%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE084+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 58.77s 12.93s
% Output : CNFRefutation 58.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 26
% Syntax : Number of formulae : 148 ( 148 unt; 8 def)
% Number of atoms : 302 ( 147 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn 136 !; 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(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(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] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
~ ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0,X1] : domain(multiplication(X0,X1)) != domain(multiplication(X0,domain(X1))),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
domain(multiplication(sK0,sK1)) != domain(multiplication(sK0,domain(sK1))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f23]) ).
fof(f25,plain,
domain(multiplication(sK0,sK1)) != domain(multiplication(sK0,domain(sK1))),
inference(cnf_transformation,[],[f24]) ).
fof(f26,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f28,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f29,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f31,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f33,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f34,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(f35,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f36,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f38,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f39,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f41,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f42,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f44,plain,
antidomain(antidomain(multiplication(sK0,sK1))) != antidomain(antidomain(multiplication(sK0,antidomain(antidomain(sK1))))),
inference(definition_unfolding,[],[f25,f29,f29,f29]) ).
tcf(c_49,negated_conjecture,
antidomain(antidomain(multiplication(sK0,antidomain(antidomain(sK1))))) != antidomain(antidomain(multiplication(sK0,sK1))),
inference(cnf_transformation,[],[f44]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f26]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_53,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f31]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f32]) ).
tcf(c_56,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f33]) ).
tcf(c_57,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,[],[f34]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f35]) ).
tcf(c_59,plain,
! [X0: $i] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[],[f36]) ).
tcf(c_60,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f37]) ).
tcf(c_61,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f38]) ).
tcf(c_62,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[],[f39]) ).
tcf(c_63,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f40]) ).
tcf(c_64,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f41]) ).
tcf(c_65,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f42]) ).
tcf(c_82,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_56,c_54,c_55]) ).
tcf(c_83,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_59,c_54,c_55]) ).
tcf(c_128,definition,
iPr_def_10 = antidomain(sK1),
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 = multiplication(sK0,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,sK1),
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,negated_conjecture,
iPr_def_14 != iPr_def_17,
inference(demodulation,[status(thm)],[c_49,c_133,c_134,c_135,c_128,c_129,c_130,c_131,c_132]) ).
tcf(c_148366,plain,
addition(iPr_def_13,antidomain(iPr_def_13)) = one,
inference(superposition,[status(thm)],[c_131,c_82]) ).
tcf(c_148368,plain,
addition(iPr_def_16,antidomain(iPr_def_16)) = one,
inference(superposition,[status(thm)],[c_134,c_82]) ).
tcf(c_148370,plain,
addition(iPr_def_16,iPr_def_17) = one,
inference(light_normalisation,[status(thm)],[c_148368,c_135]) ).
tcf(c_148371,plain,
addition(iPr_def_13,iPr_def_14) = one,
inference(light_normalisation,[status(thm)],[c_148366,c_132]) ).
tcf(c_148374,plain,
multiplication(iPr_def_10,sK1) = zero,
inference(superposition,[status(thm)],[c_128,c_58]) ).
tcf(c_148376,plain,
multiplication(iPr_def_13,iPr_def_12) = zero,
inference(superposition,[status(thm)],[c_131,c_58]) ).
tcf(c_148380,plain,
antidomain(one) = zero,
inference(superposition,[status(thm)],[c_58,c_61]) ).
tcf(c_148382,plain,
addition(zero,antidomain(zero)) = one,
inference(superposition,[status(thm)],[c_148380,c_82]) ).
tcf(c_148387,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_65,c_55]) ).
tcf(c_148401,plain,
! [X0: $i] : multiplication(sK0,multiplication(iPr_def_11,X0)) = multiplication(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_130,c_52]) ).
tcf(c_148404,plain,
! [X0: $i] : multiplication(iPr_def_13,multiplication(iPr_def_12,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_148376,c_52]) ).
tcf(c_148410,plain,
! [X0: $i] : multiplication(iPr_def_13,multiplication(iPr_def_12,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_148404,c_63]) ).
tcf(c_148423,plain,
antidomain(zero) = one,
inference(demodulation,[status(thm)],[c_148382,c_148387]) ).
tcf(c_148451,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_148468,plain,
! [X0: $i] : multiplication(addition(sK0,X0),sK1) = addition(iPr_def_15,multiplication(X0,sK1)),
inference(superposition,[status(thm)],[c_133,c_50]) ).
tcf(c_148470,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c_58,c_50]) ).
tcf(c_148535,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(superposition,[status(thm)],[c_58,c_51]) ).
tcf(c_148537,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(one,X1)),
inference(superposition,[status(thm)],[c_61,c_51]) ).
tcf(c_148538,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(coantidomain(X0),X1)) = addition(zero,multiplication(X0,X1)),
inference(superposition,[status(thm)],[c_62,c_51]) ).
tcf(c_148540,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(zero,X1)) = addition(zero,multiplication(X0,X1)),
inference(superposition,[status(thm)],[c_64,c_51]) ).
tcf(c_148549,plain,
! [X0: $i,X1: $i] : multiplication(iPr_def_13,addition(multiplication(iPr_def_12,X0),X1)) = addition(zero,multiplication(iPr_def_13,X1)),
inference(superposition,[status(thm)],[c_148410,c_51]) ).
tcf(c_148558,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(X1,zero)) = addition(multiplication(X0,X1),zero),
inference(superposition,[status(thm)],[c_64,c_51]) ).
tcf(c_148582,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(X1,zero)) = addition(zero,multiplication(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_148558,c_54,c_55]) ).
tcf(c_148592,plain,
addition(antidomain(iPr_def_15),antidomain(multiplication(sK0,antidomain(antidomain(sK1))))) = antidomain(multiplication(sK0,antidomain(antidomain(sK1)))),
inference(superposition,[status(thm)],[c_133,c_57]) ).
tcf(c_148644,plain,
addition(iPr_def_16,iPr_def_13) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_148592,c_128,c_129,c_130,c_131,c_134]) ).
tcf(c_148645,plain,
addition(iPr_def_13,iPr_def_16) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_148644,c_54,c_55]) ).
tcf(c_148650,plain,
! [X0: $i] : addition(iPr_def_13,addition(iPr_def_16,X0)) = addition(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_148645,c_54]) ).
tcf(c_149030,plain,
! [X0: $i] : addition(antidomain(X0),one) = one,
inference(superposition,[status(thm)],[c_82,c_148451]) ).
tcf(c_149036,plain,
addition(iPr_def_13,one) = one,
inference(superposition,[status(thm)],[c_148371,c_148451]) ).
tcf(c_149043,plain,
! [X0: $i] : addition(one,antidomain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_149030,c_54,c_55]) ).
tcf(c_149190,plain,
addition(iPr_def_13,one) = addition(iPr_def_13,iPr_def_17),
inference(superposition,[status(thm)],[c_148370,c_148650]) ).
tcf(c_149194,plain,
addition(iPr_def_13,iPr_def_17) = one,
inference(light_normalisation,[status(thm)],[c_149190,c_149036]) ).
tcf(c_150599,plain,
multiplication(addition(sK0,iPr_def_10),sK1) = addition(iPr_def_15,zero),
inference(superposition,[status(thm)],[c_148374,c_148468]) ).
tcf(c_150604,plain,
multiplication(addition(iPr_def_10,sK0),sK1) = addition(iPr_def_15,zero),
inference(theory_normalisation,[status(thm)],[c_150599,c_54,c_55]) ).
tcf(c_150789,plain,
multiplication(addition(iPr_def_10,sK0),sK1) = iPr_def_15,
inference(demodulation,[status(thm)],[c_150604,c_65]) ).
tcf(c_152169,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(demodulation,[status(thm)],[c_148470,c_148387,c_148540]) ).
tcf(c_152172,plain,
! [X0: $i,X1: $i] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(superposition,[status(thm)],[c_55,c_152169]) ).
tcf(c_152176,plain,
! [X0: $i] : multiplication(antidomain(antidomain(X0)),X0) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_82,c_152169]) ).
tcf(c_152180,plain,
! [X0: $i] : multiplication(addition(iPr_def_10,X0),sK1) = multiplication(X0,sK1),
inference(superposition,[status(thm)],[c_128,c_152169]) ).
tcf(c_152186,plain,
! [X0: $i] : multiplication(addition(iPr_def_17,X0),iPr_def_16) = multiplication(X0,iPr_def_16),
inference(superposition,[status(thm)],[c_135,c_152169]) ).
tcf(c_152208,plain,
! [X0: $i] : multiplication(antidomain(antidomain(X0)),X0) = X0,
inference(light_normalisation,[status(thm)],[c_152176,c_60]) ).
tcf(c_152217,plain,
multiplication(sK0,sK1) = iPr_def_15,
inference(demodulation,[status(thm)],[c_150789,c_152180]) ).
tcf(c_152222,plain,
multiplication(antidomain(iPr_def_10),sK1) = sK1,
inference(superposition,[status(thm)],[c_128,c_152208]) ).
tcf(c_152226,plain,
multiplication(antidomain(iPr_def_14),iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_132,c_152208]) ).
tcf(c_152251,plain,
multiplication(iPr_def_11,sK1) = sK1,
inference(light_normalisation,[status(thm)],[c_152222,c_129]) ).
tcf(c_152343,plain,
multiplication(sK0,sK1) = multiplication(iPr_def_12,sK1),
inference(superposition,[status(thm)],[c_152251,c_148401]) ).
tcf(c_152347,plain,
multiplication(iPr_def_12,sK1) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_152343,c_152217]) ).
tcf(c_152365,plain,
multiplication(iPr_def_13,iPr_def_15) = zero,
inference(superposition,[status(thm)],[c_152347,c_148410]) ).
tcf(c_152383,plain,
addition(antidomain(zero),antidomain(multiplication(iPr_def_13,antidomain(antidomain(iPr_def_15))))) = antidomain(multiplication(iPr_def_13,antidomain(antidomain(iPr_def_15)))),
inference(superposition,[status(thm)],[c_152365,c_57]) ).
tcf(c_152400,plain,
addition(one,antidomain(multiplication(iPr_def_13,iPr_def_17))) = antidomain(multiplication(iPr_def_13,iPr_def_17)),
inference(light_normalisation,[status(thm)],[c_152383,c_134,c_135,c_148423]) ).
tcf(c_153293,plain,
! [X0: $i] : multiplication(addition(X0,iPr_def_17),iPr_def_16) = multiplication(X0,iPr_def_16),
inference(superposition,[status(thm)],[c_55,c_152186]) ).
tcf(c_154315,plain,
multiplication(one,iPr_def_16) = multiplication(iPr_def_13,iPr_def_16),
inference(superposition,[status(thm)],[c_149194,c_153293]) ).
tcf(c_154409,plain,
multiplication(iPr_def_13,iPr_def_16) = iPr_def_16,
inference(demodulation,[status(thm)],[c_154315,c_60]) ).
tcf(c_162063,plain,
multiplication(antidomain(iPr_def_14),addition(one,iPr_def_13)) = addition(antidomain(iPr_def_14),iPr_def_13),
inference(superposition,[status(thm)],[c_152226,c_148537]) ).
tcf(c_162285,plain,
multiplication(antidomain(iPr_def_14),addition(iPr_def_13,one)) = addition(iPr_def_13,antidomain(iPr_def_14)),
inference(theory_normalisation,[status(thm)],[c_162063,c_54,c_55]) ).
tcf(c_162286,plain,
multiplication(antidomain(iPr_def_14),one) = addition(iPr_def_13,antidomain(iPr_def_14)),
inference(light_normalisation,[status(thm)],[c_162285,c_149036]) ).
tcf(c_163352,plain,
addition(iPr_def_13,antidomain(iPr_def_14)) = antidomain(iPr_def_14),
inference(demodulation,[status(thm)],[c_162286,c_61]) ).
tcf(c_163361,plain,
multiplication(antidomain(iPr_def_14),iPr_def_14) = multiplication(iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_163352,c_152172]) ).
tcf(c_163370,plain,
multiplication(iPr_def_13,iPr_def_14) = zero,
inference(demodulation,[status(thm)],[c_163361,c_58]) ).
tcf(c_163380,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(iPr_def_14,X0)) = addition(zero,multiplication(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_163370,c_51]) ).
tcf(c_164600,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(demodulation,[status(thm)],[c_148535,c_65,c_148582]) ).
tcf(c_164606,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(iPr_def_12,X0)) = multiplication(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_131,c_164600]) ).
tcf(c_165289,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(coantidomain(X0),X1)) = multiplication(X0,X1),
inference(demodulation,[status(thm)],[c_148538,c_65,c_148582]) ).
tcf(c_165297,plain,
! [X0: $i] : multiplication(X0,coantidomain(coantidomain(X0))) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_83,c_165289]) ).
tcf(c_165408,plain,
! [X0: $i] : multiplication(X0,coantidomain(coantidomain(X0))) = X0,
inference(light_normalisation,[status(thm)],[c_165297,c_61]) ).
tcf(c_168325,plain,
! [X0: $i,X1: $i] : multiplication(iPr_def_13,addition(multiplication(iPr_def_12,X0),X1)) = multiplication(iPr_def_13,addition(iPr_def_14,X1)),
inference(demodulation,[status(thm)],[c_148549,c_163380]) ).
tcf(c_168356,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(iPr_def_12,X0)) = multiplication(iPr_def_13,addition(iPr_def_14,X0)),
inference(superposition,[status(thm)],[c_165408,c_168325]) ).
tcf(c_168392,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(iPr_def_14,X0)) = multiplication(iPr_def_13,X0),
inference(light_normalisation,[status(thm)],[c_168356,c_164606]) ).
tcf(c_180343,plain,
antidomain(multiplication(iPr_def_13,iPr_def_17)) = one,
inference(demodulation,[status(thm)],[c_152400,c_149043]) ).
tcf(c_180359,plain,
multiplication(one,multiplication(iPr_def_13,iPr_def_17)) = zero,
inference(superposition,[status(thm)],[c_180343,c_58]) ).
tcf(c_180381,plain,
multiplication(iPr_def_13,iPr_def_17) = zero,
inference(demodulation,[status(thm)],[c_180359,c_60]) ).
tcf(c_180398,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(iPr_def_17,X0)) = addition(zero,multiplication(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_180381,c_51]) ).
tcf(c_180421,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(iPr_def_17,X0)) = multiplication(iPr_def_13,X0),
inference(light_normalisation,[status(thm)],[c_180398,c_163380,c_168392]) ).
tcf(c_180652,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(X0,iPr_def_17)) = multiplication(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_55,c_180421]) ).
tcf(c_180884,plain,
multiplication(iPr_def_13,one) = multiplication(iPr_def_13,iPr_def_16),
inference(superposition,[status(thm)],[c_148370,c_180652]) ).
tcf(c_180921,plain,
multiplication(iPr_def_13,one) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_180884,c_154409]) ).
tcf(c_181089,plain,
iPr_def_13 = iPr_def_16,
inference(demodulation,[status(thm)],[c_180921,c_61]) ).
tcf(c_181184,plain,
antidomain(iPr_def_13) = iPr_def_17,
inference(demodulation,[status(thm)],[c_135,c_181089]) ).
tcf(c_181186,plain,
iPr_def_14 = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_181184,c_132]) ).
tcf(c_181187,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_181186,c_136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE084+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 18:52:52 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 58.77/12.93 % SZS status Started for theBenchmark.p
% 58.77/12.93 % SZS status Theorem for theBenchmark.p
% 58.77/12.93
% 58.77/12.93 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 58.77/12.93
% 58.77/12.93 % ------ iProver source info
% 58.77/12.93
% 58.77/12.93 % git: date: 2026-07-19 20:42:38 +0200
% 58.77/12.93 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 58.77/12.93 % git: non_committed_changes: false
% 58.77/12.93
% 58.77/12.93 % ------ Parsing...
% 58.77/12.93 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 58.77/12.93 %
% 58.77/12.93
% 58.77/12.93 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 58.77/12.93
% 58.77/12.93 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 58.77/12.93 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 58.77/12.93
% 58.77/12.93 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 58.77/12.93 % ------ Proving...
% 58.77/12.93 % ------ Problem Properties
% 58.77/12.93
% 58.77/12.93 %
% 58.77/12.93 % clauses 26
% 58.77/12.93 % conjectures 1
% 58.77/12.93 % EPR 1
% 58.77/12.93 % Horn 26
% 58.77/12.93 % unary 26
% 58.77/12.93 % binary 0
% 58.77/12.93 % lits 26
% 58.77/12.93 % lits eq 26
% 58.77/12.93 % fd_pure 0
% 58.77/12.93 % fd_pseudo 0
% 58.77/12.93 % fd_cond 0
% 58.77/12.93 % fd_pseudo_cond 0
% 58.77/12.93 % AC symbols 1
% 58.77/12.93
% 58.77/12.93 % ------ Schedule UEQ
% 58.77/12.93
% 58.77/12.93 % ------ Option_UEQ Time Limit: 10.
% 58.77/12.93
% 58.77/12.93
% 58.77/12.93 % ------
% 58.77/12.93 % Current options:
% 58.77/12.93 % ------
% 58.77/12.93
% 58.77/12.93
% 58.77/12.93 %
% 58.77/12.93
% 58.77/12.93 % ------ Proving...
% 58.77/12.93 % Proof_search_loop: time out after: 2682 full_loop iterations
% 58.77/12.93
% 58.77/12.93 % ------ Option_UEQ Time Limit: 15.
% 58.77/12.93
% 58.77/12.93
% 58.77/12.93 % ------
% 58.77/12.93 % Current options:
% 58.77/12.93 % ------
% 58.77/12.93
% 58.77/12.93
% 58.77/12.93 %
% 58.77/12.93
% 58.77/12.93 % ------ Proving...
% 58.77/12.93 %
% 58.77/12.93
% 58.77/12.93 % SZS status Theorem for theBenchmark.p
% 58.77/12.93
% 58.77/12.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 58.77/12.93
% 58.77/12.93
%------------------------------------------------------------------------------