%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE120+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 01:52:27 PM UTC 2026
% Result : Theorem 68.10s 11.88s
% Output : CNFRefutation 68.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 26
% Syntax : Number of formulae : 201 ( 201 unt; 7 def)
% Number of atoms : 484 ( 200 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 9 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 162 ( 0 sgn 161 !; 1 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(f17,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(f18,axiom,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain2) ).
fof(f19,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(f20,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain4) ).
fof(f24,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).
fof(f27,conjecture,
! [X0] : addition(backward_diamond(one,domain(X0)),domain(X0)) = domain(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0] : addition(backward_diamond(one,domain(X0)),domain(X0)) = domain(X0),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0] : domain(X0) != addition(backward_diamond(one,domain(X0)),domain(X0)),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
domain(sK0) != addition(backward_diamond(one,domain(sK0)),domain(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f29]) ).
fof(f31,plain,
domain(sK0) != addition(backward_diamond(one,domain(sK0)),domain(sK0)),
inference(cnf_transformation,[],[f30]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f33,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f35,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f36,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f37,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f38,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f39,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f40,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f41,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f42,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f44,plain,
! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
inference(cnf_transformation,[],[f18]) ).
fof(f45,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f47,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f48,plain,
! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
inference(cnf_transformation,[],[f20]) ).
fof(f49,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f51,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f52,plain,
! [X0,X1] : backward_diamond(X0,X1) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X1)),X0))),
inference(definition_unfolding,[],[f42,f48,f48]) ).
fof(f53,plain,
antidomain(antidomain(sK0)) != addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK0)))),one))),antidomain(antidomain(sK0))),
inference(definition_unfolding,[],[f31,f41,f52,f41,f41]) ).
tcf(c_49,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK0)))),one))),antidomain(antidomain(sK0))) != antidomain(antidomain(sK0)),
inference(cnf_transformation,[],[f53]) ).
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,[],[f32]) ).
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,[],[f33]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f34]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[],[f37]) ).
tcf(c_56,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f39]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f40]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f43]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
inference(cnf_transformation,[],[f44]) ).
tcf(c_61,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[],[f45]) ).
tcf(c_63,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f47]) ).
tcf(c_64,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f49]) ).
tcf(c_66,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f51]) ).
tcf(c_82,negated_conjecture,
addition(antidomain(antidomain(sK0)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK0)))),one)))) != antidomain(antidomain(sK0)),
inference(theory_normalisation,[status(thm)],[c_49,c_53,c_54]) ).
tcf(c_83,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_55,c_53,c_54]) ).
tcf(c_84,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_56,c_53,c_54]) ).
tcf(c_123,plain,
addition(antidomain(antidomain(sK0)),coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(sK0))))))) != antidomain(antidomain(sK0)),
inference(demodulation,[status(thm)],[c_82,c_58]) ).
tcf(c_130,definition,
iPr_def_10 = antidomain(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_131,definition,
iPr_def_11 = antidomain(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_132,definition,
iPr_def_12 = coantidomain(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_133,definition,
iPr_def_13 = coantidomain(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_134,definition,
iPr_def_14 = coantidomain(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_135,definition,
iPr_def_15 = coantidomain(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_136,definition,
iPr_def_16 = addition(iPr_def_11,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_137,plain,
iPr_def_16 != iPr_def_11,
inference(demodulation,[status(thm)],[c_123,c_132,c_133,c_134,c_135,c_130,c_131,c_136]) ).
tcf(c_156380,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_156385,plain,
addition(iPr_def_12,coantidomain(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_132,c_83]) ).
tcf(c_156386,plain,
addition(iPr_def_13,coantidomain(iPr_def_13)) = one,
inference(superposition,[status(thm)],[c_133,c_83]) ).
tcf(c_156387,plain,
addition(iPr_def_14,coantidomain(iPr_def_14)) = one,
inference(superposition,[status(thm)],[c_134,c_83]) ).
tcf(c_156388,plain,
addition(iPr_def_15,coantidomain(iPr_def_15)) = one,
inference(superposition,[status(thm)],[c_135,c_83]) ).
tcf(c_156389,plain,
addition(iPr_def_14,iPr_def_15) = one,
inference(light_normalisation,[status(thm)],[c_156387,c_135]) ).
tcf(c_156390,plain,
addition(iPr_def_13,iPr_def_14) = one,
inference(light_normalisation,[status(thm)],[c_156386,c_134]) ).
tcf(c_156391,plain,
addition(iPr_def_12,iPr_def_13) = one,
inference(light_normalisation,[status(thm)],[c_156385,c_133]) ).
tcf(c_156394,plain,
multiplication(iPr_def_12,iPr_def_13) = zero,
inference(superposition,[status(thm)],[c_133,c_61]) ).
tcf(c_156395,plain,
multiplication(iPr_def_13,iPr_def_14) = zero,
inference(superposition,[status(thm)],[c_134,c_61]) ).
tcf(c_156396,plain,
multiplication(iPr_def_14,iPr_def_15) = zero,
inference(superposition,[status(thm)],[c_135,c_61]) ).
tcf(c_156397,plain,
coantidomain(one) = zero,
inference(superposition,[status(thm)],[c_61,c_57]) ).
tcf(c_156399,plain,
addition(zero,coantidomain(zero)) = one,
inference(superposition,[status(thm)],[c_156397,c_83]) ).
tcf(c_156402,plain,
multiplication(iPr_def_11,iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_131,c_63]) ).
tcf(c_156406,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_130,c_84]) ).
tcf(c_156407,plain,
addition(iPr_def_11,antidomain(iPr_def_11)) = one,
inference(superposition,[status(thm)],[c_131,c_84]) ).
tcf(c_156408,plain,
addition(iPr_def_10,iPr_def_11) = one,
inference(light_normalisation,[status(thm)],[c_156406,c_131]) ).
tcf(c_156409,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_66,c_54]) ).
tcf(c_156415,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_53]) ).
tcf(c_156419,plain,
! [X0: $i] : addition(iPr_def_11,addition(iPr_def_15,X0)) = addition(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_136,c_53]) ).
tcf(c_156422,plain,
! [X0: $i] : addition(iPr_def_12,addition(iPr_def_13,X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_156391,c_53]) ).
tcf(c_156431,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),multiplication(X0,X1)) = multiplication(zero,X1),
inference(superposition,[status(thm)],[c_63,c_59]) ).
tcf(c_156435,plain,
! [X0: $i] : multiplication(iPr_def_12,multiplication(iPr_def_13,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_156394,c_59]) ).
tcf(c_156439,plain,
! [X0: $i,X1: $i] : multiplication(X0,multiplication(X1,coantidomain(multiplication(X0,X1)))) = zero,
inference(superposition,[status(thm)],[c_59,c_61]) ).
tcf(c_156443,plain,
! [X0: $i] : multiplication(iPr_def_12,multiplication(iPr_def_13,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_156435,c_64]) ).
tcf(c_156448,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c_57,c_50]) ).
tcf(c_156451,plain,
! [X0: $i,X1: $i] : multiplication(addition(X0,X1),coantidomain(X0)) = addition(zero,multiplication(X1,coantidomain(X0))),
inference(superposition,[status(thm)],[c_61,c_50]) ).
tcf(c_156452,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c_63,c_50]) ).
tcf(c_156464,plain,
! [X0: $i,X1: $i] : multiplication(addition(X0,zero),X1) = addition(multiplication(X0,X1),zero),
inference(superposition,[status(thm)],[c_64,c_50]) ).
tcf(c_156481,plain,
! [X0: $i,X1: $i] : multiplication(addition(X0,zero),X1) = addition(zero,multiplication(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_156464,c_53,c_54]) ).
tcf(c_156482,plain,
! [X0: $i,X1: $i] : addition(zero,multiplication(X0,X1)) = multiplication(X0,X1),
inference(light_normalisation,[status(thm)],[c_156481,c_66]) ).
tcf(c_156507,plain,
coantidomain(zero) = one,
inference(demodulation,[status(thm)],[c_156399,c_156409]) ).
tcf(c_156511,plain,
! [X0: $i] : addition(iPr_def_11,addition(antidomain(iPr_def_11),X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_156407,c_53]) ).
tcf(c_156575,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(iPr_def_14,X0)) = addition(zero,multiplication(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_156395,c_51]) ).
tcf(c_156584,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(X1,coantidomain(X0))) = addition(multiplication(X0,X1),zero),
inference(superposition,[status(thm)],[c_61,c_51]) ).
tcf(c_156615,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(X1,coantidomain(X0))) = addition(zero,multiplication(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_156584,c_53,c_54]) ).
tcf(c_156616,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(X1,coantidomain(X0))) = multiplication(X0,X1),
inference(light_normalisation,[status(thm)],[c_156615,c_156482]) ).
tcf(c_156633,plain,
addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(iPr_def_11)),iPr_def_10))) = coantidomain(multiplication(coantidomain(coantidomain(iPr_def_11)),iPr_def_10)),
inference(superposition,[status(thm)],[c_156402,c_60]) ).
tcf(c_156656,plain,
addition(one,coantidomain(multiplication(iPr_def_13,iPr_def_10))) = coantidomain(multiplication(iPr_def_13,iPr_def_10)),
inference(light_normalisation,[status(thm)],[c_156633,c_132,c_133,c_156507]) ).
tcf(c_156793,plain,
! [X0: $i] : addition(coantidomain(X0),one) = one,
inference(superposition,[status(thm)],[c_83,c_156415]) ).
tcf(c_156794,plain,
! [X0: $i] : addition(antidomain(X0),one) = one,
inference(superposition,[status(thm)],[c_84,c_156415]) ).
tcf(c_156795,plain,
addition(iPr_def_11,iPr_def_16) = iPr_def_16,
inference(superposition,[status(thm)],[c_136,c_156415]) ).
tcf(c_156796,plain,
addition(iPr_def_15,one) = one,
inference(superposition,[status(thm)],[c_156388,c_156415]) ).
tcf(c_156797,plain,
addition(iPr_def_14,one) = one,
inference(superposition,[status(thm)],[c_156389,c_156415]) ).
tcf(c_156799,plain,
addition(iPr_def_12,one) = one,
inference(superposition,[status(thm)],[c_156391,c_156415]) ).
tcf(c_156800,plain,
addition(iPr_def_11,one) = one,
inference(superposition,[status(thm)],[c_156407,c_156415]) ).
tcf(c_156804,plain,
! [X0: $i] : addition(one,antidomain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_156794,c_53,c_54]) ).
tcf(c_156805,plain,
! [X0: $i] : addition(one,coantidomain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_156793,c_53,c_54]) ).
tcf(c_156854,plain,
! [X0: $i] : addition(iPr_def_11,addition(X0,iPr_def_15)) = addition(X0,iPr_def_16),
inference(superposition,[status(thm)],[c_136,c_156380]) ).
tcf(c_156862,plain,
! [X0: $i] : addition(iPr_def_11,addition(X0,iPr_def_16)) = addition(X0,iPr_def_16),
inference(superposition,[status(thm)],[c_156795,c_156380]) ).
tcf(c_156914,plain,
addition(iPr_def_11,one) = addition(iPr_def_16,one),
inference(superposition,[status(thm)],[c_156796,c_156419]) ).
tcf(c_156919,plain,
addition(iPr_def_16,one) = one,
inference(light_normalisation,[status(thm)],[c_156914,c_156800]) ).
tcf(c_158657,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),multiplication(X0,X1)) = zero,
inference(demodulation,[status(thm)],[c_156431,c_64]) ).
tcf(c_158798,plain,
! [X0: $i] : multiplication(addition(one,iPr_def_12),multiplication(iPr_def_13,X0)) = addition(multiplication(iPr_def_13,X0),zero),
inference(superposition,[status(thm)],[c_156443,c_156448]) ).
tcf(c_158801,plain,
! [X0: $i,X1: $i] : multiplication(addition(one,antidomain(X0)),multiplication(X0,X1)) = addition(multiplication(X0,X1),zero),
inference(superposition,[status(thm)],[c_158657,c_156448]) ).
tcf(c_158862,plain,
! [X0: $i] : multiplication(addition(iPr_def_12,one),multiplication(iPr_def_13,X0)) = addition(zero,multiplication(iPr_def_13,X0)),
inference(theory_normalisation,[status(thm)],[c_158798,c_53,c_54]) ).
tcf(c_158863,plain,
! [X0: $i] : multiplication(one,multiplication(iPr_def_13,X0)) = multiplication(iPr_def_13,addition(iPr_def_14,X0)),
inference(light_normalisation,[status(thm)],[c_158862,c_156575,c_156799]) ).
tcf(c_158872,plain,
! [X0: $i,X1: $i] : multiplication(addition(one,antidomain(X0)),multiplication(X0,X1)) = addition(zero,multiplication(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_158801,c_53,c_54]) ).
tcf(c_158873,plain,
! [X0: $i,X1: $i] : multiplication(one,multiplication(X0,X1)) = addition(zero,multiplication(X0,X1)),
inference(light_normalisation,[status(thm)],[c_158872,c_156804]) ).
tcf(c_158967,plain,
addition(antidomain(iPr_def_11),iPr_def_16) = addition(one,iPr_def_16),
inference(superposition,[status(thm)],[c_156511,c_156862]) ).
tcf(c_158970,plain,
addition(iPr_def_16,antidomain(iPr_def_11)) = addition(iPr_def_16,one),
inference(theory_normalisation,[status(thm)],[c_158967,c_53,c_54]) ).
tcf(c_158971,plain,
addition(iPr_def_16,antidomain(iPr_def_11)) = one,
inference(light_normalisation,[status(thm)],[c_158970,c_156919]) ).
tcf(c_159007,plain,
! [X0: $i] : multiplication(iPr_def_11,addition(X0,iPr_def_12)) = multiplication(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_132,c_156616]) ).
tcf(c_159008,plain,
! [X0: $i] : multiplication(iPr_def_12,addition(X0,iPr_def_13)) = multiplication(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_133,c_156616]) ).
tcf(c_159009,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(X0,iPr_def_14)) = multiplication(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_134,c_156616]) ).
tcf(c_159010,plain,
! [X0: $i] : multiplication(iPr_def_14,addition(X0,iPr_def_15)) = multiplication(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_135,c_156616]) ).
tcf(c_159044,plain,
! [X0: $i] : multiplication(iPr_def_11,addition(iPr_def_12,X0)) = multiplication(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_54,c_159007]) ).
tcf(c_159065,plain,
! [X0: $i] : multiplication(iPr_def_12,addition(iPr_def_13,X0)) = multiplication(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_54,c_159008]) ).
tcf(c_159088,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(iPr_def_14,X0)) = multiplication(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_54,c_159009]) ).
tcf(c_159092,plain,
multiplication(iPr_def_13,one) = multiplication(iPr_def_13,iPr_def_13),
inference(superposition,[status(thm)],[c_156390,c_159009]) ).
tcf(c_159179,plain,
multiplication(iPr_def_13,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_159092,c_58]) ).
tcf(c_159205,plain,
multiplication(iPr_def_14,one) = multiplication(iPr_def_14,iPr_def_14),
inference(superposition,[status(thm)],[c_156389,c_159010]) ).
tcf(c_159418,plain,
multiplication(iPr_def_11,one) = multiplication(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_156391,c_159044]) ).
tcf(c_159453,plain,
multiplication(iPr_def_12,one) = multiplication(iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_156390,c_159065]) ).
tcf(c_159536,plain,
multiplication(iPr_def_14,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_159205,c_58]) ).
tcf(c_159557,plain,
multiplication(iPr_def_11,iPr_def_13) = iPr_def_11,
inference(demodulation,[status(thm)],[c_159418,c_58]) ).
tcf(c_159563,plain,
addition(coantidomain(iPr_def_11),coantidomain(multiplication(coantidomain(coantidomain(iPr_def_11)),iPr_def_13))) = coantidomain(multiplication(coantidomain(coantidomain(iPr_def_11)),iPr_def_13)),
inference(superposition,[status(thm)],[c_159557,c_60]) ).
tcf(c_159569,plain,
multiplication(addition(one,iPr_def_11),iPr_def_13) = addition(iPr_def_13,iPr_def_11),
inference(superposition,[status(thm)],[c_159557,c_156448]) ).
tcf(c_159571,plain,
multiplication(addition(iPr_def_11,one),iPr_def_13) = addition(iPr_def_11,iPr_def_13),
inference(theory_normalisation,[status(thm)],[c_159569,c_53,c_54]) ).
tcf(c_159572,plain,
multiplication(one,iPr_def_13) = addition(iPr_def_11,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_159571,c_156800]) ).
tcf(c_159576,plain,
addition(iPr_def_12,iPr_def_14) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_159563,c_132,c_133,c_134,c_159179]) ).
tcf(c_159580,plain,
multiplication(iPr_def_13,iPr_def_12) = multiplication(iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_159576,c_159009]) ).
tcf(c_159586,plain,
multiplication(iPr_def_13,iPr_def_12) = zero,
inference(light_normalisation,[status(thm)],[c_159580,c_156395]) ).
tcf(c_159593,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(iPr_def_12,X0)) = addition(zero,multiplication(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_159586,c_51]) ).
tcf(c_159612,plain,
multiplication(iPr_def_12,iPr_def_14) = iPr_def_12,
inference(demodulation,[status(thm)],[c_159453,c_58]) ).
tcf(c_159618,plain,
addition(coantidomain(iPr_def_12),coantidomain(multiplication(coantidomain(coantidomain(iPr_def_12)),iPr_def_14))) = coantidomain(multiplication(coantidomain(coantidomain(iPr_def_12)),iPr_def_14)),
inference(superposition,[status(thm)],[c_159612,c_60]) ).
tcf(c_159633,plain,
addition(iPr_def_13,iPr_def_15) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_159618,c_133,c_134,c_135,c_159536]) ).
tcf(c_159637,plain,
multiplication(iPr_def_14,iPr_def_13) = multiplication(iPr_def_14,iPr_def_15),
inference(superposition,[status(thm)],[c_159633,c_159010]) ).
tcf(c_159643,plain,
addition(one,iPr_def_15) = addition(iPr_def_12,iPr_def_15),
inference(superposition,[status(thm)],[c_159633,c_156422]) ).
tcf(c_159644,plain,
addition(iPr_def_12,iPr_def_15) = addition(iPr_def_15,one),
inference(theory_normalisation,[status(thm)],[c_159643,c_53,c_54]) ).
tcf(c_159645,plain,
addition(iPr_def_12,iPr_def_15) = one,
inference(light_normalisation,[status(thm)],[c_159644,c_156796]) ).
tcf(c_159652,plain,
multiplication(iPr_def_14,iPr_def_13) = zero,
inference(light_normalisation,[status(thm)],[c_159637,c_156396]) ).
tcf(c_159657,plain,
multiplication(iPr_def_14,one) = multiplication(iPr_def_14,iPr_def_12),
inference(superposition,[status(thm)],[c_159645,c_159010]) ).
tcf(c_159661,plain,
addition(iPr_def_11,one) = addition(iPr_def_12,iPr_def_16),
inference(superposition,[status(thm)],[c_159645,c_156854]) ).
tcf(c_159663,plain,
addition(iPr_def_12,iPr_def_16) = one,
inference(light_normalisation,[status(thm)],[c_159661,c_156800]) ).
tcf(c_159701,plain,
! [X0: $i] : multiplication(iPr_def_14,multiplication(iPr_def_13,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_159652,c_59]) ).
tcf(c_159709,plain,
! [X0: $i] : multiplication(iPr_def_14,multiplication(iPr_def_13,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_159701,c_64]) ).
tcf(c_159803,plain,
! [X0: $i,X1: $i] : multiplication(addition(X0,X1),coantidomain(X0)) = multiplication(X1,coantidomain(X0)),
inference(demodulation,[status(thm)],[c_156451,c_57,c_158873]) ).
tcf(c_159864,plain,
multiplication(one,coantidomain(iPr_def_12)) = multiplication(iPr_def_16,coantidomain(iPr_def_12)),
inference(superposition,[status(thm)],[c_159663,c_159803]) ).
tcf(c_159884,plain,
multiplication(one,iPr_def_13) = multiplication(iPr_def_16,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_159864,c_133]) ).
tcf(c_159991,plain,
! [X0: $i] : multiplication(addition(one,iPr_def_14),multiplication(iPr_def_13,X0)) = addition(multiplication(iPr_def_13,X0),zero),
inference(superposition,[status(thm)],[c_159709,c_156448]) ).
tcf(c_159993,plain,
! [X0: $i] : multiplication(addition(iPr_def_14,one),multiplication(iPr_def_13,X0)) = addition(zero,multiplication(iPr_def_13,X0)),
inference(theory_normalisation,[status(thm)],[c_159991,c_53,c_54]) ).
tcf(c_159994,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(iPr_def_12,X0)) = multiplication(iPr_def_13,X0),
inference(light_normalisation,[status(thm)],[c_159993,c_156797,c_158863,c_159088,c_159593]) ).
tcf(c_160074,plain,
multiplication(iPr_def_16,iPr_def_13) = addition(iPr_def_11,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_159572,c_159884]) ).
tcf(c_160092,plain,
multiplication(iPr_def_14,iPr_def_12) = iPr_def_14,
inference(demodulation,[status(thm)],[c_159657,c_58]) ).
tcf(c_160105,plain,
multiplication(addition(one,iPr_def_14),iPr_def_12) = addition(iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_160092,c_156448]) ).
tcf(c_160107,plain,
multiplication(addition(iPr_def_14,one),iPr_def_12) = addition(iPr_def_12,iPr_def_14),
inference(theory_normalisation,[status(thm)],[c_160105,c_53,c_54]) ).
tcf(c_160108,plain,
multiplication(one,iPr_def_12) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_160107,c_159576,c_156797]) ).
tcf(c_160113,plain,
iPr_def_12 = iPr_def_14,
inference(demodulation,[status(thm)],[c_160108,c_57]) ).
tcf(c_160146,plain,
coantidomain(iPr_def_12) = iPr_def_15,
inference(demodulation,[status(thm)],[c_135,c_160113]) ).
tcf(c_160148,plain,
iPr_def_13 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_160146,c_133]) ).
tcf(c_160175,plain,
addition(iPr_def_11,iPr_def_13) = iPr_def_16,
inference(demodulation,[status(thm)],[c_136,c_160148]) ).
tcf(c_160176,plain,
multiplication(iPr_def_16,iPr_def_13) = iPr_def_16,
inference(demodulation,[status(thm)],[c_160074,c_160175]) ).
tcf(c_160247,plain,
! [X0: $i,X1: $i] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(demodulation,[status(thm)],[c_156452,c_57,c_158873]) ).
tcf(c_160250,plain,
! [X0: $i,X1: $i] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(superposition,[status(thm)],[c_54,c_160247]) ).
tcf(c_160457,plain,
multiplication(one,iPr_def_13) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_159884,c_160176]) ).
tcf(c_160458,plain,
iPr_def_13 = iPr_def_16,
inference(demodulation,[status(thm)],[c_160457,c_57]) ).
tcf(c_160467,plain,
addition(iPr_def_13,antidomain(iPr_def_11)) = one,
inference(demodulation,[status(thm)],[c_158971,c_160458]) ).
tcf(c_160480,plain,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_137,c_160458]) ).
tcf(c_164485,plain,
multiplication(one,iPr_def_11) = multiplication(iPr_def_13,iPr_def_11),
inference(superposition,[status(thm)],[c_160467,c_160250]) ).
tcf(c_164585,plain,
multiplication(iPr_def_13,iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_164485,c_57]) ).
tcf(c_169980,plain,
coantidomain(multiplication(iPr_def_13,iPr_def_10)) = one,
inference(demodulation,[status(thm)],[c_156656,c_156805]) ).
tcf(c_169994,plain,
multiplication(iPr_def_13,multiplication(iPr_def_10,one)) = zero,
inference(superposition,[status(thm)],[c_169980,c_156439]) ).
tcf(c_170004,plain,
multiplication(iPr_def_13,iPr_def_10) = zero,
inference(demodulation,[status(thm)],[c_169994,c_58]) ).
tcf(c_170016,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(iPr_def_10,X0)) = addition(zero,multiplication(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_170004,c_51]) ).
tcf(c_171754,plain,
! [X0: $i] : multiplication(iPr_def_13,addition(iPr_def_10,X0)) = multiplication(iPr_def_13,X0),
inference(light_normalisation,[status(thm)],[c_159593,c_159994,c_170016]) ).
tcf(c_171762,plain,
multiplication(iPr_def_13,one) = multiplication(iPr_def_13,iPr_def_11),
inference(superposition,[status(thm)],[c_156408,c_171754]) ).
tcf(c_171807,plain,
multiplication(iPr_def_13,one) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_171762,c_164585]) ).
tcf(c_171907,plain,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_171807,c_58]) ).
tcf(c_171908,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_171907,c_160480]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE120+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 18:59:58 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/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
% 0.14/0.43 % Proving...
% 68.10/11.88 % SZS status Started for theBenchmark.p
% 68.10/11.88 % SZS status Theorem for theBenchmark.p
% 68.10/11.88
% 68.10/11.88 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 68.10/11.88
% 68.10/11.88 % ------ iProver source info
% 68.10/11.88
% 68.10/11.88 % git: date: 2026-07-19 20:42:38 +0200
% 68.10/11.88 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 68.10/11.88 % git: non_committed_changes: false
% 68.10/11.88
% 68.10/11.88 % ------ Parsing...
% 68.10/11.88 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 68.10/11.88 %
% 68.10/11.88
% 68.10/11.88 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 68.10/11.88
% 68.10/11.88 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 68.10/11.88 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 68.10/11.88
% 68.10/11.88 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 68.10/11.88 % ------ Proving...
% 68.10/11.88 % ------ Problem Properties
% 68.10/11.88
% 68.10/11.88 %
% 68.10/11.88 % clauses 25
% 68.10/11.88 % conjectures 0
% 68.10/11.88 % EPR 1
% 68.10/11.88 % Horn 25
% 68.10/11.88 % unary 25
% 68.10/11.88 % binary 0
% 68.10/11.88 % lits 25
% 68.10/11.88 % lits eq 25
% 68.10/11.88 % fd_pure 0
% 68.10/11.88 % fd_pseudo 0
% 68.10/11.88 % fd_cond 0
% 68.10/11.88 % fd_pseudo_cond 0
% 68.10/11.88 % AC symbols 1
% 68.10/11.88
% 68.10/11.88 % ------ Schedule UEQ
% 68.10/11.88
% 68.10/11.88 % ------ Option_UEQ Time Limit: 10.
% 68.10/11.88
% 68.10/11.88
% 68.10/11.88 % ------
% 68.10/11.88 % Current options:
% 68.10/11.88 % ------
% 68.10/11.88
% 68.10/11.88
% 68.10/11.88 %
% 68.10/11.88
% 68.10/11.88 % ------ Proving...
% 68.10/11.88 % Proof_search_loop: time out after: 2752 full_loop iterations
% 68.10/11.88
% 68.10/11.88 % ------ Option_UEQ Time Limit: 15.
% 68.10/11.88
% 68.10/11.88
% 68.10/11.88 % ------
% 68.10/11.88 % Current options:
% 68.10/11.88 % ------
% 68.10/11.88
% 68.10/11.88
% 68.10/11.88 %
% 68.10/11.88
% 68.10/11.88 % ------ Proving...
% 68.10/11.88 %
% 68.10/11.88
% 68.10/11.88 % SZS status Theorem for theBenchmark.p
% 68.10/11.88
% 68.10/11.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 68.10/11.88
% 68.10/11.88
%------------------------------------------------------------------------------