,c_55]) ).
tcf(c_85,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_64,c_54,c_55]) ).
tcf(c_132,definition,
iPr_def_10 = antidomain(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_133,definition,
iPr_def_11 = antidomain(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_134,definition,
iPr_def_12 = antidomain(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_135,definition,
iPr_def_13 = addition(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_136,definition,
iPr_def_14 = multiplication(iPr_def_12,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_137,negated_conjecture,
iPr_def_13 != iPr_def_10,
inference(demodulation,[status(thm)],[c_83,c_133,c_134,c_132,c_135]) ).
tcf(c_138,negated_conjecture,
iPr_def_14 = zero,
inference(demodulation,[status(thm)],[c_50,c_136]) ).
tcf(c_226,plain,
! [X0: $i] : multiplication(iPr_def_14,X0) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_58,c_138]) ).
tcf(c_231,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_132,c_84]) ).
tcf(c_232,plain,
addition(iPr_def_11,antidomain(iPr_def_11)) = one,
inference(superposition,[status(thm)],[c_133,c_84]) ).
tcf(c_233,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_134,c_84]) ).
tcf(c_234,plain,
addition(iPr_def_11,iPr_def_12) = one,
inference(light_normalisation,[status(thm)],[c_232,c_134]) ).
tcf(c_235,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = addition(iPr_def_11,iPr_def_12),
inference(demodulation,[status(thm)],[c_84,c_234]) ).
tcf(c_236,plain,
! [X0: $i] : addition(X0,iPr_def_14) = X0,
inference(light_normalisation,[status(thm)],[c_60,c_138]) ).
tcf(c_237,plain,
! [X0: $i] : multiplication(addition(iPr_def_11,iPr_def_12),X0) = X0,
inference(light_normalisation,[status(thm)],[c_66,c_234]) ).
tcf(c_238,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(iPr_def_12,X0)) = X0,
inference(demodulation,[status(thm)],[c_237,c_51]) ).
tcf(c_242,plain,
! [X0: $i] : multiplication(X0,addition(iPr_def_11,iPr_def_12)) = X0,
inference(light_normalisation,[status(thm)],[c_67,c_234]) ).
tcf(c_243,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_12)) = X0,
inference(demodulation,[status(thm)],[c_242,c_52]) ).
tcf(c_249,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_56,c_138]) ).
tcf(c_253,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_57,c_138]) ).
tcf(c_257,plain,
addition(iPr_def_14,multiplication(antidomain(iPr_def_11),iPr_def_12)) = antidomain(iPr_def_11),
inference(superposition,[status(thm)],[c_253,c_243]) ).
tcf(c_260,plain,
addition(iPr_def_14,multiplication(iPr_def_12,iPr_def_12)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_257,c_134]) ).
tcf(c_265,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = addition(iPr_def_11,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_85,c_234]) ).
tcf(c_266,plain,
! [X0: $i] : addition(iPr_def_14,X0) = X0,
inference(superposition,[status(thm)],[c_236,c_55]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i] : addition(multiplication(iPr_def_11,X0),addition(multiplication(iPr_def_12,X0),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_238,c_54]) ).
tcf(c_278,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,iPr_def_11),addition(multiplication(X0,iPr_def_12),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_243,c_54]) ).
tcf(c_286,plain,
! [X0: $i] : multiplication(iPr_def_12,multiplication(sK1,X0)) = multiplication(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_136,c_61]) ).
tcf(c_299,plain,
! [X0: $i] : multiplication(iPr_def_12,multiplication(sK1,X0)) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_286,c_226]) ).
tcf(c_329,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = addition(iPr_def_11,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_231,c_234]) ).
tcf(c_331,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(antidomain(iPr_def_10),X0)) = multiplication(addition(iPr_def_11,iPr_def_12),X0),
inference(superposition,[status(thm)],[c_329,c_51]) ).
tcf(c_333,plain,
addition(iPr_def_12,antidomain(iPr_def_12)) = addition(iPr_def_11,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_233,c_234]) ).
tcf(c_335,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(antidomain(iPr_def_12),X0)) = multiplication(addition(iPr_def_11,iPr_def_12),X0),
inference(superposition,[status(thm)],[c_333,c_51]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,coantidomain(X1)),multiplication(X0,coantidomain(coantidomain(X1)))) = multiplication(X0,addition(iPr_def_11,iPr_def_12)),
inference(superposition,[status(thm)],[c_265,c_52]) ).
tcf(c_415,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,antidomain(iPr_def_10))) = multiplication(X0,addition(iPr_def_11,iPr_def_12)),
inference(superposition,[status(thm)],[c_329,c_52]) ).
tcf(c_420,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,multiplication(X1,iPr_def_11)),multiplication(X0,multiplication(X1,iPr_def_12))) = multiplication(X0,X1),
inference(superposition,[status(thm)],[c_243,c_52]) ).
tcf(c_423,plain,
! [X0: $i,X1: $i] : addition(multiplication(antidomain(addition(X0,X1)),X0),multiplication(antidomain(addition(X0,X1)),X1)) = iPr_def_14,
inference(superposition,[status(thm)],[c_52,c_253]) ).
tcf(c_451,plain,
! [X0: $i] : addition(antidomain(iPr_def_14),antidomain(multiplication(iPr_def_12,antidomain(antidomain(multiplication(sK1,X0)))))) = antidomain(multiplication(iPr_def_12,antidomain(antidomain(multiplication(sK1,X0))))),
inference(superposition,[status(thm)],[c_299,c_63]) ).
tcf(c_506,plain,
multiplication(iPr_def_12,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_260,c_266]) ).
tcf(c_768,plain,
! [X0: $i] : addition(antidomain(X0),addition(iPr_def_11,iPr_def_12)) = addition(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_235,c_273]) ).
tcf(c_790,plain,
! [X0: $i] : addition(iPr_def_11,addition(iPr_def_12,antidomain(X0))) = addition(iPr_def_11,iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_768,c_54,c_55]) ).
tcf(c_896,plain,
antidomain(addition(iPr_def_11,iPr_def_12)) = iPr_def_14,
inference(superposition,[status(thm)],[c_423,c_243]) ).
tcf(c_1035,plain,
addition(iPr_def_14,antidomain(iPr_def_14)) = addition(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_896,c_235]) ).
tcf(c_1317,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,X0),multiplication(iPr_def_12,X0)) = addition(X0,multiplication(iPr_def_12,X0)),
inference(superposition,[status(thm)],[c_53,c_277]) ).
tcf(c_1369,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_12,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1317,c_238]) ).
tcf(c_1793,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_12)) = addition(X0,multiplication(iPr_def_12,multiplication(X0,iPr_def_12))),
inference(superposition,[status(thm)],[c_1369,c_278]) ).
tcf(c_1824,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_12,multiplication(X0,iPr_def_12))) = X0,
inference(light_normalisation,[status(thm)],[c_1793,c_243]) ).
tcf(c_2246,plain,
addition(iPr_def_11,iPr_def_12) = antidomain(iPr_def_14),
inference(demodulation,[status(thm)],[c_1035,c_266]) ).
tcf(c_6435,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(antidomain(iPr_def_10),X0)) = X0,
inference(demodulation,[status(thm)],[c_331,c_51,c_238]) ).
tcf(c_6470,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),X0) = X0,
inference(superposition,[status(thm)],[c_6435,c_273]) ).
tcf(c_6484,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_10,X0)) = X0,
inference(theory_normalisation,[status(thm)],[c_6470,c_54,c_55]) ).
tcf(c_7005,plain,
! [X0: $i] : addition(multiplication(antidomain(X0),X0),multiplication(antidomain(X0),multiplication(iPr_def_10,X0))) = iPr_def_14,
inference(superposition,[status(thm)],[c_6484,c_423]) ).
tcf(c_7040,plain,
! [X0: $i] : addition(iPr_def_14,multiplication(antidomain(X0),multiplication(iPr_def_10,X0))) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_7005,c_253]) ).
tcf(c_7050,plain,
! [X0: $i] : multiplication(antidomain(X0),multiplication(iPr_def_10,X0)) = iPr_def_14,
inference(demodulation,[status(thm)],[c_7040,c_266]) ).
tcf(c_7053,plain,
multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_11)) = iPr_def_14,
inference(superposition,[status(thm)],[c_134,c_7050]) ).
tcf(c_7255,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(antidomain(iPr_def_12),X0)) = X0,
inference(demodulation,[status(thm)],[c_335,c_51,c_238]) ).
tcf(c_7302,plain,
addition(multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_12)),iPr_def_14) = multiplication(iPr_def_10,iPr_def_12),
inference(superposition,[status(thm)],[c_7050,c_7255]) ).
tcf(c_7334,plain,
addition(iPr_def_14,multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_12))) = multiplication(iPr_def_10,iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_7302,c_54,c_55]) ).
tcf(c_14273,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,coantidomain(X1)),multiplication(X0,coantidomain(coantidomain(X1)))) = X0,
inference(demodulation,[status(thm)],[c_412,c_52,c_243]) ).
tcf(c_14276,plain,
! [X0: $i] : addition(iPr_def_14,multiplication(X0,coantidomain(coantidomain(X0)))) = X0,
inference(superposition,[status(thm)],[c_249,c_14273]) ).
tcf(c_14350,plain,
! [X0: $i] : multiplication(X0,coantidomain(coantidomain(X0))) = X0,
inference(demodulation,[status(thm)],[c_14276,c_266]) ).
tcf(c_17128,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,antidomain(iPr_def_10))) = X0,
inference(demodulation,[status(thm)],[c_415,c_52,c_243]) ).
tcf(c_21192,plain,
addition(iPr_def_14,multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_12))) = multiplication(iPr_def_12,iPr_def_10),
inference(superposition,[status(thm)],[c_7053,c_420]) ).
tcf(c_21310,plain,
multiplication(iPr_def_10,iPr_def_12) = multiplication(iPr_def_12,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_21192,c_7334]) ).
tcf(c_32187,plain,
! [X0: $i] : addition(addition(iPr_def_11,iPr_def_12),antidomain(multiplication(iPr_def_12,antidomain(antidomain(multiplication(sK1,X0)))))) = antidomain(multiplication(iPr_def_12,antidomain(antidomain(multiplication(sK1,X0))))),
inference(light_normalisation,[status(thm)],[c_451,c_2246]) ).
tcf(c_32188,plain,
! [X0: $i] : antidomain(multiplication(iPr_def_12,antidomain(antidomain(multiplication(sK1,X0))))) = addition(iPr_def_11,iPr_def_12),
inference(demodulation,[status(thm)],[c_32187,c_54,c_790]) ).
tcf(c_32258,plain,
! [X0: $i] : multiplication(addition(iPr_def_11,iPr_def_12),multiplication(iPr_def_12,antidomain(antidomain(multiplication(sK1,X0))))) = iPr_def_14,
inference(superposition,[status(thm)],[c_32188,c_253]) ).
tcf(c_33056,plain,
! [X0: $i] : multiplication(iPr_def_12,antidomain(antidomain(multiplication(sK1,X0)))) = iPr_def_14,
inference(demodulation,[status(thm)],[c_32258,c_51,c_238]) ).
tcf(c_33074,plain,
multiplication(iPr_def_12,antidomain(antidomain(sK1))) = iPr_def_14,
inference(superposition,[status(thm)],[c_14350,c_33056]) ).
tcf(c_33153,plain,
multiplication(iPr_def_12,antidomain(iPr_def_10)) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_33074,c_132]) ).
tcf(c_33718,plain,
addition(multiplication(iPr_def_12,iPr_def_10),iPr_def_14) = iPr_def_12,
inference(superposition,[status(thm)],[c_33153,c_17128]) ).
tcf(c_33719,plain,
addition(iPr_def_14,multiplication(iPr_def_12,iPr_def_10)) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_33718,c_54,c_55]) ).
tcf(c_33720,plain,
addition(iPr_def_14,multiplication(iPr_def_10,iPr_def_12)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_33719,c_21310]) ).
tcf(c_33737,plain,
multiplication(iPr_def_10,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_33720,c_266]) ).
tcf(c_33760,plain,
addition(iPr_def_10,multiplication(iPr_def_12,iPr_def_12)) = iPr_def_10,
inference(superposition,[status(thm)],[c_33737,c_1824]) ).
tcf(c_33776,plain,
iPr_def_10 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_33760,c_135,c_506]) ).
tcf(c_33829,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_137,c_33776]) ).
tcf(c_33830,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_33829]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE088+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 18:53:35 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 6.24/2.18 % SZS status Started for theBenchmark.p
% 6.24/2.18 % SZS status Theorem for theBenchmark.p
% 6.24/2.18
% 6.24/2.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.24/2.18
% 6.24/2.18 % ------ iProver source info
% 6.24/2.18
% 6.24/2.18 % git: date: 2026-07-19 20:42:38 +0200
% 6.24/2.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.24/2.18 % git: non_committed_changes: false
% 6.24/2.18
% 6.24/2.18 % ------ Parsing...
% 6.24/2.18 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 6.24/2.18 %
% 6.24/2.18
% 6.24/2.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 6.24/2.18
% 6.24/2.18 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 6.24/2.18 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.24/2.18
% 6.24/2.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 6.24/2.18 % ------ Proving...
% 6.24/2.18 % ------ Problem Properties
% 6.24/2.18
% 6.24/2.18 %
% 6.24/2.18 % clauses 24
% 6.24/2.18 % conjectures 2
% 6.24/2.18 % EPR 2
% 6.24/2.18 % Horn 24
% 6.24/2.18 % unary 24
% 6.24/2.18 % binary 0
% 6.24/2.18 % lits 24
% 6.24/2.18 % lits eq 24
% 6.24/2.18 % fd_pure 0
% 6.24/2.18 % fd_pseudo 0
% 6.24/2.18 % fd_cond 0
% 6.24/2.18 % fd_pseudo_cond 0
% 6.24/2.18 % AC symbols 1
% 6.24/2.18
% 6.24/2.18 % ------ Schedule UEQ
% 6.24/2.18
% 6.24/2.18 % ------ Option_UEQ Time Limit: 10.
% 6.24/2.18
% 6.24/2.18
% 6.24/2.18 % ------
% 6.24/2.18 % Current options:
% 6.24/2.18 % ------
% 6.24/2.18
% 6.24/2.18
% 6.24/2.18 %
% 6.24/2.18
% 6.24/2.18 % ------ Proving...
% 6.24/2.18 %
% 6.24/2.18
% 6.24/2.18 % SZS status Theorem for theBenchmark.p
% 6.24/2.18
% 6.24/2.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.24/2.18
% 6.24/2.18
%------------------------------------------------------------------------------