%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE010+4 : 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 : n015.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 01:52:08 PM UTC 2026
% Result : Theorem 10.78s 2.26s
% Output : CNFRefutation 10.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 20
% Syntax : Number of formulae : 126 ( 84 unt; 8 def)
% Number of atoms : 316 ( 95 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 140 ( 62 ~; 47 |; 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 : 110 ( 0 sgn 103 !; 7 ?; 38 :)
% 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(f19,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(f20,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)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f22,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f29,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,[],[f20]) ).
fof(f30,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,[],[f29]) ).
fof(f31,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f32,plain,
! [X0] :
( ( ~ test(X0)
| ? [X2] : complement(X2,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(rectify,[],[f31]) ).
fof(f33,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))],[f32]) ).
fof(f34,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(f35,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,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f37,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)],[f30]) ).
fof(f38,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f39,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f41,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f43,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f45,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f46,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f49,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f50,plain,
! [X0] :
( ~ test(X0)
| complement(sK0(X0),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f52,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f35]) ).
fof(f56,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f61,plain,
test(sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f62,plain,
test(sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f63,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,[],[f37]) ).
fof(f64,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f56]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f38]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f39]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f41]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f43]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f44]) ).
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,[],[f45]) ).
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,[],[f46]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_62,plain,
! [X0: $i] :
( complement(sK0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_68,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_72,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,[],[f63]) ).
tcf(c_73,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f62]) ).
tcf(c_74,negated_conjecture,
test(sK1),
inference(cnf_transformation,[],[f61]) ).
tcf(c_95,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_72,c_50,c_49]) ).
tcf(c_240,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_95,c_56,c_56,c_50,c_49]) ).
tcf(c_241,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_240,c_57,c_57,c_50,c_49]) ).
tcf(c_242,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_241,c_50,c_49]) ).
tcf(c_401,definition,
iPr_def_10 = multiplication(sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_402,definition,
iPr_def_11 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_403,definition,
iPr_def_12 = addition(sK2,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_404,definition,
iPr_def_13 = multiplication(iPr_def_12,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_405,definition,
iPr_def_14 = c(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_406,definition,
iPr_def_15 = multiplication(iPr_def_14,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_407,definition,
iPr_def_16 = addition(iPr_def_13,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_408,definition,
iPr_def_17 = addition(iPr_def_10,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_409,plain,
( ~ leq(iPr_def_17,one)
| ~ leq(one,iPr_def_17) ),
inference(demodulation,[status(thm)],[c_242,c_405,c_406,c_402,c_403,c_404,c_407,c_401,c_408]) ).
tcf(c_410,negated_conjecture,
test(sK1),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_411,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_741,plain,
addition(iPr_def_11,sK2) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_403,c_50,c_49]) ).
tcf(c_755,plain,
( complement(sK2,iPr_def_11)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_402,c_68]) ).
tcf(c_756,plain,
( complement(sK1,iPr_def_14)
| ~ test(sK1) ),
inference(superposition,[status(thm)],[c_405,c_68]) ).
tcf(c_760,plain,
complement(sK1,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_756,c_410]) ).
tcf(c_761,plain,
complement(sK2,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_755,c_411]) ).
tcf(c_846,plain,
addition(iPr_def_11,sK2) = one,
inference(superposition,[status(thm)],[c_761,c_66]) ).
tcf(c_847,plain,
addition(iPr_def_14,sK1) = one,
inference(superposition,[status(thm)],[c_760,c_66]) ).
tcf(c_848,plain,
one = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_846,c_741]) ).
tcf(c_855,plain,
! [X0: $i] : multiplication(iPr_def_12,X0) = X0,
inference(demodulation,[status(thm)],[c_55,c_848]) ).
tcf(c_856,plain,
! [X0: $i] : multiplication(X0,iPr_def_12) = X0,
inference(demodulation,[status(thm)],[c_54,c_848]) ).
tcf(c_857,plain,
( ~ leq(iPr_def_17,iPr_def_12)
| ~ leq(iPr_def_12,iPr_def_17) ),
inference(demodulation,[status(thm)],[c_409,c_848]) ).
tcf(c_860,plain,
iPr_def_14 = iPr_def_15,
inference(demodulation,[status(thm)],[c_406,c_856]) ).
tcf(c_862,plain,
addition(iPr_def_13,iPr_def_14) = iPr_def_16,
inference(demodulation,[status(thm)],[c_407,c_860]) ).
tcf(c_865,plain,
sK1 = iPr_def_13,
inference(demodulation,[status(thm)],[c_404,c_855]) ).
tcf(c_909,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_959,plain,
addition(iPr_def_14,iPr_def_13) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_847,c_848,c_865]) ).
tcf(c_960,plain,
iPr_def_12 = iPr_def_16,
inference(demodulation,[status(thm)],[c_959,c_49,c_862]) ).
tcf(c_962,plain,
addition(iPr_def_10,iPr_def_12) = iPr_def_17,
inference(demodulation,[status(thm)],[c_408,c_960]) ).
tcf(c_1604,plain,
! [X0: $i] : leq(X0,X0),
inference(superposition,[status(thm)],[c_52,c_60]) ).
tcf(c_2798,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_909,c_60]) ).
tcf(c_2822,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_2798]) ).
tcf(c_2915,plain,
leq(iPr_def_12,iPr_def_17),
inference(superposition,[status(thm)],[c_962,c_2822]) ).
tcf(c_16022,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_16035,plain,
addition(iPr_def_11,sK2) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_403,c_50,c_49]) ).
tcf(c_16036,plain,
! [X0: $i] : addition(iPr_def_11,addition(sK2,X0)) = addition(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_16035,c_50]) ).
tcf(c_16051,plain,
( complement(sK2,iPr_def_11)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_402,c_68]) ).
tcf(c_16052,plain,
( complement(sK1,iPr_def_14)
| ~ test(sK1) ),
inference(superposition,[status(thm)],[c_405,c_68]) ).
tcf(c_16056,plain,
complement(sK1,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_16052,c_410]) ).
tcf(c_16057,plain,
complement(sK2,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_16051,c_411]) ).
tcf(c_16154,plain,
! [X0: $i] :
( ( addition(X0,sK0(X0)) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_62,c_66]) ).
tcf(c_16156,plain,
addition(iPr_def_11,sK2) = one,
inference(superposition,[status(thm)],[c_16057,c_66]) ).
tcf(c_16157,plain,
addition(iPr_def_14,sK1) = one,
inference(superposition,[status(thm)],[c_16056,c_66]) ).
tcf(c_16158,plain,
one = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_16156,c_16035]) ).
tcf(c_16165,plain,
! [X0: $i] : multiplication(iPr_def_12,X0) = X0,
inference(demodulation,[status(thm)],[c_55,c_16158]) ).
tcf(c_16166,plain,
! [X0: $i] : multiplication(X0,iPr_def_12) = X0,
inference(demodulation,[status(thm)],[c_54,c_16158]) ).
tcf(c_16167,plain,
( ~ leq(iPr_def_17,iPr_def_12)
| ~ leq(iPr_def_12,iPr_def_17) ),
inference(demodulation,[status(thm)],[c_409,c_16158]) ).
tcf(c_16170,plain,
iPr_def_14 = iPr_def_15,
inference(demodulation,[status(thm)],[c_406,c_16166]) ).
tcf(c_16172,plain,
addition(iPr_def_13,iPr_def_14) = iPr_def_16,
inference(demodulation,[status(thm)],[c_407,c_16170]) ).
tcf(c_16175,plain,
sK1 = iPr_def_13,
inference(demodulation,[status(thm)],[c_404,c_16165]) ).
tcf(c_16179,plain,
multiplication(iPr_def_13,sK2) = iPr_def_10,
inference(demodulation,[status(thm)],[c_401,c_16175]) ).
tcf(c_16181,plain,
test(iPr_def_13),
inference(demodulation,[status(thm)],[c_410,c_16175]) ).
tcf(c_16241,plain,
addition(iPr_def_14,iPr_def_13) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_16157,c_16158,c_16175]) ).
tcf(c_16242,plain,
iPr_def_12 = iPr_def_16,
inference(demodulation,[status(thm)],[c_16241,c_49,c_16172]) ).
tcf(c_16244,plain,
addition(iPr_def_10,iPr_def_12) = iPr_def_17,
inference(demodulation,[status(thm)],[c_408,c_16242]) ).
tcf(c_16526,plain,
~ leq(iPr_def_17,iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_16167,c_857,c_2915]) ).
tcf(c_16936,plain,
! [X0: $i] :
( ( addition(X0,sK0(X0)) = iPr_def_12 )
| ~ test(X0) ),
inference(light_normalisation,[status(thm)],[c_16154,c_16158]) ).
tcf(c_16948,plain,
addition(iPr_def_13,sK0(iPr_def_13)) = iPr_def_12,
inference(superposition,[status(thm)],[c_16181,c_16936]) ).
tcf(c_17034,plain,
addition(iPr_def_13,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_16948,c_16022]) ).
tcf(c_17044,plain,
addition(iPr_def_12,iPr_def_13) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_17034,c_50,c_49]) ).
tcf(c_17337,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)) = multiplication(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_17044,c_57]) ).
tcf(c_17343,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_13,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_17337,c_16165]) ).
tcf(c_19346,plain,
addition(iPr_def_12,multiplication(iPr_def_13,sK2)) = addition(iPr_def_11,sK2),
inference(superposition,[status(thm)],[c_17343,c_16036]) ).
tcf(c_19350,plain,
addition(iPr_def_12,iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_19346,c_16035,c_16179]) ).
tcf(c_19351,plain,
addition(iPr_def_10,iPr_def_12) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_19350,c_50,c_49]) ).
tcf(c_19357,plain,
iPr_def_12 = iPr_def_17,
inference(demodulation,[status(thm)],[c_16244,c_19351]) ).
tcf(c_19362,plain,
~ leq(iPr_def_12,iPr_def_12),
inference(demodulation,[status(thm)],[c_16526,c_19357]) ).
tcf(c_19365,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_19362,c_1604]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE010+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 18:37:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 10.78/2.26 % SZS status Started for theBenchmark.p
% 10.78/2.26 % SZS status Theorem for theBenchmark.p
% 10.78/2.26
% 10.78/2.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.78/2.26
% 10.78/2.26 % ------ iProver source info
% 10.78/2.26
% 10.78/2.26 % git: date: 2026-07-19 20:42:38 +0200
% 10.78/2.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.78/2.26 % git: non_committed_changes: false
% 10.78/2.26
% 10.78/2.26 % ------ Parsing...
% 10.78/2.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.78/2.26
% 10.78/2.26 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 10.78/2.26
% 10.78/2.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.78/2.26
% 10.78/2.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.78/2.26 % ------ Proving...
% 10.78/2.26 % ------ Problem Properties
% 10.78/2.26
% 10.78/2.26 %
% 10.78/2.26 % clauses 34
% 10.78/2.26 % conjectures 2
% 10.78/2.26 % EPR 4
% 10.78/2.26 % Horn 33
% 10.78/2.26 % unary 21
% 10.78/2.26 % binary 9
% 10.78/2.26 % lits 52
% 10.78/2.26 % lits eq 30
% 10.78/2.26 % fd_pure 0
% 10.78/2.26 % fd_pseudo 0
% 10.78/2.26 % fd_cond 0
% 10.78/2.26 % fd_pseudo_cond 1
% 10.78/2.26 % AC symbols 1
% 10.78/2.26
% 10.78/2.26 % ------ Schedule dynamic 5 is on
% 10.78/2.26
% 10.78/2.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.78/2.26
% 10.78/2.26
% 10.78/2.26 % ------
% 10.78/2.26 % Current options:
% 10.78/2.26 % ------
% 10.78/2.26
% 10.78/2.26
% 10.78/2.26 %
% 10.78/2.26
% 10.78/2.26 % ------ Proving...
% 10.78/2.26 %
% 10.78/2.26
% 10.78/2.26 % SZS status Theorem for theBenchmark.p
% 10.78/2.26
% 10.78/2.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.78/2.26
% 10.78/2.26
%------------------------------------------------------------------------------