%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE023+2 : 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 : n001.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 01:52:11 PM UTC 2026
% Result : Theorem 17.79s 3.77s
% Output : CNFRefutation 17.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 23
% Syntax : Number of formulae : 192 ( 151 unt; 8 def)
% Number of atoms : 500 ( 186 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 134 ( 55 ~; 47 |; 23 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 170 ( 0 sgn 161 !; 9 ?; 82 :)
% 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(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f19,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
=> addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
=> addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f27,plain,
? [X0,X1,X2] :
( test(X2)
& test(X1)
& addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
& multiplication(c(X1),X0) != addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f28,plain,
? [X0,X1,X2] :
( test(X2)
& test(X1)
& addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
& multiplication(c(X1),X0) != addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f30,plain,
! [X0] :
( ( ~ test(X0)
| ? [X2] : complement(X2,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(rectify,[],[f29]) ).
fof(f31,plain,
! [X0] :
( ( ~ test(X0)
| complement(sK0(X0),X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) )
& ( addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| complement(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) )
& ( addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| complement(X1,X0) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f35,plain,
( test(sK3)
& test(sK2)
& multiplication(sK1,sK3) = addition(multiplication(sK2,sK1),multiplication(sK1,sK3))
& multiplication(c(sK2),sK1) != addition(multiplication(sK1,c(sK3)),multiplication(c(sK2),sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f28]) ).
fof(f36,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f37,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f38,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f39,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f40,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f41,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f42,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f43,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f44,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f45,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f46,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f47,plain,
! [X0] :
( ~ test(X0)
| complement(sK0(X0),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| test(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f33]) ).
fof(f50,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f51,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
! [X0,X1] :
( ~ test(X0)
| ~ complement(X0,X1)
| c(X0) = X1 ),
inference(cnf_transformation,[],[f34]) ).
fof(f58,plain,
test(sK3),
inference(cnf_transformation,[],[f35]) ).
fof(f59,plain,
test(sK2),
inference(cnf_transformation,[],[f35]) ).
fof(f60,plain,
multiplication(sK1,sK3) = addition(multiplication(sK2,sK1),multiplication(sK1,sK3)),
inference(cnf_transformation,[],[f35]) ).
fof(f61,plain,
multiplication(c(sK2),sK1) != addition(multiplication(sK1,c(sK3)),multiplication(c(sK2),sK1)),
inference(cnf_transformation,[],[f35]) ).
fof(f62,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f53]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f36]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f38]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f39]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f40]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f41]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f42]) ).
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,[],[f43]) ).
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,[],[f44]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f45]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f46]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( test(X1)
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_61,plain,
! [X0: $i] :
( complement(sK0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( multiplication(X1,X0) = zero )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( multiplication(X0,X1) = zero )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( c(X0) = X1 )
| ~ test(X0)
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_67,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_71,negated_conjecture,
addition(multiplication(sK1,c(sK3)),multiplication(c(sK2),sK1)) != multiplication(c(sK2),sK1),
inference(cnf_transformation,[],[f61]) ).
tcf(c_72,negated_conjecture,
addition(multiplication(sK2,sK1),multiplication(sK1,sK3)) = multiplication(sK1,sK3),
inference(cnf_transformation,[],[f60]) ).
tcf(c_73,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f59]) ).
tcf(c_74,negated_conjecture,
test(sK3),
inference(cnf_transformation,[],[f58]) ).
tcf(c_93,negated_conjecture,
addition(multiplication(sK1,sK3),multiplication(sK2,sK1)) = multiplication(sK1,sK3),
inference(theory_normalisation,[status(thm)],[c_72,c_50,c_49]) ).
tcf(c_382,definition,
iPr_def_10 = multiplication(sK1,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_383,definition,
iPr_def_11 = multiplication(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_384,definition,
iPr_def_12 = addition(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_385,definition,
iPr_def_13 = c(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_386,definition,
iPr_def_14 = multiplication(sK1,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_387,definition,
iPr_def_15 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_388,definition,
iPr_def_16 = multiplication(iPr_def_15,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_389,definition,
iPr_def_17 = addition(iPr_def_14,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_390,negated_conjecture,
iPr_def_12 = iPr_def_10,
inference(demodulation,[status(thm)],[c_93,c_383,c_382,c_384]) ).
tcf(c_391,negated_conjecture,
test(sK3),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_392,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_393,negated_conjecture,
iPr_def_17 != iPr_def_16,
inference(demodulation,[status(thm)],[c_71,c_387,c_388,c_385,c_386,c_389]) ).
tcf(c_684,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_689,plain,
addition(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_384,c_390]) ).
tcf(c_699,plain,
( complement(sK2,iPr_def_15)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_387,c_67]) ).
tcf(c_700,plain,
( complement(sK3,iPr_def_13)
| ~ test(sK3) ),
inference(superposition,[status(thm)],[c_385,c_67]) ).
tcf(c_704,plain,
complement(sK3,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_700,c_391]) ).
tcf(c_705,plain,
complement(sK2,iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_699,c_392]) ).
tcf(c_707,plain,
test(iPr_def_15),
inference(superposition,[status(thm)],[c_705,c_60]) ).
tcf(c_731,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_740,plain,
! [X0: $i] :
( ( multiplication(c(X0),X0) = zero )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_67,c_63]) ).
tcf(c_741,plain,
multiplication(iPr_def_15,sK2) = zero,
inference(superposition,[status(thm)],[c_705,c_63]) ).
tcf(c_751,plain,
! [X0: $i] :
( ( multiplication(sK0(X0),X0) = zero )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_61,c_64]) ).
tcf(c_753,plain,
multiplication(sK2,iPr_def_15) = zero,
inference(superposition,[status(thm)],[c_705,c_64]) ).
tcf(c_754,plain,
multiplication(sK3,iPr_def_13) = zero,
inference(superposition,[status(thm)],[c_704,c_64]) ).
tcf(c_847,plain,
! [X0: $i] :
( ( addition(X0,sK0(X0)) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_61,c_65]) ).
tcf(c_848,plain,
! [X0: $i] :
( ( addition(c(X0),X0) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_67,c_65]) ).
tcf(c_849,plain,
addition(iPr_def_15,sK2) = one,
inference(superposition,[status(thm)],[c_705,c_65]) ).
tcf(c_850,plain,
addition(iPr_def_13,sK3) = one,
inference(superposition,[status(thm)],[c_704,c_65]) ).
tcf(c_851,plain,
! [X0: $i] :
( ( addition(X0,c(X0)) = one )
| ~ test(X0) ),
inference(theory_normalisation,[status(thm)],[c_848,c_50,c_49]) ).
tcf(c_910,plain,
! [X0: $i] : multiplication(sK1,multiplication(sK3,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_382,c_53]) ).
tcf(c_911,plain,
! [X0: $i] : multiplication(sK2,multiplication(sK1,X0)) = multiplication(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_383,c_53]) ).
tcf(c_913,plain,
! [X0: $i] : multiplication(iPr_def_15,multiplication(sK1,X0)) = multiplication(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_388,c_53]) ).
tcf(c_914,plain,
! [X0: $i] : multiplication(iPr_def_15,multiplication(sK2,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_741,c_53]) ).
tcf(c_923,plain,
! [X0: $i] : multiplication(iPr_def_15,multiplication(sK2,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_914,c_59]) ).
tcf(c_971,plain,
! [X0: $i] : addition(iPr_def_15,addition(sK2,X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_849,c_50]) ).
tcf(c_972,plain,
! [X0: $i] : addition(iPr_def_15,addition(X0,sK2)) = addition(X0,one),
inference(superposition,[status(thm)],[c_849,c_684]) ).
tcf(c_980,plain,
! [X0: $i] : addition(iPr_def_13,addition(sK3,X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_850,c_50]) ).
tcf(c_981,plain,
! [X0: $i] : addition(iPr_def_13,addition(X0,sK3)) = addition(X0,one),
inference(superposition,[status(thm)],[c_850,c_684]) ).
tcf(c_993,plain,
addition(one,sK2) = addition(iPr_def_15,sK2),
inference(superposition,[status(thm)],[c_52,c_971]) ).
tcf(c_1000,plain,
addition(one,sK2) = one,
inference(light_normalisation,[status(thm)],[c_993,c_849]) ).
tcf(c_1032,plain,
addition(one,one) = addition(iPr_def_15,one),
inference(superposition,[status(thm)],[c_1000,c_972]) ).
tcf(c_1050,plain,
addition(one,sK3) = addition(iPr_def_13,sK3),
inference(superposition,[status(thm)],[c_52,c_980]) ).
tcf(c_1057,plain,
addition(one,sK3) = one,
inference(light_normalisation,[status(thm)],[c_1050,c_850]) ).
tcf(c_1096,plain,
addition(one,one) = addition(iPr_def_13,one),
inference(superposition,[status(thm)],[c_1057,c_981]) ).
tcf(c_1132,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_15),multiplication(X0,sK2)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_849,c_56]) ).
tcf(c_1133,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),multiplication(X0,sK3)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_850,c_56]) ).
tcf(c_1150,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),multiplication(X0,sK3)) = X0,
inference(light_normalisation,[status(thm)],[c_1133,c_54]) ).
tcf(c_1151,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_15),multiplication(X0,sK2)) = X0,
inference(light_normalisation,[status(thm)],[c_1132,c_54]) ).
tcf(c_1201,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_11,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_689,c_57]) ).
tcf(c_1202,plain,
! [X0: $i] : addition(multiplication(iPr_def_14,X0),multiplication(iPr_def_16,X0)) = multiplication(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_389,c_57]) ).
tcf(c_1214,plain,
! [X0: $i] : addition(multiplication(one,X0),multiplication(sK2,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_1000,c_57]) ).
tcf(c_1224,plain,
! [X0: $i] : addition(X0,multiplication(sK2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1214,c_55]) ).
tcf(c_1844,plain,
multiplication(iPr_def_15,iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_383,c_923]) ).
tcf(c_1856,plain,
multiplication(sK3,iPr_def_13) = multiplication(iPr_def_15,iPr_def_11),
inference(demodulation,[status(thm)],[c_754,c_1844]) ).
tcf(c_1857,plain,
multiplication(sK2,iPr_def_15) = multiplication(iPr_def_15,iPr_def_11),
inference(demodulation,[status(thm)],[c_753,c_1844]) ).
tcf(c_1860,plain,
! [X0: $i] : addition(multiplication(iPr_def_15,iPr_def_11),X0) = X0,
inference(demodulation,[status(thm)],[c_731,c_1844]) ).
tcf(c_1864,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_15,iPr_def_11),X0) = multiplication(iPr_def_15,iPr_def_11),
inference(demodulation,[status(thm)],[c_59,c_1844]) ).
tcf(c_1865,plain,
! [X0: $i] : multiplication(X0,multiplication(iPr_def_15,iPr_def_11)) = multiplication(iPr_def_15,iPr_def_11),
inference(demodulation,[status(thm)],[c_58,c_1844]) ).
tcf(c_1949,plain,
addition(iPr_def_13,one) = addition(iPr_def_15,one),
inference(light_normalisation,[status(thm)],[c_1032,c_1096]) ).
tcf(c_1964,plain,
addition(iPr_def_13,one) = one,
inference(demodulation,[status(thm)],[c_1096,c_52]) ).
tcf(c_1965,plain,
addition(iPr_def_15,one) = one,
inference(demodulation,[status(thm)],[c_1949,c_1964]) ).
tcf(c_1967,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),multiplication(X0,one)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_1964,c_56]) ).
tcf(c_1973,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),X0) = X0,
inference(light_normalisation,[status(thm)],[c_1967,c_54]) ).
tcf(c_1974,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_13)) = X0,
inference(theory_normalisation,[status(thm)],[c_1973,c_50,c_49]) ).
tcf(c_1988,plain,
! [X0: $i] : addition(multiplication(iPr_def_15,X0),multiplication(one,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_1965,c_57]) ).
tcf(c_1990,plain,
! [X0: $i] : addition(multiplication(iPr_def_15,X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_1988,c_55]) ).
tcf(c_1991,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_15,X0)) = X0,
inference(theory_normalisation,[status(thm)],[c_1990,c_50,c_49]) ).
tcf(c_3058,plain,
addition(sK1,iPr_def_16) = sK1,
inference(superposition,[status(thm)],[c_388,c_1991]) ).
tcf(c_3077,plain,
addition(iPr_def_16,sK1) = sK1,
inference(theory_normalisation,[status(thm)],[c_3058,c_50,c_49]) ).
tcf(c_3537,plain,
! [X0: $i] :
( ( multiplication(c(X0),X0) = multiplication(iPr_def_15,iPr_def_11) )
| ~ test(X0) ),
inference(light_normalisation,[status(thm)],[c_740,c_1844]) ).
tcf(c_3549,plain,
multiplication(c(iPr_def_15),iPr_def_15) = multiplication(iPr_def_15,iPr_def_11),
inference(superposition,[status(thm)],[c_707,c_3537]) ).
tcf(c_3567,plain,
! [X0: $i] :
( ( multiplication(sK0(X0),X0) = multiplication(iPr_def_15,iPr_def_11) )
| ~ test(X0) ),
inference(light_normalisation,[status(thm)],[c_751,c_1844]) ).
tcf(c_3575,plain,
multiplication(sK0(sK2),sK2) = multiplication(iPr_def_15,iPr_def_11),
inference(superposition,[status(thm)],[c_392,c_3567]) ).
tcf(c_3654,plain,
! [X0: $i] : multiplication(c(iPr_def_15),multiplication(iPr_def_15,X0)) = multiplication(multiplication(iPr_def_15,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_3549,c_53]) ).
tcf(c_3657,plain,
! [X0: $i] : multiplication(c(iPr_def_15),multiplication(iPr_def_15,X0)) = multiplication(iPr_def_15,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_3654,c_1864]) ).
tcf(c_4037,plain,
addition(sK2,sK0(sK2)) = one,
inference(superposition,[status(thm)],[c_392,c_847]) ).
tcf(c_4073,plain,
! [X0: $i] : addition(multiplication(sK2,X0),multiplication(sK0(sK2),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_4037,c_57]) ).
tcf(c_4077,plain,
! [X0: $i] : addition(multiplication(sK2,X0),multiplication(sK0(sK2),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4073,c_55]) ).
tcf(c_4346,plain,
addition(iPr_def_15,c(iPr_def_15)) = one,
inference(superposition,[status(thm)],[c_707,c_851]) ).
tcf(c_4705,plain,
! [X0: $i] : addition(multiplication(iPr_def_15,X0),multiplication(c(iPr_def_15),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_4346,c_57]) ).
tcf(c_4707,plain,
! [X0: $i] : addition(multiplication(iPr_def_15,X0),multiplication(c(iPr_def_15),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4705,c_55]) ).
tcf(c_5590,plain,
multiplication(sK1,multiplication(iPr_def_15,iPr_def_11)) = multiplication(iPr_def_10,iPr_def_13),
inference(superposition,[status(thm)],[c_1856,c_910]) ).
tcf(c_5601,plain,
multiplication(sK2,iPr_def_14) = multiplication(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_386,c_911]) ).
tcf(c_5935,plain,
multiplication(iPr_def_15,iPr_def_14) = multiplication(iPr_def_16,iPr_def_13),
inference(superposition,[status(thm)],[c_386,c_913]) ).
tcf(c_5987,plain,
addition(iPr_def_16,multiplication(iPr_def_15,iPr_def_14)) = iPr_def_16,
inference(superposition,[status(thm)],[c_5935,c_1974]) ).
tcf(c_6090,plain,
addition(multiplication(iPr_def_15,iPr_def_11),multiplication(sK0(sK2),iPr_def_15)) = iPr_def_15,
inference(superposition,[status(thm)],[c_1857,c_4077]) ).
tcf(c_8135,plain,
addition(multiplication(sK1,iPr_def_13),iPr_def_10) = sK1,
inference(superposition,[status(thm)],[c_382,c_1150]) ).
tcf(c_8152,plain,
addition(iPr_def_10,multiplication(sK1,iPr_def_13)) = sK1,
inference(theory_normalisation,[status(thm)],[c_8135,c_50,c_49]) ).
tcf(c_8153,plain,
addition(iPr_def_10,iPr_def_14) = sK1,
inference(light_normalisation,[status(thm)],[c_8152,c_386]) ).
tcf(c_8176,plain,
addition(iPr_def_16,addition(iPr_def_10,iPr_def_14)) = addition(iPr_def_10,iPr_def_14),
inference(demodulation,[status(thm)],[c_3077,c_8153]) ).
tcf(c_8186,plain,
addition(iPr_def_10,addition(iPr_def_14,iPr_def_16)) = addition(iPr_def_10,iPr_def_14),
inference(theory_normalisation,[status(thm)],[c_8176,c_50,c_49]) ).
tcf(c_8187,plain,
addition(iPr_def_10,iPr_def_14) = addition(iPr_def_10,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_8186,c_389]) ).
tcf(c_9204,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_17,X0)) = multiplication(addition(iPr_def_10,iPr_def_14),X0),
inference(superposition,[status(thm)],[c_8187,c_57]) ).
tcf(c_9211,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),addition(multiplication(iPr_def_14,X0),multiplication(iPr_def_16,X0))) = multiplication(addition(iPr_def_10,iPr_def_14),X0),
inference(light_normalisation,[status(thm)],[c_9204,c_1202]) ).
tcf(c_9722,plain,
addition(multiplication(sK0(sK2),iPr_def_15),multiplication(iPr_def_15,iPr_def_11)) = sK0(sK2),
inference(superposition,[status(thm)],[c_3575,c_1151]) ).
tcf(c_9735,plain,
addition(multiplication(iPr_def_15,iPr_def_11),multiplication(sK0(sK2),iPr_def_15)) = sK0(sK2),
inference(theory_normalisation,[status(thm)],[c_9722,c_50,c_49]) ).
tcf(c_9736,plain,
sK0(sK2) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_9735,c_6090]) ).
tcf(c_9801,plain,
( complement(iPr_def_15,sK2)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_9736,c_61]) ).
tcf(c_9802,plain,
complement(iPr_def_15,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_9801,c_392]) ).
tcf(c_9803,plain,
( ( c(iPr_def_15) = sK2 )
| ~ test(iPr_def_15) ),
inference(superposition,[status(thm)],[c_9802,c_66]) ).
tcf(c_9806,plain,
c(iPr_def_15) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_9803,c_707]) ).
tcf(c_9828,plain,
multiplication(c(iPr_def_15),iPr_def_14) = multiplication(iPr_def_11,iPr_def_13),
inference(demodulation,[status(thm)],[c_5601,c_9806]) ).
tcf(c_9839,plain,
! [X0: $i] : addition(X0,multiplication(c(iPr_def_15),X0)) = X0,
inference(demodulation,[status(thm)],[c_1224,c_9806]) ).
tcf(c_15701,plain,
multiplication(addition(iPr_def_10,iPr_def_14),multiplication(iPr_def_15,iPr_def_11)) = multiplication(iPr_def_10,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_5590,c_8153]) ).
tcf(c_15702,plain,
multiplication(iPr_def_10,iPr_def_13) = multiplication(iPr_def_15,iPr_def_11),
inference(demodulation,[status(thm)],[c_15701,c_1860,c_1865,c_9211]) ).
tcf(c_15725,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,iPr_def_13),X0) = X0,
inference(demodulation,[status(thm)],[c_1860,c_15702]) ).
tcf(c_16942,plain,
! [X0: $i] : multiplication(c(iPr_def_15),multiplication(iPr_def_15,X0)) = multiplication(iPr_def_10,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_3657,c_15702]) ).
tcf(c_16958,plain,
! [X0: $i] : addition(multiplication(iPr_def_15,X0),multiplication(iPr_def_10,iPr_def_13)) = multiplication(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_16942,c_9839]) ).
tcf(c_16959,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,iPr_def_13),multiplication(iPr_def_15,X0)) = multiplication(iPr_def_15,X0),
inference(theory_normalisation,[status(thm)],[c_16958,c_50,c_49]) ).
tcf(c_17160,plain,
multiplication(iPr_def_10,iPr_def_13) = multiplication(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_15725,c_1201]) ).
tcf(c_17246,plain,
multiplication(c(iPr_def_15),iPr_def_14) = multiplication(iPr_def_10,iPr_def_13),
inference(demodulation,[status(thm)],[c_9828,c_17160]) ).
tcf(c_22129,plain,
addition(multiplication(iPr_def_15,iPr_def_14),multiplication(iPr_def_10,iPr_def_13)) = iPr_def_14,
inference(superposition,[status(thm)],[c_17246,c_4707]) ).
tcf(c_22149,plain,
addition(multiplication(iPr_def_10,iPr_def_13),multiplication(iPr_def_15,iPr_def_14)) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_22129,c_50,c_49]) ).
tcf(c_25248,plain,
multiplication(iPr_def_15,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_22149,c_16959]) ).
tcf(c_25250,plain,
addition(iPr_def_16,iPr_def_14) = iPr_def_16,
inference(demodulation,[status(thm)],[c_5987,c_25248]) ).
tcf(c_25252,plain,
addition(iPr_def_14,iPr_def_16) = iPr_def_16,
inference(theory_normalisation,[status(thm)],[c_25250,c_50,c_49]) ).
tcf(c_25254,plain,
iPr_def_16 = iPr_def_17,
inference(demodulation,[status(thm)],[c_389,c_25252]) ).
tcf(c_25265,plain,
iPr_def_16 != iPr_def_16,
inference(demodulation,[status(thm)],[c_393,c_25254]) ).
tcf(c_25266,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_25265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE023+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.36 % Computer : n001.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Wed Sep 23 18:45:36 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.40 Running first-order theorem proving
% 0.16/0.40 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
% 0.16/0.42
% 0.16/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.42
% 0.16/0.42 % Detected problem language: tptp
% 0.16/0.43 % Proving...
% 17.79/3.77 % SZS status Started for theBenchmark.p
% 17.79/3.77 % SZS status Theorem for theBenchmark.p
% 17.79/3.77
% 17.79/3.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.79/3.77
% 17.79/3.77 % ------ iProver source info
% 17.79/3.77
% 17.79/3.77 % git: date: 2026-07-19 20:42:38 +0200
% 17.79/3.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.79/3.77 % git: non_committed_changes: false
% 17.79/3.77
% 17.79/3.77 % ------ Parsing...
% 17.79/3.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.79/3.77
% 17.79/3.77 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 17.79/3.77
% 17.79/3.77 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.79/3.77
% 17.79/3.77 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.79/3.77 % ------ Proving...
% 17.79/3.77 % ------ Problem Properties
% 17.79/3.77
% 17.79/3.77 %
% 17.79/3.77 % clauses 34
% 17.79/3.77 % conjectures 4
% 17.79/3.77 % EPR 5
% 17.79/3.77 % Horn 33
% 17.79/3.77 % unary 23
% 17.79/3.77 % binary 7
% 17.79/3.77 % lits 50
% 17.79/3.77 % lits eq 31
% 17.79/3.77 % fd_pure 0
% 17.79/3.77 % fd_pseudo 0
% 17.79/3.77 % fd_cond 0
% 17.79/3.77 % fd_pseudo_cond 1
% 17.79/3.77 % AC symbols 1
% 17.79/3.77
% 17.79/3.77 % ------ Schedule dynamic 5 is on
% 17.79/3.77
% 17.79/3.77 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.79/3.77
% 17.79/3.77
% 17.79/3.77 % ------
% 17.79/3.77 % Current options:
% 17.79/3.77 % ------
% 17.79/3.77
% 17.79/3.77
% 17.79/3.77 %
% 17.79/3.77
% 17.79/3.77 % ------ Proving...
% 17.79/3.77 %
% 17.79/3.77
% 17.79/3.77 % SZS status Theorem for theBenchmark.p
% 17.79/3.77
% 17.79/3.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.79/3.77
% 17.79/3.77
%------------------------------------------------------------------------------