%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE027+3 : 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 : n014.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 01:52:13 PM UTC 2026
% Result : Theorem 4.92s 7.59s
% Output : CNFRefutation 4.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 21
% Syntax : Number of formulae : 115 ( 80 unt; 8 def)
% Number of atoms : 305 ( 120 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 133 ( 57 ~; 49 |; 20 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 143 ( 0 sgn 130 !; 13 ?; 50 :)
% 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(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] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f19,conjecture,
! [X0,X1,X2,X3,X4] :
( ( test(X4)
& test(X3) )
=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( test(X4)
& test(X3) )
=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
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,X3,X4] :
( test(X4)
& test(X3)
& addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) != addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f28,plain,
? [X0,X1,X2,X3,X4] :
( test(X4)
& test(X3)
& addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) != addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
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(sK5)
& test(sK4)
& addition(multiplication(sK4,addition(multiplication(sK4,sK1),multiplication(c(sK4),sK2))),multiplication(c(sK4),sK3)) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4),skolemize(X4,sK5)],[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(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(f46,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
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(f52,plain,
! [X0,X1] :
( addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| complement(X1,X0) ),
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(f59,plain,
test(sK4),
inference(cnf_transformation,[],[f35]) ).
fof(f60,plain,
addition(multiplication(sK4,addition(multiplication(sK4,sK1),multiplication(c(sK4),sK2))),multiplication(c(sK4),sK3)) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3)),
inference(cnf_transformation,[],[f35]) ).
fof(f61,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_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_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_62,plain,
! [X0: $i,X1: $i] :
( complement(X1,X0)
| ( multiplication(X1,X0) != zero )
| ( multiplication(X0,X1) != zero )
| ( addition(X0,X1) != one ) ),
inference(cnf_transformation,[],[f52]) ).
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,[],[f61]) ).
tcf(c_71,negated_conjecture,
addition(multiplication(sK4,addition(multiplication(sK4,sK1),multiplication(c(sK4),sK2))),multiplication(c(sK4),sK3)) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3)),
inference(cnf_transformation,[],[f60]) ).
tcf(c_72,negated_conjecture,
test(sK4),
inference(cnf_transformation,[],[f59]) ).
tcf(c_92,negated_conjecture,
addition(multiplication(c(sK4),sK3),multiplication(sK4,addition(multiplication(sK4,sK1),multiplication(c(sK4),sK2)))) != addition(multiplication(sK4,sK1),multiplication(c(sK4),sK3)),
inference(theory_normalisation,[status(thm)],[c_71,c_50,c_49]) ).
tcf(c_379,definition,
iPr_def_10 = c(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_380,definition,
iPr_def_11 = multiplication(iPr_def_10,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_381,definition,
iPr_def_12 = multiplication(sK4,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_382,definition,
iPr_def_13 = multiplication(iPr_def_10,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_383,definition,
iPr_def_14 = addition(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_384,definition,
iPr_def_15 = multiplication(sK4,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_385,definition,
iPr_def_16 = addition(iPr_def_11,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_386,definition,
iPr_def_17 = addition(iPr_def_12,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_387,negated_conjecture,
iPr_def_16 != iPr_def_17,
inference(demodulation,[status(thm)],[c_92,c_386,c_382,c_381,c_383,c_384,c_379,c_380,c_385]) ).
tcf(c_389,negated_conjecture,
test(sK4),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_681,plain,
addition(iPr_def_11,iPr_def_12) = iPr_def_17,
inference(theory_normalisation,[status(thm)],[c_386,c_50,c_49]) ).
tcf(c_691,plain,
( complement(sK4,iPr_def_10)
| ~ test(sK4) ),
inference(superposition,[status(thm)],[c_379,c_67]) ).
tcf(c_695,plain,
complement(sK4,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_691,c_389]) ).
tcf(c_696,plain,
test(iPr_def_10),
inference(superposition,[status(thm)],[c_695,c_60]) ).
tcf(c_706,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_738,plain,
multiplication(iPr_def_10,sK4) = zero,
inference(superposition,[status(thm)],[c_695,c_63]) ).
tcf(c_749,plain,
multiplication(sK4,iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_695,c_64]) ).
tcf(c_760,plain,
addition(iPr_def_10,sK4) = one,
inference(superposition,[status(thm)],[c_695,c_65]) ).
tcf(c_976,plain,
! [X0: $i] : multiplication(sK4,multiplication(iPr_def_14,X0)) = multiplication(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_384,c_53]) ).
tcf(c_977,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(sK4,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_738,c_53]) ).
tcf(c_978,plain,
! [X0: $i] : multiplication(sK4,multiplication(iPr_def_10,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_749,c_53]) ).
tcf(c_981,plain,
! [X0: $i] : multiplication(sK4,multiplication(iPr_def_10,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_978,c_59]) ).
tcf(c_982,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(sK4,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_977,c_59]) ).
tcf(c_1118,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0)) = multiplication(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_383,c_57]) ).
tcf(c_1122,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(sK4,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_760,c_57]) ).
tcf(c_1143,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(sK4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1122,c_55]) ).
tcf(c_1191,plain,
multiplication(sK4,iPr_def_13) = zero,
inference(superposition,[status(thm)],[c_382,c_981]) ).
tcf(c_1223,plain,
multiplication(iPr_def_10,iPr_def_12) = zero,
inference(superposition,[status(thm)],[c_381,c_982]) ).
tcf(c_1232,plain,
multiplication(sK4,iPr_def_10) = multiplication(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_749,c_1223]) ).
tcf(c_1233,plain,
multiplication(iPr_def_10,sK4) = multiplication(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_738,c_1223]) ).
tcf(c_1234,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,iPr_def_12),X0) = X0,
inference(demodulation,[status(thm)],[c_706,c_1223]) ).
tcf(c_1238,plain,
! [X0: $i] : multiplication(multiplication(iPr_def_10,iPr_def_12),X0) = multiplication(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_59,c_1223]) ).
tcf(c_1240,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_10,iPr_def_12)) = X0,
inference(demodulation,[status(thm)],[c_51,c_1223]) ).
tcf(c_1436,plain,
! [X0: $i,X1: $i] :
( complement(X1,X0)
| ( multiplication(X1,X0) != multiplication(iPr_def_10,iPr_def_12) )
| ( multiplication(X0,X1) != multiplication(iPr_def_10,iPr_def_12) )
| ( addition(X0,X1) != one ) ),
inference(light_normalisation,[status(thm)],[c_62,c_1223]) ).
tcf(c_1457,plain,
( complement(iPr_def_10,sK4)
| ( multiplication(sK4,iPr_def_10) != multiplication(iPr_def_10,iPr_def_12) )
| ( addition(sK4,iPr_def_10) != one ) ),
inference(superposition,[status(thm)],[c_1233,c_1436]) ).
tcf(c_1465,plain,
( complement(iPr_def_10,sK4)
| ( multiplication(sK4,iPr_def_10) != multiplication(iPr_def_10,iPr_def_12) )
| ( addition(iPr_def_10,sK4) != one ) ),
inference(theory_normalisation,[status(thm)],[c_1457,c_50,c_49]) ).
tcf(c_1466,plain,
complement(iPr_def_10,sK4),
inference(ground_joinability,[status(thm)],[c_1465,c_760,c_1232]) ).
tcf(c_1535,plain,
multiplication(sK4,iPr_def_13) = multiplication(iPr_def_10,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_1191,c_1223]) ).
tcf(c_1557,plain,
( ( c(iPr_def_10) = sK4 )
| ~ test(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1466,c_66]) ).
tcf(c_1561,plain,
c(iPr_def_10) = sK4,
inference(forward_subsumption_resolution,[status(thm)],[c_1557,c_696]) ).
tcf(c_1563,plain,
multiplication(c(iPr_def_10),iPr_def_13) = multiplication(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_1535,c_1561]) ).
tcf(c_1565,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(c(iPr_def_10),X0)) = X0,
inference(demodulation,[status(thm)],[c_1143,c_1561]) ).
tcf(c_2964,plain,
! [X0: $i] : multiplication(c(iPr_def_10),multiplication(iPr_def_13,X0)) = multiplication(multiplication(iPr_def_10,iPr_def_12),X0),
inference(superposition,[status(thm)],[c_1563,c_53]) ).
tcf(c_2966,plain,
! [X0: $i] : multiplication(c(iPr_def_10),multiplication(iPr_def_13,X0)) = multiplication(iPr_def_10,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_2964,c_1238]) ).
tcf(c_5464,plain,
! [X0: $i] : multiplication(c(iPr_def_10),addition(multiplication(iPr_def_12,X0),multiplication(iPr_def_13,X0))) = multiplication(iPr_def_15,X0),
inference(light_normalisation,[status(thm)],[c_976,c_1118,c_1561]) ).
tcf(c_5465,plain,
! [X0: $i] : multiplication(c(iPr_def_10),multiplication(iPr_def_12,X0)) = multiplication(iPr_def_15,X0),
inference(demodulation,[status(thm)],[c_5464,c_56,c_1240,c_2966]) ).
tcf(c_5466,plain,
multiplication(c(iPr_def_10),iPr_def_12) = multiplication(iPr_def_15,one),
inference(superposition,[status(thm)],[c_54,c_5465]) ).
tcf(c_5479,plain,
multiplication(c(iPr_def_10),iPr_def_12) = iPr_def_15,
inference(demodulation,[status(thm)],[c_5466,c_54]) ).
tcf(c_11484,plain,
multiplication(c(iPr_def_10),iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_1565,c_1234]) ).
tcf(c_11506,plain,
iPr_def_12 = iPr_def_15,
inference(demodulation,[status(thm)],[c_5479,c_11484]) ).
tcf(c_11522,plain,
addition(iPr_def_11,iPr_def_12) = iPr_def_16,
inference(demodulation,[status(thm)],[c_385,c_11506]) ).
tcf(c_11523,plain,
iPr_def_16 = iPr_def_17,
inference(demodulation,[status(thm)],[c_681,c_11522]) ).
tcf(c_11524,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11523,c_387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE027+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.62 % Computer : n014.cluster.edu
% 0.16/5.62 % Model : x86_64 x86_64
% 0.16/5.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.62 % Memory : 8046.5625MB
% 0.16/5.62 % OS : Linux 6.8.0-71-generic
% 0.16/5.62 % CPULimit : 300
% 0.16/5.62 % WCLimit : 300
% 0.16/5.62 % DateTime : Wed Sep 23 18:40:42 UTC 2026
% 0.16/5.62 % CPUTime :
% 0.16/5.62 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.68 Running first-order theorem proving
% 0.16/5.68 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
% 0.16/5.69
% 0.16/5.69 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.69
% 0.16/5.69 % Detected problem language: tptp
% 0.21/5.71 % Proving...
% 4.92/7.59 % SZS status Started for theBenchmark.p
% 4.92/7.59 % SZS status Theorem for theBenchmark.p
% 4.92/7.59
% 4.92/7.59 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.92/7.59
% 4.92/7.59 % ------ iProver source info
% 4.92/7.59
% 4.92/7.59 % git: date: 2026-07-19 20:42:38 +0200
% 4.92/7.59 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.92/7.59 % git: non_committed_changes: false
% 4.92/7.59
% 4.92/7.59 % ------ Parsing...
% 4.92/7.59 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.92/7.59
% 4.92/7.59 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.92/7.59
% 4.92/7.59 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.92/7.59
% 4.92/7.59 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.92/7.59 % ------ Proving...
% 4.92/7.59 % ------ Problem Properties
% 4.92/7.59
% 4.92/7.59 %
% 4.92/7.59 % clauses 33
% 4.92/7.59 % conjectures 3
% 4.92/7.59 % EPR 4
% 4.92/7.59 % Horn 32
% 4.92/7.59 % unary 22
% 4.92/7.59 % binary 7
% 4.92/7.59 % lits 49
% 4.92/7.59 % lits eq 30
% 4.92/7.59 % fd_pure 0
% 4.92/7.59 % fd_pseudo 0
% 4.92/7.59 % fd_cond 0
% 4.92/7.59 % fd_pseudo_cond 1
% 4.92/7.59 % AC symbols 1
% 4.92/7.59
% 4.92/7.59 % ------ Schedule dynamic 5 is on
% 4.92/7.59
% 4.92/7.59 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.92/7.59
% 4.92/7.59
% 4.92/7.59 % ------
% 4.92/7.59 % Current options:
% 4.92/7.59 % ------
% 4.92/7.59
% 4.92/7.59
% 4.92/7.59 %
% 4.92/7.59
% 4.92/7.59 % ------ Proving...
% 4.92/7.59 %
% 4.92/7.59
% 4.92/7.59 % SZS status Theorem for theBenchmark.p
% 4.92/7.59
% 4.92/7.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.92/7.60
% 4.92/7.60
%------------------------------------------------------------------------------