%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE117+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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:52:26 PM UTC 2026
% Result : Theorem 33.13s 28.62s
% Output : CNFRefutation 33.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 28
% Syntax : Number of formulae : 147 ( 143 unt; 12 def)
% Number of atoms : 332 ( 150 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 13 ( 9 ~; 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 : 14 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn 129 !; 3 ?; 69 :)
% 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(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] :
( addition(X0,X1) = X1
=> ! [X2] : addition(forward_diamond(X0,domain(X2)),forward_diamond(X1,domain(X2))) = forward_diamond(X1,domain(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
( addition(X0,X1) = X1
=> ! [X2] : addition(forward_diamond(X0,domain(X2)),forward_diamond(X1,domain(X2))) = forward_diamond(X1,domain(X2)) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1] :
( addition(X0,X1) = X1
& ? [X2] : forward_diamond(X1,domain(X2)) != addition(forward_diamond(X0,domain(X2)),forward_diamond(X1,domain(X2))) ),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
( sK1 = addition(sK0,sK1)
& forward_diamond(sK1,domain(sK2)) != addition(forward_diamond(sK0,domain(sK2)),forward_diamond(sK1,domain(sK2))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f29]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f41,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f42,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f43,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(f44,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f52,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f56,plain,
sK1 = addition(sK0,sK1),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
forward_diamond(sK1,domain(sK2)) != addition(forward_diamond(sK0,domain(sK2)),forward_diamond(sK1,domain(sK2))),
inference(cnf_transformation,[],[f30]) ).
fof(f62,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f52,f45,f45]) ).
fof(f64,plain,
antidomain(antidomain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(sK2))))))) != addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK2))))))),antidomain(antidomain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(sK2)))))))),
inference(definition_unfolding,[],[f57,f62,f45,f62,f45,f62,f45]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f34]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f37]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f39]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f41]) ).
tcf(c_60,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f42]) ).
tcf(c_61,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,[],[f43]) ).
tcf(c_62,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f44]) ).
tcf(c_66,negated_conjecture,
addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK2))))))),antidomain(antidomain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(sK2)))))))) != antidomain(antidomain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(sK2))))))),
inference(cnf_transformation,[],[f64]) ).
tcf(c_67,negated_conjecture,
addition(sK0,sK1) = sK1,
inference(cnf_transformation,[],[f56]) ).
tcf(c_83,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_85,negated_conjecture,
addition(antidomain(antidomain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(sK2))))))),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK2)))))))) != antidomain(antidomain(multiplication(sK1,antidomain(antidomain(antidomain(antidomain(sK2))))))),
inference(theory_normalisation,[status(thm)],[c_66,c_50,c_49]) ).
tcf(c_86,negated_conjecture,
addition(sK1,sK0) = sK1,
inference(theory_normalisation,[status(thm)],[c_67,c_50,c_49]) ).
tcf(c_133,definition,
iPr_def_10 = addition(sK1,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_134,definition,
iPr_def_11 = antidomain(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_135,definition,
iPr_def_12 = antidomain(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_136,definition,
iPr_def_13 = antidomain(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_137,definition,
iPr_def_14 = antidomain(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_138,definition,
iPr_def_15 = multiplication(sK1,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_139,definition,
iPr_def_16 = antidomain(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_140,definition,
iPr_def_17 = antidomain(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_141,definition,
iPr_def_18 = multiplication(sK0,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_142,definition,
iPr_def_19 = antidomain(iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_143,definition,
iPr_def_20 = antidomain(iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_144,definition,
iPr_def_21 = addition(iPr_def_17,iPr_def_20),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_145,negated_conjecture,
iPr_def_10 = sK1,
inference(demodulation,[status(thm)],[c_86,c_133]) ).
tcf(c_146,negated_conjecture,
iPr_def_21 != iPr_def_17,
inference(demodulation,[status(thm)],[c_85,c_141,c_142,c_143,c_134,c_135,c_136,c_137,c_138,c_139,c_140,c_144]) ).
tcf(c_49707,plain,
addition(iPr_def_16,antidomain(iPr_def_16)) = one,
inference(superposition,[status(thm)],[c_139,c_83]) ).
tcf(c_49708,plain,
addition(iPr_def_16,iPr_def_17) = one,
inference(light_normalisation,[status(thm)],[c_49707,c_140]) ).
tcf(c_49709,plain,
addition(iPr_def_17,antidomain(iPr_def_17)) = one,
inference(superposition,[status(thm)],[c_140,c_83]) ).
tcf(c_49712,plain,
addition(iPr_def_20,antidomain(iPr_def_20)) = one,
inference(superposition,[status(thm)],[c_143,c_83]) ).
tcf(c_49840,plain,
addition(iPr_def_10,sK0) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_133,c_145]) ).
tcf(c_49847,plain,
multiplication(iPr_def_10,iPr_def_14) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_138,c_145]) ).
tcf(c_50088,plain,
multiplication(iPr_def_16,iPr_def_15) = zero,
inference(superposition,[status(thm)],[c_139,c_60]) ).
tcf(c_50089,plain,
multiplication(iPr_def_17,iPr_def_16) = zero,
inference(superposition,[status(thm)],[c_140,c_60]) ).
tcf(c_50092,plain,
antidomain(one) = zero,
inference(superposition,[status(thm)],[c_60,c_54]) ).
tcf(c_50126,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_49,c_51]) ).
tcf(c_50191,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_50194,plain,
! [X0: $i] : addition(iPr_def_17,addition(iPr_def_20,X0)) = addition(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_144,c_50]) ).
tcf(c_50258,plain,
addition(zero,antidomain(zero)) = one,
inference(superposition,[status(thm)],[c_50092,c_83]) ).
tcf(c_50612,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),multiplication(X0,X1)) = multiplication(zero,X1),
inference(superposition,[status(thm)],[c_60,c_53]) ).
tcf(c_50627,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(superposition,[status(thm)],[c_60,c_56]) ).
tcf(c_50661,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_50667,plain,
! [X0: $i] : addition(iPr_def_15,multiplication(X0,iPr_def_14)) = multiplication(addition(iPr_def_10,X0),iPr_def_14),
inference(superposition,[status(thm)],[c_49847,c_57]) ).
tcf(c_50717,plain,
! [X0: $i] : addition(antidomain(multiplication(X0,iPr_def_18)),antidomain(multiplication(X0,antidomain(iPr_def_19)))) = antidomain(multiplication(X0,antidomain(iPr_def_19))),
inference(superposition,[status(thm)],[c_142,c_61]) ).
tcf(c_50730,plain,
! [X0: $i] : addition(antidomain(multiplication(X0,iPr_def_18)),antidomain(multiplication(X0,iPr_def_20))) = antidomain(multiplication(X0,iPr_def_20)),
inference(light_normalisation,[status(thm)],[c_50717,c_143]) ).
tcf(c_50739,plain,
! [X0: $i] : addition(iPr_def_16,addition(iPr_def_17,X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_49708,c_50]) ).
tcf(c_50792,plain,
multiplication(addition(iPr_def_10,sK0),iPr_def_14) = addition(iPr_def_15,iPr_def_18),
inference(superposition,[status(thm)],[c_141,c_50667]) ).
tcf(c_50798,plain,
addition(iPr_def_15,iPr_def_18) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_50792,c_49840,c_49847]) ).
tcf(c_50868,plain,
! [X0: $i] : addition(zero,multiplication(iPr_def_16,X0)) = multiplication(iPr_def_16,addition(iPr_def_15,X0)),
inference(superposition,[status(thm)],[c_50088,c_56]) ).
tcf(c_50878,plain,
! [X0: $i] : addition(zero,multiplication(X0,iPr_def_16)) = multiplication(addition(iPr_def_17,X0),iPr_def_16),
inference(superposition,[status(thm)],[c_50089,c_57]) ).
tcf(c_50879,plain,
! [X0: $i] : addition(zero,multiplication(iPr_def_17,X0)) = multiplication(iPr_def_17,addition(iPr_def_16,X0)),
inference(superposition,[status(thm)],[c_50089,c_56]) ).
tcf(c_50880,plain,
! [X0: $i] : multiplication(iPr_def_17,multiplication(iPr_def_16,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_50089,c_53]) ).
tcf(c_50883,plain,
! [X0: $i] : multiplication(iPr_def_17,multiplication(iPr_def_16,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_50880,c_59]) ).
tcf(c_51050,plain,
antidomain(zero) = one,
inference(demodulation,[status(thm)],[c_50258,c_50126]) ).
tcf(c_51981,plain,
! [X0: $i] : addition(antidomain(X0),one) = one,
inference(superposition,[status(thm)],[c_83,c_50191]) ).
tcf(c_51983,plain,
addition(iPr_def_17,iPr_def_21) = iPr_def_21,
inference(superposition,[status(thm)],[c_144,c_50191]) ).
tcf(c_51986,plain,
addition(iPr_def_17,one) = one,
inference(superposition,[status(thm)],[c_49709,c_50191]) ).
tcf(c_52005,plain,
addition(iPr_def_20,one) = one,
inference(superposition,[status(thm)],[c_49712,c_50191]) ).
tcf(c_52062,plain,
! [X0: $i] : addition(one,antidomain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_51981,c_50,c_49]) ).
tcf(c_52367,plain,
! [X0: $i,X1: $i] : addition(one,addition(antidomain(X0),X1)) = addition(one,X1),
inference(superposition,[status(thm)],[c_52062,c_50]) ).
tcf(c_52555,plain,
addition(iPr_def_17,one) = addition(iPr_def_21,one),
inference(superposition,[status(thm)],[c_52005,c_50194]) ).
tcf(c_52556,plain,
addition(iPr_def_21,one) = one,
inference(light_normalisation,[status(thm)],[c_52555,c_51986]) ).
tcf(c_55020,plain,
addition(one,iPr_def_21) = addition(iPr_def_16,iPr_def_21),
inference(superposition,[status(thm)],[c_51983,c_50739]) ).
tcf(c_55072,plain,
addition(iPr_def_16,iPr_def_21) = addition(iPr_def_21,one),
inference(theory_normalisation,[status(thm)],[c_55020,c_50,c_49]) ).
tcf(c_55073,plain,
addition(iPr_def_16,iPr_def_21) = one,
inference(light_normalisation,[status(thm)],[c_55072,c_52556]) ).
tcf(c_64353,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),multiplication(X0,X1)) = zero,
inference(demodulation,[status(thm)],[c_50612,c_59]) ).
tcf(c_66426,plain,
! [X0: $i,X1: $i] : addition(one,addition(X0,antidomain(X1))) = addition(one,X0),
inference(superposition,[status(thm)],[c_49,c_52367]) ).
tcf(c_74205,plain,
! [X0: $i] : multiplication(addition(one,iPr_def_17),multiplication(iPr_def_16,X0)) = addition(multiplication(iPr_def_16,X0),zero),
inference(superposition,[status(thm)],[c_50883,c_50661]) ).
tcf(c_74208,plain,
! [X0: $i,X1: $i] : multiplication(addition(one,antidomain(X0)),multiplication(X0,X1)) = addition(multiplication(X0,X1),zero),
inference(superposition,[status(thm)],[c_64353,c_50661]) ).
tcf(c_74415,plain,
! [X0: $i] : multiplication(addition(iPr_def_17,one),multiplication(iPr_def_16,X0)) = addition(zero,multiplication(iPr_def_16,X0)),
inference(theory_normalisation,[status(thm)],[c_74205,c_50,c_49]) ).
tcf(c_74416,plain,
! [X0: $i] : multiplication(one,multiplication(iPr_def_16,X0)) = multiplication(iPr_def_16,addition(iPr_def_15,X0)),
inference(light_normalisation,[status(thm)],[c_74415,c_50868,c_51986]) ).
tcf(c_74429,plain,
! [X0: $i,X1: $i] : multiplication(addition(one,antidomain(X0)),multiplication(X0,X1)) = addition(zero,multiplication(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_74208,c_50,c_49]) ).
tcf(c_74430,plain,
! [X0: $i,X1: $i] : addition(zero,multiplication(X0,X1)) = multiplication(one,multiplication(X0,X1)),
inference(light_normalisation,[status(thm)],[c_74429,c_52062]) ).
tcf(c_89148,plain,
! [X0: $i] : multiplication(addition(iPr_def_17,X0),iPr_def_16) = multiplication(X0,iPr_def_16),
inference(demodulation,[status(thm)],[c_50878,c_55,c_74430]) ).
tcf(c_89155,plain,
multiplication(antidomain(iPr_def_17),iPr_def_16) = multiplication(one,iPr_def_16),
inference(superposition,[status(thm)],[c_49709,c_89148]) ).
tcf(c_90715,plain,
! [X0: $i] : multiplication(iPr_def_17,addition(iPr_def_16,X0)) = multiplication(iPr_def_17,X0),
inference(demodulation,[status(thm)],[c_50879,c_55,c_74430]) ).
tcf(c_90727,plain,
multiplication(iPr_def_17,one) = multiplication(iPr_def_17,iPr_def_21),
inference(superposition,[status(thm)],[c_55073,c_90715]) ).
tcf(c_94066,plain,
multiplication(iPr_def_17,iPr_def_21) = iPr_def_17,
inference(demodulation,[status(thm)],[c_90727,c_54]) ).
tcf(c_94073,plain,
! [X0: $i] : addition(iPr_def_17,multiplication(X0,iPr_def_21)) = multiplication(addition(iPr_def_17,X0),iPr_def_21),
inference(superposition,[status(thm)],[c_94066,c_57]) ).
tcf(c_97633,plain,
multiplication(antidomain(iPr_def_17),iPr_def_16) = iPr_def_16,
inference(demodulation,[status(thm)],[c_89155,c_55]) ).
tcf(c_97676,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X0,X1)) = multiplication(antidomain(X0),X1),
inference(demodulation,[status(thm)],[c_50627,c_55,c_74430]) ).
tcf(c_97682,plain,
! [X0: $i] : multiplication(iPr_def_16,addition(iPr_def_15,X0)) = multiplication(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_139,c_97676]) ).
tcf(c_97687,plain,
! [X0: $i,X1: $i] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(superposition,[status(thm)],[c_49,c_97676]) ).
tcf(c_97696,plain,
multiplication(antidomain(iPr_def_17),iPr_def_20) = multiplication(antidomain(iPr_def_17),iPr_def_21),
inference(superposition,[status(thm)],[c_144,c_97676]) ).
tcf(c_97739,plain,
multiplication(antidomain(iPr_def_15),iPr_def_15) = multiplication(antidomain(iPr_def_15),iPr_def_18),
inference(superposition,[status(thm)],[c_50798,c_97676]) ).
tcf(c_97838,plain,
multiplication(iPr_def_16,iPr_def_18) = zero,
inference(light_normalisation,[status(thm)],[c_97739,c_139,c_50088]) ).
tcf(c_98104,plain,
addition(antidomain(zero),antidomain(multiplication(iPr_def_16,antidomain(antidomain(iPr_def_18))))) = antidomain(multiplication(iPr_def_16,antidomain(antidomain(iPr_def_18)))),
inference(superposition,[status(thm)],[c_97838,c_61]) ).
tcf(c_98123,plain,
addition(one,antidomain(multiplication(iPr_def_16,iPr_def_20))) = antidomain(multiplication(iPr_def_16,iPr_def_20)),
inference(light_normalisation,[status(thm)],[c_98104,c_142,c_143,c_51050]) ).
tcf(c_120144,plain,
! [X0: $i] : addition(one,antidomain(multiplication(X0,iPr_def_18))) = addition(one,antidomain(multiplication(X0,iPr_def_20))),
inference(superposition,[status(thm)],[c_50730,c_66426]) ).
tcf(c_151573,plain,
multiplication(antidomain(iPr_def_17),one) = multiplication(antidomain(iPr_def_17),iPr_def_16),
inference(superposition,[status(thm)],[c_49708,c_97687]) ).
tcf(c_151904,plain,
multiplication(antidomain(iPr_def_17),one) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_151573,c_97633]) ).
tcf(c_152221,plain,
antidomain(iPr_def_17) = iPr_def_16,
inference(demodulation,[status(thm)],[c_151904,c_54]) ).
tcf(c_152233,plain,
multiplication(iPr_def_16,iPr_def_20) = multiplication(iPr_def_16,iPr_def_21),
inference(demodulation,[status(thm)],[c_97696,c_152221]) ).
tcf(c_153992,plain,
antidomain(multiplication(iPr_def_16,iPr_def_20)) = one,
inference(demodulation,[status(thm)],[c_98123,c_52062,c_120144]) ).
tcf(c_154020,plain,
multiplication(one,multiplication(iPr_def_16,iPr_def_20)) = zero,
inference(superposition,[status(thm)],[c_153992,c_60]) ).
tcf(c_154062,plain,
multiplication(iPr_def_16,iPr_def_20) = zero,
inference(demodulation,[status(thm)],[c_154020,c_74416,c_97682]) ).
tcf(c_155655,plain,
multiplication(iPr_def_16,iPr_def_21) = zero,
inference(light_normalisation,[status(thm)],[c_152233,c_154062]) ).
tcf(c_155694,plain,
multiplication(addition(iPr_def_17,iPr_def_16),iPr_def_21) = addition(iPr_def_17,zero),
inference(superposition,[status(thm)],[c_155655,c_94073]) ).
tcf(c_155698,plain,
multiplication(addition(iPr_def_16,iPr_def_17),iPr_def_21) = addition(iPr_def_17,zero),
inference(theory_normalisation,[status(thm)],[c_155694,c_50,c_49]) ).
tcf(c_155699,plain,
addition(iPr_def_17,zero) = multiplication(one,iPr_def_21),
inference(light_normalisation,[status(thm)],[c_155698,c_49708]) ).
tcf(c_156726,plain,
iPr_def_17 = iPr_def_21,
inference(demodulation,[status(thm)],[c_155699,c_51,c_55]) ).
tcf(c_156836,plain,
iPr_def_17 != iPr_def_17,
inference(demodulation,[status(thm)],[c_146,c_156726]) ).
tcf(c_156837,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_156836]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE117+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n018.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 19:01:23 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 33.13/28.62 % SZS status Started for theBenchmark.p
% 33.13/28.62 % SZS status Theorem for theBenchmark.p
% 33.13/28.62
% 33.13/28.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 33.13/28.62
% 33.13/28.62 % ------ iProver source info
% 33.13/28.62
% 33.13/28.62 % git: date: 2026-07-19 20:42:38 +0200
% 33.13/28.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 33.13/28.62 % git: non_committed_changes: false
% 33.13/28.62
% 33.13/28.62 % ------ Parsing...
% 33.13/28.62 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 33.13/28.62 %
% 33.13/28.62
% 33.13/28.62 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 33.13/28.62
% 33.13/28.62 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 33.13/28.62 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 33.13/28.62
% 33.13/28.62 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 33.13/28.62 % ------ Proving...
% 33.13/28.62 % ------ Problem Properties
% 33.13/28.62
% 33.13/28.62 %
% 33.13/28.62 % clauses 31
% 33.13/28.62 % conjectures 2
% 33.13/28.62 % EPR 2
% 33.13/28.62 % Horn 31
% 33.13/28.62 % unary 31
% 33.13/28.62 % binary 0
% 33.13/28.62 % lits 31
% 33.13/28.62 % lits eq 31
% 33.13/28.62 % fd_pure 0
% 33.13/28.62 % fd_pseudo 0
% 33.13/28.62 % fd_cond 0
% 33.13/28.62 % fd_pseudo_cond 0
% 33.13/28.62 % AC symbols 1
% 33.13/28.62
% 33.13/28.62 % ------ Schedule UEQ
% 33.13/28.62
% 33.13/28.62 % ------ Option_UEQ Time Limit: 10.
% 33.13/28.62
% 33.13/28.62
% 33.13/28.62 % ------
% 33.13/28.62 % Current options:
% 33.13/28.62 % ------
% 33.13/28.62
% 33.13/28.62
% 33.13/28.62 %
% 33.13/28.62
% 33.13/28.62 % ------ Proving...
% 33.13/28.62 % Proof_search_loop: time out after: 820 full_loop iterations
% 33.13/28.62
% 33.13/28.62 % ------ Option_UEQ Time Limit: 15.
% 33.13/28.62
% 33.13/28.62
% 33.13/28.62 % ------
% 33.13/28.62 % Current options:
% 33.13/28.62 % ------
% 33.13/28.62
% 33.13/28.62
% 33.13/28.62 %
% 33.13/28.62
% 33.13/28.62 % ------ Proving...
% 33.13/28.62 %
% 33.13/28.62
% 33.13/28.62 % SZS status Theorem for theBenchmark.p
% 33.13/28.62
% 33.13/28.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 33.13/28.63
% 33.13/28.63
%------------------------------------------------------------------------------