%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE010+1 : 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 : n006.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 0.40s 1.60s
% Output : CNFRefutation 4.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 19
% Syntax : Number of formulae : 129 ( 89 unt; 8 def)
% Number of atoms : 346 ( 126 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 147 ( 66 ~; 54 |; 20 &)
% ( 4 <=>; 3 =>; 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 : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 114 ( 0 sgn 107 !; 7 ?; 40 :)
% 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(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) )
=> 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) )
=> 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] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& 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(f22,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& 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,[],[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)
& 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)],[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(f33,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
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(f41,plain,
! [X0] :
( ~ test(X0)
| complement(sK0(X0),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| test(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(f46,plain,
! [X0,X1] :
( addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| complement(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f48,plain,
! [X0,X1] :
( ~ test(X0)
| ~ complement(X0,X1)
| c(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,
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,[],[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_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f33]) ).
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_60,plain,
! [X0: $i,X1: $i] :
( test(X1)
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_61,plain,
! [X0: $i] :
( complement(sK0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f41]) ).
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,[],[f46]) ).
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_66,plain,
! [X0: $i,X1: $i] :
( ( c(X0) = X1 )
| ~ test(X0)
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_67,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_69,negated_conjecture,
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,[],[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_88,negated_conjecture,
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_69,c_50,c_49]) ).
tcf(c_199,plain,
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_88,c_56,c_50,c_49]) ).
tcf(c_200,plain,
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_199,c_57,c_50,c_49]) ).
tcf(c_201,plain,
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_200,c_50,c_49]) ).
tcf(c_473,definition,
iPr_def_10 = multiplication(sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_474,definition,
iPr_def_11 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_475,definition,
iPr_def_12 = addition(sK2,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_476,definition,
iPr_def_13 = multiplication(iPr_def_12,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_477,definition,
iPr_def_14 = c(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_478,definition,
iPr_def_15 = multiplication(iPr_def_14,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_479,definition,
iPr_def_16 = addition(iPr_def_13,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_480,definition,
iPr_def_17 = addition(iPr_def_10,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_481,plain,
iPr_def_17 != one,
inference(demodulation,[status(thm)],[c_201,c_477,c_478,c_474,c_475,c_476,c_479,c_473,c_480]) ).
tcf(c_482,negated_conjecture,
test(sK1),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_483,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_751,plain,
addition(iPr_def_11,sK2) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_475,c_50,c_49]) ).
tcf(c_761,plain,
( complement(sK2,iPr_def_11)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_474,c_67]) ).
tcf(c_762,plain,
( complement(sK1,iPr_def_14)
| ~ test(sK1) ),
inference(superposition,[status(thm)],[c_477,c_67]) ).
tcf(c_766,plain,
complement(sK1,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_762,c_482]) ).
tcf(c_767,plain,
complement(sK2,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_761,c_483]) ).
tcf(c_769,plain,
test(iPr_def_11),
inference(superposition,[status(thm)],[c_767,c_60]) ).
tcf(c_812,plain,
multiplication(iPr_def_11,sK2) = zero,
inference(superposition,[status(thm)],[c_767,c_63]) ).
tcf(c_813,plain,
multiplication(iPr_def_14,sK1) = zero,
inference(superposition,[status(thm)],[c_766,c_63]) ).
tcf(c_824,plain,
multiplication(sK2,iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_767,c_64]) ).
tcf(c_825,plain,
multiplication(sK1,iPr_def_14) = zero,
inference(superposition,[status(thm)],[c_766,c_64]) ).
tcf(c_846,plain,
addition(iPr_def_11,sK2) = one,
inference(superposition,[status(thm)],[c_767,c_65]) ).
tcf(c_847,plain,
addition(iPr_def_14,sK1) = one,
inference(superposition,[status(thm)],[c_766,c_65]) ).
tcf(c_848,plain,
one = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_846,c_751]) ).
tcf(c_854,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = iPr_def_12 )
| ~ complement(X0,X1) ),
inference(demodulation,[status(thm)],[c_65,c_848]) ).
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,
iPr_def_12 != iPr_def_17,
inference(demodulation,[status(thm)],[c_481,c_848]) ).
tcf(c_858,plain,
iPr_def_14 = iPr_def_15,
inference(demodulation,[status(thm)],[c_478,c_856]) ).
tcf(c_859,plain,
addition(iPr_def_13,iPr_def_14) = iPr_def_16,
inference(demodulation,[status(thm)],[c_479,c_858]) ).
tcf(c_860,plain,
sK1 = iPr_def_13,
inference(demodulation,[status(thm)],[c_476,c_855]) ).
tcf(c_861,plain,
multiplication(iPr_def_13,iPr_def_14) = zero,
inference(demodulation,[status(thm)],[c_825,c_860]) ).
tcf(c_862,plain,
multiplication(iPr_def_14,iPr_def_13) = zero,
inference(demodulation,[status(thm)],[c_813,c_860]) ).
tcf(c_864,plain,
multiplication(iPr_def_13,sK2) = iPr_def_10,
inference(demodulation,[status(thm)],[c_473,c_860]) ).
tcf(c_867,plain,
multiplication(sK2,iPr_def_11) = multiplication(iPr_def_14,iPr_def_13),
inference(demodulation,[status(thm)],[c_824,c_862]) ).
tcf(c_868,plain,
multiplication(iPr_def_11,sK2) = multiplication(iPr_def_14,iPr_def_13),
inference(demodulation,[status(thm)],[c_812,c_862]) ).
tcf(c_895,plain,
addition(iPr_def_14,iPr_def_13) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_847,c_848,c_860]) ).
tcf(c_896,plain,
iPr_def_12 = iPr_def_16,
inference(demodulation,[status(thm)],[c_895,c_49,c_859]) ).
tcf(c_897,plain,
addition(iPr_def_10,iPr_def_12) = iPr_def_17,
inference(demodulation,[status(thm)],[c_480,c_896]) ).
tcf(c_898,plain,
multiplication(iPr_def_13,iPr_def_14) = multiplication(iPr_def_14,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_862,c_861]) ).
tcf(c_949,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_1021,plain,
multiplication(sK2,iPr_def_11) = multiplication(iPr_def_13,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_867,c_898]) ).
tcf(c_1025,plain,
multiplication(iPr_def_11,sK2) = multiplication(iPr_def_13,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_868,c_898]) ).
tcf(c_1102,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_62,c_848,c_861]) ).
tcf(c_1119,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_1021,c_1102]) ).
tcf(c_1126,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_1119,c_50,c_49]) ).
tcf(c_1127,plain,
complement(iPr_def_11,sK2),
inference(ground_joinability,[status(thm)],[c_1126,c_751,c_1025]) ).
tcf(c_1173,plain,
addition(iPr_def_13,iPr_def_14) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_859,c_896]) ).
tcf(c_1195,plain,
( ( c(iPr_def_11) = sK2 )
| ~ test(iPr_def_11) ),
inference(superposition,[status(thm)],[c_1127,c_66]) ).
tcf(c_1197,plain,
c(iPr_def_11) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_1195,c_769]) ).
tcf(c_1199,plain,
multiplication(iPr_def_13,c(iPr_def_11)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_864,c_1197]) ).
tcf(c_1206,plain,
test(c(iPr_def_11)),
inference(demodulation,[status(thm)],[c_483,c_1197]) ).
tcf(c_1369,plain,
! [X0: $i] :
( ( addition(X0,sK0(X0)) = iPr_def_12 )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_61,c_854]) ).
tcf(c_1509,plain,
addition(iPr_def_13,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_1173,c_949]) ).
tcf(c_1519,plain,
addition(iPr_def_12,iPr_def_13) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_1509,c_50,c_49]) ).
tcf(c_1679,plain,
! [X0: $i] : addition(iPr_def_12,addition(iPr_def_13,X0)) = addition(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_1519,c_50]) ).
tcf(c_1900,plain,
addition(c(iPr_def_11),sK0(c(iPr_def_11))) = iPr_def_12,
inference(superposition,[status(thm)],[c_1206,c_1369]) ).
tcf(c_2251,plain,
addition(c(iPr_def_11),iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_1900,c_949]) ).
tcf(c_2257,plain,
addition(iPr_def_12,c(iPr_def_11)) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_2251,c_50,c_49]) ).
tcf(c_2635,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,c(iPr_def_11))) = multiplication(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_2257,c_56]) ).
tcf(c_2640,plain,
! [X0: $i] : addition(X0,multiplication(X0,c(iPr_def_11))) = X0,
inference(light_normalisation,[status(thm)],[c_2635,c_856]) ).
tcf(c_3812,plain,
addition(iPr_def_12,multiplication(iPr_def_13,c(iPr_def_11))) = addition(iPr_def_12,iPr_def_13),
inference(superposition,[status(thm)],[c_2640,c_1679]) ).
tcf(c_3827,plain,
addition(iPr_def_12,iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_3812,c_1199,c_1519]) ).
tcf(c_3828,plain,
addition(iPr_def_10,iPr_def_12) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_3827,c_50,c_49]) ).
tcf(c_3840,plain,
iPr_def_12 = iPr_def_17,
inference(demodulation,[status(thm)],[c_897,c_3828]) ).
tcf(c_3841,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3840,c_857]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE010+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.77 % Computer : n006.cluster.edu
% 0.10/0.77 % Model : x86_64 x86_64
% 0.10/0.77 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.77 % Memory : 8046.5625MB
% 0.10/0.77 % OS : Linux 6.8.0-71-generic
% 0.10/0.77 % CPULimit : 300
% 0.10/0.77 % WCLimit : 300
% 0.10/0.77 % DateTime : Wed Sep 23 18:35:01 UTC 2026
% 0.10/0.77 % CPUTime :
% 0.10/0.77 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.81 Running first-order theorem proving
% 0.13/0.81 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
% 0.13/0.82
% 0.13/0.82 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.82
% 0.13/0.82 % Detected problem language: tptp
% 0.13/0.84 % Proving...
% 0.40/1.60 % SZS status Started for theBenchmark.p
% 0.40/1.60 % SZS status Theorem for theBenchmark.p
% 0.40/1.60
% 0.40/1.60 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.40/1.60
% 0.40/1.60 % ------ iProver source info
% 0.40/1.60
% 0.40/1.60 % git: date: 2026-07-19 20:42:38 +0200
% 0.40/1.60 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.40/1.60 % git: non_committed_changes: false
% 0.40/1.60
% 0.40/1.60 % ------ Parsing...
% 0.40/1.60 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.40/1.60
% 0.40/1.60 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.40/1.60
% 0.40/1.60 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.40/1.60
% 0.40/1.60 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.40/1.60 % ------ Proving...
% 0.40/1.60 % ------ Problem Properties
% 0.40/1.60
% 0.40/1.60 %
% 0.40/1.60 % clauses 31
% 0.40/1.60 % conjectures 2
% 0.40/1.60 % EPR 4
% 0.40/1.60 % Horn 30
% 0.40/1.60 % unary 22
% 0.40/1.60 % binary 7
% 0.40/1.60 % lits 43
% 0.40/1.60 % lits eq 28
% 0.40/1.60 % fd_pure 0
% 0.40/1.60 % fd_pseudo 0
% 0.40/1.60 % fd_cond 0
% 0.40/1.60 % fd_pseudo_cond 1
% 0.40/1.60 % AC symbols 1
% 0.40/1.60
% 0.40/1.60 % ------ Schedule dynamic 5 is on
% 0.40/1.60
% 0.40/1.60 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.40/1.60
% 0.40/1.60
% 0.40/1.60 % ------
% 0.40/1.60 % Current options:
% 0.40/1.60 % ------
% 0.40/1.60
% 0.40/1.60
% 0.40/1.60 %
% 0.40/1.60
% 0.40/1.60 % ------ Proving...
% 0.40/1.60 %
% 0.40/1.60
% 0.40/1.60 % SZS status Theorem for theBenchmark.p
% 0.40/1.60
% 0.40/1.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.47/1.60
% 4.47/1.60
%------------------------------------------------------------------------------