%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE012+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 01:52:09 PM UTC 2026
% Result : Theorem 10.66s 2.62s
% Output : CNFRefutation 10.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 16
% Syntax : Number of formulae : 131 ( 99 unt; 2 def)
% Number of atoms : 251 ( 129 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 106 ( 43 ~; 36 |; 20 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 129 ( 0 sgn 122 !; 7 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(f13,axiom,
! [X0] :
( 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(f17,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> multiplication(X0,X1) = multiplication(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> multiplication(X0,X1) = multiplication(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& multiplication(X0,X1) != multiplication(X1,X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& multiplication(X0,X1) != multiplication(X1,X0) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0] :
( ( ~ test(X0)
| ? [X2] : complement(X2,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(rectify,[],[f23]) ).
fof(f25,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))],[f24]) ).
fof(f26,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(f27,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,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f29,plain,
( test(sK1)
& test(sK2)
& multiplication(sK1,sK2) != multiplication(sK2,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f22]) ).
fof(f30,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f31,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f35,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f36,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f37,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f40,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f41,plain,
! [X0] :
( ~ test(X0)
| complement(sK0(X0),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f27]) ).
fof(f44,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f45,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
test(sK1),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
test(sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
multiplication(sK1,sK2) != multiplication(sK2,sK1),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f47]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f30]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f31]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f32]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f35]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f36]) ).
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,[],[f37]) ).
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,[],[f38]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f40]) ).
tcf(c_61,plain,
! [X0: $i] :
( complement(sK0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( multiplication(X1,X0) = zero )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( multiplication(X0,X1) = zero )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_67,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_69,negated_conjecture,
multiplication(sK1,sK2) != multiplication(sK2,sK1),
inference(cnf_transformation,[],[f52]) ).
tcf(c_70,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f51]) ).
tcf(c_71,negated_conjecture,
test(sK1),
inference(cnf_transformation,[],[f50]) ).
tcf(c_468,definition,
iPr_def_10 = multiplication(sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_469,definition,
iPr_def_11 = multiplication(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_470,negated_conjecture,
test(sK1),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_471,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_472,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_69,c_469,c_468]) ).
tcf(c_726,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_739,plain,
! [X0: $i] :
( ( multiplication(c(X0),X0) = zero )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_67,c_63]) ).
tcf(c_748,plain,
! [X0: $i] :
( ( multiplication(sK0(X0),X0) = zero )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_61,c_64]) ).
tcf(c_749,plain,
! [X0: $i] :
( ( multiplication(X0,c(X0)) = zero )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_67,c_64]) ).
tcf(c_758,plain,
! [X0: $i] :
( ( addition(X0,sK0(X0)) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_61,c_65]) ).
tcf(c_759,plain,
! [X0: $i] :
( ( addition(c(X0),X0) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_67,c_65]) ).
tcf(c_760,plain,
! [X0: $i] :
( ( addition(X0,c(X0)) = one )
| ~ test(X0) ),
inference(theory_normalisation,[status(thm)],[c_759,c_50,c_49]) ).
tcf(c_786,plain,
multiplication(c(sK1),sK1) = zero,
inference(superposition,[status(thm)],[c_470,c_739]) ).
tcf(c_818,plain,
! [X0: $i] : multiplication(sK1,multiplication(sK2,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_468,c_53]) ).
tcf(c_1099,plain,
multiplication(sK0(sK2),sK2) = zero,
inference(superposition,[status(thm)],[c_471,c_748]) ).
tcf(c_1109,plain,
! [X0: $i] : multiplication(sK0(sK2),multiplication(sK2,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_1099,c_53]) ).
tcf(c_1111,plain,
! [X0: $i] : multiplication(sK0(sK2),multiplication(sK2,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_1109,c_59]) ).
tcf(c_1138,plain,
multiplication(sK0(sK2),iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_469,c_1111]) ).
tcf(c_1191,plain,
multiplication(sK1,c(sK1)) = zero,
inference(superposition,[status(thm)],[c_470,c_749]) ).
tcf(c_1295,plain,
addition(sK2,sK0(sK2)) = one,
inference(superposition,[status(thm)],[c_471,c_758]) ).
tcf(c_1309,plain,
! [X0: $i] : addition(multiplication(sK2,X0),multiplication(sK0(sK2),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_1295,c_57]) ).
tcf(c_1310,plain,
! [X0: $i] : addition(multiplication(sK2,X0),multiplication(sK0(sK2),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1309,c_55]) ).
tcf(c_1370,plain,
addition(sK2,c(sK2)) = one,
inference(superposition,[status(thm)],[c_471,c_760]) ).
tcf(c_1371,plain,
addition(sK1,c(sK1)) = one,
inference(superposition,[status(thm)],[c_470,c_760]) ).
tcf(c_1384,plain,
! [X0: $i] : addition(sK2,addition(c(sK2),X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_1370,c_50]) ).
tcf(c_1409,plain,
! [X0: $i] : addition(multiplication(X0,sK1),multiplication(X0,c(sK1))) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_1371,c_56]) ).
tcf(c_1410,plain,
! [X0: $i] : addition(multiplication(sK1,X0),multiplication(c(sK1),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_1371,c_57]) ).
tcf(c_1411,plain,
! [X0: $i] : addition(multiplication(sK1,X0),multiplication(c(sK1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1410,c_55]) ).
tcf(c_1412,plain,
! [X0: $i] : addition(multiplication(X0,sK1),multiplication(X0,c(sK1))) = X0,
inference(light_normalisation,[status(thm)],[c_1409,c_54]) ).
tcf(c_1565,plain,
! [X0: $i] : addition(sK2,addition(X0,c(sK2))) = addition(one,X0),
inference(superposition,[status(thm)],[c_49,c_1384]) ).
tcf(c_1568,plain,
addition(one,c(sK2)) = addition(sK2,c(sK2)),
inference(superposition,[status(thm)],[c_52,c_1384]) ).
tcf(c_1575,plain,
addition(one,c(sK2)) = one,
inference(light_normalisation,[status(thm)],[c_1568,c_1370]) ).
tcf(c_1588,plain,
multiplication(sK1,iPr_def_11) = multiplication(iPr_def_10,sK1),
inference(superposition,[status(thm)],[c_469,c_818]) ).
tcf(c_2940,plain,
addition(multiplication(sK2,iPr_def_11),zero) = iPr_def_11,
inference(superposition,[status(thm)],[c_1138,c_1310]) ).
tcf(c_2946,plain,
addition(zero,multiplication(sK2,iPr_def_11)) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_2940,c_50,c_49]) ).
tcf(c_3035,plain,
multiplication(sK2,iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2946,c_726]) ).
tcf(c_3038,plain,
multiplication(sK1,iPr_def_11) = multiplication(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_3035,c_818]) ).
tcf(c_3042,plain,
multiplication(iPr_def_10,sK1) = multiplication(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_1588,c_3038]) ).
tcf(c_4456,plain,
addition(one,one) = addition(sK2,one),
inference(superposition,[status(thm)],[c_1575,c_1565]) ).
tcf(c_4461,plain,
addition(one,one) = addition(one,sK2),
inference(theory_normalisation,[status(thm)],[c_4456,c_50,c_49]) ).
tcf(c_4598,plain,
addition(one,sK2) = one,
inference(demodulation,[status(thm)],[c_4461,c_52]) ).
tcf(c_4601,plain,
! [X0: $i] : addition(multiplication(X0,one),multiplication(X0,sK2)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_4598,c_56]) ).
tcf(c_4602,plain,
! [X0: $i] : addition(multiplication(one,X0),multiplication(sK2,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_4598,c_57]) ).
tcf(c_4603,plain,
! [X0: $i] : addition(X0,multiplication(sK2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4602,c_55]) ).
tcf(c_4604,plain,
! [X0: $i] : addition(X0,multiplication(X0,sK2)) = X0,
inference(light_normalisation,[status(thm)],[c_4601,c_54]) ).
tcf(c_4625,plain,
addition(sK1,iPr_def_11) = sK1,
inference(superposition,[status(thm)],[c_469,c_4603]) ).
tcf(c_4645,plain,
addition(iPr_def_11,sK1) = sK1,
inference(theory_normalisation,[status(thm)],[c_4625,c_50,c_49]) ).
tcf(c_4699,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,sK1)) = multiplication(X0,sK1),
inference(superposition,[status(thm)],[c_4645,c_56]) ).
tcf(c_4789,plain,
addition(sK1,iPr_def_10) = sK1,
inference(superposition,[status(thm)],[c_468,c_4604]) ).
tcf(c_4806,plain,
addition(iPr_def_10,sK1) = sK1,
inference(theory_normalisation,[status(thm)],[c_4789,c_50,c_49]) ).
tcf(c_4827,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(sK1,X0)) = multiplication(sK1,X0),
inference(superposition,[status(thm)],[c_4806,c_57]) ).
tcf(c_22311,plain,
addition(multiplication(c(sK1),iPr_def_11),zero) = zero,
inference(superposition,[status(thm)],[c_786,c_4699]) ).
tcf(c_22332,plain,
addition(zero,multiplication(c(sK1),iPr_def_11)) = zero,
inference(theory_normalisation,[status(thm)],[c_22311,c_50,c_49]) ).
tcf(c_22432,plain,
multiplication(c(sK1),iPr_def_11) = zero,
inference(demodulation,[status(thm)],[c_22332,c_726]) ).
tcf(c_22445,plain,
addition(multiplication(sK1,iPr_def_11),zero) = iPr_def_11,
inference(superposition,[status(thm)],[c_22432,c_1411]) ).
tcf(c_22451,plain,
addition(zero,multiplication(sK1,iPr_def_11)) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_22445,c_50,c_49]) ).
tcf(c_22452,plain,
addition(zero,multiplication(iPr_def_10,iPr_def_11)) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_22451,c_3038]) ).
tcf(c_22453,plain,
addition(multiplication(iPr_def_10,iPr_def_11),zero) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_22452,c_50,c_49]) ).
tcf(c_23329,plain,
multiplication(iPr_def_10,iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_22453,c_51]) ).
tcf(c_23338,plain,
multiplication(iPr_def_10,sK1) = iPr_def_11,
inference(demodulation,[status(thm)],[c_3042,c_23329]) ).
tcf(c_24520,plain,
addition(multiplication(iPr_def_10,c(sK1)),zero) = zero,
inference(superposition,[status(thm)],[c_1191,c_4827]) ).
tcf(c_24547,plain,
addition(zero,multiplication(iPr_def_10,c(sK1))) = zero,
inference(theory_normalisation,[status(thm)],[c_24520,c_50,c_49]) ).
tcf(c_25148,plain,
multiplication(iPr_def_10,c(sK1)) = zero,
inference(demodulation,[status(thm)],[c_24547,c_726]) ).
tcf(c_25168,plain,
addition(multiplication(iPr_def_10,sK1),zero) = iPr_def_10,
inference(superposition,[status(thm)],[c_25148,c_1412]) ).
tcf(c_25170,plain,
addition(zero,multiplication(iPr_def_10,sK1)) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_25168,c_50,c_49]) ).
tcf(c_25171,plain,
addition(zero,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_25170,c_23338]) ).
tcf(c_25172,plain,
addition(iPr_def_11,zero) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_25171,c_50,c_49]) ).
tcf(c_25507,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_25172,c_51]) ).
tcf(c_25508,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_25507,c_472]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE012+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n007.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 18:33:38 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 10.66/2.62 % SZS status Started for theBenchmark.p
% 10.66/2.62 % SZS status Theorem for theBenchmark.p
% 10.66/2.62
% 10.66/2.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.66/2.62
% 10.66/2.62 % ------ iProver source info
% 10.66/2.62
% 10.66/2.62 % git: date: 2026-07-19 20:42:38 +0200
% 10.66/2.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.66/2.62 % git: non_committed_changes: false
% 10.66/2.62
% 10.66/2.62 % ------ Parsing...
% 10.66/2.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.66/2.62
% 10.66/2.62 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 10.66/2.62
% 10.66/2.62 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.66/2.62
% 10.66/2.62 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.66/2.62 % ------ Proving...
% 10.66/2.62 % ------ Problem Properties
% 10.66/2.62
% 10.66/2.62 %
% 10.66/2.62 % clauses 25
% 10.66/2.62 % conjectures 3
% 10.66/2.62 % EPR 4
% 10.66/2.62 % Horn 24
% 10.66/2.62 % unary 16
% 10.66/2.62 % binary 7
% 10.66/2.62 % lits 37
% 10.66/2.62 % lits eq 22
% 10.66/2.62 % fd_pure 0
% 10.66/2.62 % fd_pseudo 0
% 10.66/2.62 % fd_cond 0
% 10.66/2.62 % fd_pseudo_cond 1
% 10.66/2.62 % AC symbols 1
% 10.66/2.62
% 10.66/2.62 % ------ Schedule dynamic 5 is on
% 10.66/2.62
% 10.66/2.62 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.66/2.62
% 10.66/2.62
% 10.66/2.62 % ------
% 10.66/2.62 % Current options:
% 10.66/2.62 % ------
% 10.66/2.62
% 10.66/2.62
% 10.66/2.62 %
% 10.66/2.62
% 10.66/2.62 % ------ Proving...
% 10.66/2.62 %
% 10.66/2.62
% 10.66/2.62 % SZS status Theorem for theBenchmark.p
% 10.66/2.62
% 10.66/2.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.66/2.62
%------------------------------------------------------------------------------