%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE010+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 : n020.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 01:52:07 PM UTC 2026
% Result : Theorem 29.25s 9.84s
% Output : CNFRefutation 29.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 20
% Syntax : Number of formulae : 133 ( 86 unt; 8 def)
% Number of atoms : 360 ( 110 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 168 ( 75 ~; 62 |; 22 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 128 ( 0 sgn 121 !; 7 ?; 47 :)
% 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(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
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(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
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(f17,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& ( ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f24,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& ( ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f26,plain,
! [X0] :
( ( ~ test(X0)
| ? [X2] : complement(X2,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(rectify,[],[f25]) ).
fof(f27,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))],[f26]) ).
fof(f28,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(f29,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,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f31,plain,
( test(sK1)
& test(sK2)
& ( ~ leq(addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f24]) ).
fof(f32,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f33,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f35,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f38,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f40,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f43,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f45,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| test(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f29]) ).
fof(f47,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f48,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f49,plain,
! [X0,X1] :
( addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| complement(X1,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f50,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X0,X1] :
( ~ test(X0)
| ~ complement(X0,X1)
| c(X0) = X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
test(sK1),
inference(cnf_transformation,[],[f31]) ).
fof(f54,plain,
test(sK2),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
( ~ leq(addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2)))) ),
inference(cnf_transformation,[],[f31]) ).
fof(f56,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f50]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f32]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f37]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f38]) ).
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,[],[f39]) ).
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,[],[f40]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( test(X1)
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( complement(X1,X0)
| ( multiplication(X1,X0) != zero )
| ( multiplication(X0,X1) != zero )
| ( addition(X0,X1) != one ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( multiplication(X1,X0) = zero )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( multiplication(X0,X1) = zero )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( c(X0) = X1 )
| ~ test(X0)
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_68,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_70,negated_conjecture,
( ~ leq(one,addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))))
| ~ leq(addition(addition(addition(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),multiplication(sK1,sK2)),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),one) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_71,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f54]) ).
tcf(c_72,negated_conjecture,
test(sK1),
inference(cnf_transformation,[],[f53]) ).
tcf(c_91,negated_conjecture,
( ~ leq(one,addition(multiplication(sK2,sK1),addition(multiplication(sK1,sK2),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2)))))))
| ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(sK1,sK2),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2)))))),one) ),
inference(theory_normalisation,[status(thm)],[c_70,c_50,c_49]) ).
tcf(c_212,plain,
( ~ leq(one,addition(multiplication(sK2,sK1),addition(multiplication(sK1,sK2),addition(multiplication(c(sK2),sK1),multiplication(c(sK1),addition(c(sK2),sK2))))))
| ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(sK1,sK2),addition(multiplication(c(sK2),sK1),multiplication(c(sK1),addition(c(sK2),sK2))))),one) ),
inference(ac_demodulation,[status(thm)],[c_91,c_56,c_56,c_50,c_49]) ).
tcf(c_213,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(c(sK1),addition(c(sK2),sK2)),multiplication(addition(c(sK2),sK2),sK1))))
| ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(c(sK1),addition(c(sK2),sK2)),multiplication(addition(c(sK2),sK2),sK1))),one) ),
inference(ac_demodulation,[status(thm)],[c_212,c_57,c_57,c_50,c_49]) ).
tcf(c_214,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(c(sK1),addition(sK2,c(sK2))))))
| ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(c(sK1),addition(sK2,c(sK2))))),one) ),
inference(theory_normalisation,[status(thm)],[c_213,c_50,c_49]) ).
tcf(c_492,definition,
iPr_def_10 = multiplication(sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_493,definition,
iPr_def_11 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_494,definition,
iPr_def_12 = addition(sK2,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_495,definition,
iPr_def_13 = multiplication(iPr_def_12,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_496,definition,
iPr_def_14 = c(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_497,definition,
iPr_def_15 = multiplication(iPr_def_14,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_498,definition,
iPr_def_16 = addition(iPr_def_13,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_499,definition,
iPr_def_17 = addition(iPr_def_10,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_500,plain,
( ~ leq(iPr_def_17,one)
| ~ leq(one,iPr_def_17) ),
inference(demodulation,[status(thm)],[c_214,c_496,c_497,c_493,c_494,c_495,c_498,c_492,c_499]) ).
tcf(c_501,negated_conjecture,
test(sK1),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_502,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_808,plain,
addition(iPr_def_11,sK2) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_494,c_50,c_49]) ).
tcf(c_822,plain,
complement(sK2,c(sK2)),
inference(superposition,[status(thm)],[c_502,c_68]) ).
tcf(c_823,plain,
complement(sK1,c(sK1)),
inference(superposition,[status(thm)],[c_501,c_68]) ).
tcf(c_824,plain,
complement(sK1,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_823,c_496]) ).
tcf(c_825,plain,
complement(sK2,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_822,c_493]) ).
tcf(c_827,plain,
test(iPr_def_11),
inference(superposition,[status(thm)],[c_825,c_61]) ).
tcf(c_867,plain,
multiplication(iPr_def_14,sK1) = zero,
inference(superposition,[status(thm)],[c_824,c_64]) ).
tcf(c_868,plain,
multiplication(iPr_def_11,sK2) = zero,
inference(superposition,[status(thm)],[c_825,c_64]) ).
tcf(c_876,plain,
multiplication(sK1,iPr_def_14) = zero,
inference(superposition,[status(thm)],[c_824,c_65]) ).
tcf(c_877,plain,
multiplication(sK2,iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_825,c_65]) ).
tcf(c_891,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_918,plain,
addition(iPr_def_14,sK1) = one,
inference(superposition,[status(thm)],[c_824,c_66]) ).
tcf(c_919,plain,
addition(iPr_def_11,sK2) = one,
inference(superposition,[status(thm)],[c_825,c_66]) ).
tcf(c_922,plain,
one = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_919,c_808]) ).
tcf(c_928,plain,
! [X0: $i] : multiplication(iPr_def_12,X0) = X0,
inference(demodulation,[status(thm)],[c_55,c_922]) ).
tcf(c_929,plain,
! [X0: $i] : multiplication(X0,iPr_def_12) = X0,
inference(demodulation,[status(thm)],[c_54,c_922]) ).
tcf(c_930,plain,
( ~ leq(iPr_def_17,iPr_def_12)
| ~ leq(iPr_def_12,iPr_def_17) ),
inference(demodulation,[status(thm)],[c_500,c_922]) ).
tcf(c_933,plain,
iPr_def_14 = iPr_def_15,
inference(demodulation,[status(thm)],[c_497,c_929]) ).
tcf(c_934,plain,
addition(iPr_def_13,iPr_def_14) = iPr_def_16,
inference(demodulation,[status(thm)],[c_498,c_933]) ).
tcf(c_935,plain,
sK1 = iPr_def_13,
inference(demodulation,[status(thm)],[c_495,c_928]) ).
tcf(c_936,plain,
multiplication(iPr_def_13,iPr_def_14) = zero,
inference(demodulation,[status(thm)],[c_876,c_935]) ).
tcf(c_937,plain,
multiplication(iPr_def_14,iPr_def_13) = zero,
inference(demodulation,[status(thm)],[c_867,c_935]) ).
tcf(c_939,plain,
multiplication(iPr_def_13,sK2) = iPr_def_10,
inference(demodulation,[status(thm)],[c_492,c_935]) ).
tcf(c_944,plain,
multiplication(sK2,iPr_def_11) = multiplication(iPr_def_14,iPr_def_13),
inference(demodulation,[status(thm)],[c_877,c_937]) ).
tcf(c_945,plain,
multiplication(iPr_def_11,sK2) = multiplication(iPr_def_14,iPr_def_13),
inference(demodulation,[status(thm)],[c_868,c_937]) ).
tcf(c_1023,plain,
addition(iPr_def_14,iPr_def_13) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_918,c_922,c_935]) ).
tcf(c_1024,plain,
iPr_def_12 = iPr_def_16,
inference(demodulation,[status(thm)],[c_1023,c_49,c_934]) ).
tcf(c_1025,plain,
addition(iPr_def_10,iPr_def_12) = iPr_def_17,
inference(demodulation,[status(thm)],[c_499,c_1024]) ).
tcf(c_1026,plain,
multiplication(iPr_def_13,iPr_def_14) = multiplication(iPr_def_14,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_937,c_936]) ).
tcf(c_1029,plain,
multiplication(sK2,iPr_def_11) = multiplication(iPr_def_13,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_944,c_1026]) ).
tcf(c_1033,plain,
multiplication(iPr_def_11,sK2) = multiplication(iPr_def_13,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_945,c_1026]) ).
tcf(c_1068,plain,
! [X0: $i,X1: $i] :
( complement(X1,X0)
| ( multiplication(X1,X0) != multiplication(iPr_def_13,iPr_def_14) )
| ( multiplication(X0,X1) != multiplication(iPr_def_13,iPr_def_14) )
| ( addition(X0,X1) != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_63,c_922,c_936]) ).
tcf(c_1085,plain,
( complement(iPr_def_11,sK2)
| ( multiplication(iPr_def_11,sK2) != multiplication(iPr_def_13,iPr_def_14) )
| ( addition(sK2,iPr_def_11) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_1029,c_1068]) ).
tcf(c_1091,plain,
( complement(iPr_def_11,sK2)
| ( multiplication(iPr_def_11,sK2) != multiplication(iPr_def_13,iPr_def_14) )
| ( addition(iPr_def_11,sK2) != iPr_def_12 ) ),
inference(theory_normalisation,[status(thm)],[c_1085,c_50,c_49]) ).
tcf(c_1092,plain,
complement(iPr_def_11,sK2),
inference(ground_joinability,[status(thm)],[c_1091,c_808,c_1033]) ).
tcf(c_1125,plain,
( ( c(iPr_def_11) = sK2 )
| ~ test(iPr_def_11) ),
inference(superposition,[status(thm)],[c_1092,c_67]) ).
tcf(c_1127,plain,
c(iPr_def_11) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_1125,c_827]) ).
tcf(c_1133,plain,
addition(iPr_def_11,c(iPr_def_11)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_808,c_1127]) ).
tcf(c_1158,plain,
! [X0: $i] : addition(iPr_def_11,addition(c(iPr_def_11),X0)) = addition(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_1133,c_50]) ).
tcf(c_1228,plain,
addition(iPr_def_13,iPr_def_14) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_934,c_1024]) ).
tcf(c_1234,plain,
! [X0: $i] : addition(multiplication(iPr_def_13,X0),multiplication(iPr_def_14,X0)) = multiplication(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_1228,c_57]) ).
tcf(c_1237,plain,
! [X0: $i] : addition(multiplication(iPr_def_13,X0),multiplication(iPr_def_14,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1234,c_928]) ).
tcf(c_1271,plain,
multiplication(iPr_def_13,c(iPr_def_11)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_939,c_1127]) ).
tcf(c_1461,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_891,c_60]) ).
tcf(c_1477,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_1461]) ).
tcf(c_1480,plain,
! [X0: $i,X1: $i,X2: $i] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(superposition,[status(thm)],[c_50,c_1461]) ).
tcf(c_1521,plain,
leq(iPr_def_12,iPr_def_17),
inference(superposition,[status(thm)],[c_1025,c_1477]) ).
tcf(c_1524,plain,
~ leq(iPr_def_17,iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_930,c_1521]) ).
tcf(c_1773,plain,
! [X0: $i,X1: $i] : leq(addition(X0,multiplication(iPr_def_13,X1)),addition(X0,X1)),
inference(superposition,[status(thm)],[c_1237,c_1480]) ).
tcf(c_75918,plain,
addition(iPr_def_11,c(iPr_def_11)) = addition(iPr_def_12,c(iPr_def_11)),
inference(superposition,[status(thm)],[c_52,c_1158]) ).
tcf(c_76324,plain,
addition(iPr_def_12,c(iPr_def_11)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_75918,c_1133]) ).
tcf(c_77279,plain,
leq(addition(iPr_def_12,multiplication(iPr_def_13,c(iPr_def_11))),iPr_def_12),
inference(superposition,[status(thm)],[c_76324,c_1773]) ).
tcf(c_77517,plain,
leq(addition(iPr_def_12,iPr_def_10),iPr_def_12),
inference(light_normalisation,[status(thm)],[c_77279,c_1271]) ).
tcf(c_77518,plain,
leq(addition(iPr_def_10,iPr_def_12),iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_77517,c_50,c_49]) ).
tcf(c_77519,plain,
leq(iPr_def_17,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_77518,c_1025]) ).
tcf(c_77520,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_77519,c_1524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n020.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Wed Sep 23 18:36:11 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.42 Running first-order theorem proving
% 0.16/5.42 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
% 0.16/5.43
% 0.16/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.43
% 0.16/5.43 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 29.25/9.84 % SZS status Started for theBenchmark.p
% 29.25/9.84 % SZS status Theorem for theBenchmark.p
% 29.25/9.84
% 29.25/9.84 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 29.25/9.84
% 29.25/9.84 % ------ iProver source info
% 29.25/9.84
% 29.25/9.84 % git: date: 2026-07-19 20:42:38 +0200
% 29.25/9.84 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 29.25/9.84 % git: non_committed_changes: false
% 29.25/9.84
% 29.25/9.84 % ------ Parsing...
% 29.25/9.84 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 29.25/9.84
% 29.25/9.84 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 29.25/9.84
% 29.25/9.84 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 29.25/9.84
% 29.25/9.84 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 29.25/9.84 % ------ Proving...
% 29.25/9.84 % ------ Problem Properties
% 29.25/9.84
% 29.25/9.84 %
% 29.25/9.84 % clauses 32
% 29.25/9.84 % conjectures 2
% 29.25/9.84 % EPR 4
% 29.25/9.84 % Horn 31
% 29.25/9.84 % unary 21
% 29.25/9.84 % binary 9
% 29.25/9.84 % lits 46
% 29.25/9.84 % lits eq 28
% 29.25/9.84 % fd_pure 0
% 29.25/9.84 % fd_pseudo 0
% 29.25/9.84 % fd_cond 0
% 29.25/9.84 % fd_pseudo_cond 1
% 29.25/9.84 % AC symbols 1
% 29.25/9.84
% 29.25/9.84 % ------ Schedule dynamic 5 is on
% 29.25/9.84
% 29.25/9.84 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 29.25/9.84
% 29.25/9.84
% 29.25/9.84 % ------
% 29.25/9.84 % Current options:
% 29.25/9.84 % ------
% 29.25/9.84
% 29.25/9.84
% 29.25/9.84 %
% 29.25/9.84
% 29.25/9.84 % ------ Proving...
% 29.25/9.84 %
% 29.25/9.84
% 29.25/9.84 % SZS status Theorem for theBenchmark.p
% 29.25/9.84
% 29.25/9.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 29.25/9.84
% 29.25/9.84
%------------------------------------------------------------------------------