%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE011+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 : n026.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 3.74s 1.20s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 21
% Syntax : Number of formulae : 207 ( 114 unt; 9 def)
% Number of atoms : 705 ( 210 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 261 ( 112 ~; 117 |; 22 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 144 ( 0 sgn 137 !; 7 ?; 63 :)
% 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(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
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(f16,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_4) ).
fof(f17,axiom,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> c(addition(X0,X1)) = multiplication(c(X0),c(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax',test_deMorgan1) ).
fof(f18,axiom,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax',test_deMorgan2) ).
fof(f19,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0] :
( test(X0)
| c(X0) = zero ),
inference(ennf_transformation,[],[f16]) ).
fof(f23,plain,
! [X0,X1] :
( ~ test(X1)
| ~ test(X0)
| c(addition(X0,X1)) = multiplication(c(X0),c(X1)) ),
inference(ennf_transformation,[],[f17]) ).
fof(f24,plain,
! [X0,X1] :
( ~ test(X1)
| ~ test(X0)
| c(addition(X0,X1)) = multiplication(c(X0),c(X1)) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ~ test(X1)
| ~ test(X0)
| c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f26,plain,
! [X0,X1] :
( ~ test(X1)
| ~ test(X0)
| c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& one != addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
inference(ennf_transformation,[],[f20]) ).
fof(f28,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& one != addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
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(sK1)
& test(sK2)
& one != addition(addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(addition(sK1,c(sK1)),sK2)),multiplication(c(sK1),c(sK2))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[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(f39,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f42,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f47,plain,
! [X0] :
( ~ test(X0)
| complement(sK0(X0),X0) ),
inference(cnf_transformation,[],[f31]) ).
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(f55,plain,
! [X0] :
( test(X0)
| zero = c(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f56,plain,
! [X0,X1] :
( ~ test(X1)
| ~ test(X0)
| c(addition(X0,X1)) = multiplication(c(X0),c(X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f57,plain,
! [X0,X1] :
( ~ test(X1)
| ~ test(X0)
| c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f58,plain,
test(sK1),
inference(cnf_transformation,[],[f35]) ).
fof(f59,plain,
test(sK2),
inference(cnf_transformation,[],[f35]) ).
fof(f60,plain,
one != addition(addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(addition(sK1,c(sK1)),sK2)),multiplication(c(sK1),c(sK2))),
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_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f39]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f42]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( test(X1)
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_61,plain,
! [X0: $i] :
( complement(sK0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f47]) ).
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_68,plain,
! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( ( multiplication(c(X0),c(X1)) = c(addition(X0,X1)) )
| ~ test(X1)
| ~ test(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( addition(c(X0),c(X1)) = c(multiplication(X0,X1)) )
| ~ test(X1)
| ~ test(X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_71,negated_conjecture,
addition(addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(addition(sK1,c(sK1)),sK2)),multiplication(c(sK1),c(sK2))) != one,
inference(cnf_transformation,[],[f60]) ).
tcf(c_72,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f59]) ).
tcf(c_73,negated_conjecture,
test(sK1),
inference(cnf_transformation,[],[f58]) ).
tcf(c_92,negated_conjecture,
addition(multiplication(c(sK1),c(sK2)),addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(addition(sK1,c(sK1)),sK2))) != one,
inference(theory_normalisation,[status(thm)],[c_71,c_50,c_49]) ).
tcf(c_379,definition,
iPr_def_10 = c(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_380,definition,
iPr_def_11 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_381,definition,
iPr_def_12 = multiplication(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_382,definition,
iPr_def_13 = addition(sK2,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_383,definition,
iPr_def_14 = multiplication(iPr_def_13,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_384,definition,
iPr_def_15 = addition(sK1,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_385,definition,
iPr_def_16 = multiplication(iPr_def_15,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_386,definition,
iPr_def_17 = addition(iPr_def_14,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_387,definition,
iPr_def_18 = addition(iPr_def_12,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_388,negated_conjecture,
iPr_def_18 != one,
inference(demodulation,[status(thm)],[c_92,c_384,c_385,c_382,c_383,c_386,c_380,c_379,c_381,c_387]) ).
tcf(c_389,negated_conjecture,
test(sK1),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_390,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_686,plain,
addition(iPr_def_11,sK2) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_382,c_50,c_49]) ).
tcf(c_687,plain,
addition(iPr_def_10,sK1) = iPr_def_15,
inference(theory_normalisation,[status(thm)],[c_384,c_50,c_49]) ).
tcf(c_697,plain,
( complement(sK2,iPr_def_11)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_380,c_67]) ).
tcf(c_698,plain,
( complement(sK1,iPr_def_10)
| ~ test(sK1) ),
inference(superposition,[status(thm)],[c_379,c_67]) ).
tcf(c_699,plain,
! [X0: $i] :
( test(c(X0))
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_67,c_60]) ).
tcf(c_702,plain,
complement(sK1,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_698,c_389]) ).
tcf(c_703,plain,
complement(sK2,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_697,c_390]) ).
tcf(c_704,plain,
test(iPr_def_10),
inference(superposition,[status(thm)],[c_702,c_60]) ).
tcf(c_705,plain,
test(iPr_def_11),
inference(superposition,[status(thm)],[c_703,c_60]) ).
tcf(c_735,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_743,plain,
! [X0: $i] :
( ( multiplication(X0,sK0(X0)) = zero )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_61,c_63]) ).
tcf(c_745,plain,
multiplication(iPr_def_11,sK2) = zero,
inference(superposition,[status(thm)],[c_703,c_63]) ).
tcf(c_746,plain,
multiplication(iPr_def_10,sK1) = zero,
inference(superposition,[status(thm)],[c_702,c_63]) ).
tcf(c_755,plain,
! [X0: $i] :
( ( multiplication(sK0(X0),X0) = zero )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_61,c_64]) ).
tcf(c_757,plain,
multiplication(sK2,iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_703,c_64]) ).
tcf(c_758,plain,
multiplication(sK1,iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_702,c_64]) ).
tcf(c_783,plain,
! [X0: $i] :
( ( addition(X0,sK0(X0)) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_61,c_65]) ).
tcf(c_784,plain,
! [X0: $i] :
( ( addition(c(X0),X0) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_67,c_65]) ).
tcf(c_785,plain,
addition(iPr_def_11,sK2) = one,
inference(superposition,[status(thm)],[c_703,c_65]) ).
tcf(c_786,plain,
addition(iPr_def_10,sK1) = one,
inference(superposition,[status(thm)],[c_702,c_65]) ).
tcf(c_787,plain,
one = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_786,c_687]) ).
tcf(c_788,plain,
one = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_785,c_686]) ).
tcf(c_789,plain,
! [X0: $i] :
( ( addition(X0,c(X0)) = one )
| ~ test(X0) ),
inference(theory_normalisation,[status(thm)],[c_784,c_50,c_49]) ).
tcf(c_795,plain,
! [X0: $i] : multiplication(iPr_def_15,X0) = X0,
inference(demodulation,[status(thm)],[c_55,c_787]) ).
tcf(c_797,plain,
iPr_def_15 != iPr_def_18,
inference(demodulation,[status(thm)],[c_388,c_787]) ).
tcf(c_798,plain,
sK2 = iPr_def_16,
inference(demodulation,[status(thm)],[c_385,c_795]) ).
tcf(c_799,plain,
multiplication(iPr_def_16,iPr_def_11) = zero,
inference(demodulation,[status(thm)],[c_757,c_798]) ).
tcf(c_800,plain,
multiplication(iPr_def_11,iPr_def_16) = zero,
inference(demodulation,[status(thm)],[c_745,c_798]) ).
tcf(c_802,plain,
addition(iPr_def_11,iPr_def_16) = iPr_def_13,
inference(demodulation,[status(thm)],[c_686,c_798]) ).
tcf(c_803,plain,
c(iPr_def_16) = iPr_def_11,
inference(demodulation,[status(thm)],[c_380,c_798]) ).
tcf(c_804,plain,
test(iPr_def_16),
inference(demodulation,[status(thm)],[c_390,c_798]) ).
tcf(c_805,plain,
multiplication(sK1,iPr_def_10) = multiplication(iPr_def_11,iPr_def_16),
inference(demodulation,[status(thm)],[c_758,c_800]) ).
tcf(c_806,plain,
multiplication(iPr_def_10,sK1) = multiplication(iPr_def_11,iPr_def_16),
inference(demodulation,[status(thm)],[c_746,c_800]) ).
tcf(c_807,plain,
! [X0: $i] : addition(multiplication(iPr_def_11,iPr_def_16),X0) = X0,
inference(demodulation,[status(thm)],[c_735,c_800]) ).
tcf(c_810,plain,
! [X0: $i] :
( test(X0)
| ( multiplication(iPr_def_11,iPr_def_16) = c(X0) ) ),
inference(demodulation,[status(thm)],[c_68,c_800]) ).
tcf(c_833,plain,
iPr_def_13 = iPr_def_15,
inference(demodulation,[status(thm)],[c_787,c_788]) ).
tcf(c_834,plain,
iPr_def_13 != iPr_def_18,
inference(demodulation,[status(thm)],[c_797,c_833]) ).
tcf(c_835,plain,
addition(iPr_def_10,sK1) = iPr_def_13,
inference(demodulation,[status(thm)],[c_687,c_833]) ).
tcf(c_886,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_887,plain,
! [X0: $i] : addition(iPr_def_14,addition(iPr_def_16,X0)) = addition(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_386,c_50]) ).
tcf(c_971,plain,
multiplication(iPr_def_11,iPr_def_16) = multiplication(iPr_def_16,iPr_def_11),
inference(demodulation,[status(thm)],[c_799,c_800]) ).
tcf(c_983,plain,
! [X0: $i] : multiplication(iPr_def_13,X0) = X0,
inference(light_normalisation,[status(thm)],[c_795,c_833]) ).
tcf(c_984,plain,
sK1 = iPr_def_14,
inference(demodulation,[status(thm)],[c_383,c_983]) ).
tcf(c_985,plain,
multiplication(iPr_def_10,iPr_def_14) = multiplication(iPr_def_11,iPr_def_16),
inference(demodulation,[status(thm)],[c_806,c_984]) ).
tcf(c_986,plain,
multiplication(iPr_def_11,iPr_def_16) = multiplication(iPr_def_14,iPr_def_10),
inference(demodulation,[status(thm)],[c_805,c_984]) ).
tcf(c_989,plain,
c(iPr_def_14) = iPr_def_10,
inference(demodulation,[status(thm)],[c_379,c_984]) ).
tcf(c_990,plain,
test(iPr_def_14),
inference(demodulation,[status(thm)],[c_389,c_984]) ).
tcf(c_991,plain,
multiplication(iPr_def_10,iPr_def_14) = zero,
inference(demodulation,[status(thm)],[c_800,c_985]) ).
tcf(c_992,plain,
multiplication(iPr_def_10,iPr_def_14) = multiplication(iPr_def_16,iPr_def_11),
inference(demodulation,[status(thm)],[c_971,c_985]) ).
tcf(c_1046,plain,
! [X0: $i] :
( ( multiplication(c(iPr_def_14),c(X0)) = c(addition(iPr_def_14,X0)) )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_990,c_69]) ).
tcf(c_1047,plain,
! [X0: $i] :
( ( multiplication(iPr_def_10,c(X0)) = c(addition(iPr_def_14,X0)) )
| ~ test(X0) ),
inference(light_normalisation,[status(thm)],[c_1046,c_989]) ).
tcf(c_1076,plain,
! [X0: $i] :
( ( addition(c(iPr_def_10),c(X0)) = c(multiplication(iPr_def_10,X0)) )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_704,c_70]) ).
tcf(c_1102,plain,
! [X0: $i,X1: $i] :
( complement(X1,X0)
| ( multiplication(X1,X0) != multiplication(iPr_def_10,iPr_def_14) )
| ( multiplication(X0,X1) != multiplication(iPr_def_10,iPr_def_14) )
| ( addition(X0,X1) != one ) ),
inference(light_normalisation,[status(thm)],[c_62,c_991]) ).
tcf(c_1103,plain,
! [X0: $i,X1: $i] :
( complement(X1,X0)
| ( multiplication(X1,X0) != multiplication(iPr_def_10,iPr_def_14) )
| ( multiplication(X0,X1) != multiplication(iPr_def_10,iPr_def_14) )
| ( addition(X0,X1) != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_1102,c_788]) ).
tcf(c_1176,plain,
addition(iPr_def_10,iPr_def_14) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_835,c_984]) ).
tcf(c_1195,plain,
multiplication(iPr_def_10,c(iPr_def_16)) = c(addition(iPr_def_14,iPr_def_16)),
inference(superposition,[status(thm)],[c_804,c_1047]) ).
tcf(c_1198,plain,
c(iPr_def_17) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_1195,c_381,c_386,c_803]) ).
tcf(c_1220,plain,
( test(iPr_def_12)
| ~ test(iPr_def_17) ),
inference(superposition,[status(thm)],[c_1198,c_699]) ).
tcf(c_1363,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,iPr_def_14),X0) = X0,
inference(light_normalisation,[status(thm)],[c_807,c_985]) ).
tcf(c_1370,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_10,iPr_def_14)) = X0,
inference(superposition,[status(thm)],[c_1363,c_49]) ).
tcf(c_1429,plain,
multiplication(iPr_def_10,iPr_def_14) = multiplication(iPr_def_14,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_986,c_985]) ).
tcf(c_1430,plain,
( complement(iPr_def_10,iPr_def_14)
| ( multiplication(iPr_def_10,iPr_def_14) != multiplication(iPr_def_10,iPr_def_14) )
| ( addition(iPr_def_14,iPr_def_10) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1429,c_1103]) ).
tcf(c_1432,plain,
( complement(iPr_def_10,iPr_def_14)
| ( addition(iPr_def_14,iPr_def_10) != iPr_def_13 ) ),
inference(equality_resolution_simp,[status(thm)],[c_1430]) ).
tcf(c_1433,plain,
( complement(iPr_def_10,iPr_def_14)
| ( addition(iPr_def_10,iPr_def_14) != iPr_def_13 ) ),
inference(theory_normalisation,[status(thm)],[c_1432,c_50,c_49]) ).
tcf(c_1434,plain,
complement(iPr_def_10,iPr_def_14),
inference(ground_joinability,[status(thm)],[c_1433,c_1176]) ).
tcf(c_1605,plain,
( complement(iPr_def_11,iPr_def_16)
| ( multiplication(iPr_def_10,iPr_def_14) != multiplication(iPr_def_11,iPr_def_16) )
| ( addition(iPr_def_16,iPr_def_11) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_992,c_1103]) ).
tcf(c_1608,plain,
( complement(iPr_def_11,iPr_def_16)
| ( multiplication(iPr_def_10,iPr_def_14) != multiplication(iPr_def_11,iPr_def_16) )
| ( addition(iPr_def_11,iPr_def_16) != iPr_def_13 ) ),
inference(theory_normalisation,[status(thm)],[c_1605,c_50,c_49]) ).
tcf(c_1609,plain,
complement(iPr_def_11,iPr_def_16),
inference(ground_joinability,[status(thm)],[c_1608,c_802,c_985]) ).
tcf(c_1650,plain,
( ( c(iPr_def_10) = iPr_def_14 )
| ~ test(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1434,c_66]) ).
tcf(c_1652,plain,
c(iPr_def_10) = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_1650,c_704]) ).
tcf(c_1663,plain,
( ( c(iPr_def_11) = iPr_def_16 )
| ~ test(iPr_def_11) ),
inference(superposition,[status(thm)],[c_1609,c_66]) ).
tcf(c_1665,plain,
c(iPr_def_11) = iPr_def_16,
inference(forward_subsumption_resolution,[status(thm)],[c_1663,c_705]) ).
tcf(c_1729,plain,
! [X0: $i] :
( ( addition(iPr_def_14,c(X0)) = c(multiplication(iPr_def_10,X0)) )
| ~ test(X0) ),
inference(light_normalisation,[status(thm)],[c_1076,c_1652]) ).
tcf(c_1738,plain,
addition(iPr_def_14,c(iPr_def_11)) = c(multiplication(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_705,c_1729]) ).
tcf(c_1745,plain,
c(iPr_def_12) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_1738,c_381,c_386,c_1665]) ).
tcf(c_1771,plain,
( test(iPr_def_17)
| ~ test(iPr_def_12) ),
inference(superposition,[status(thm)],[c_1745,c_699]) ).
tcf(c_1814,plain,
! [X0: $i] :
( test(X0)
| ( multiplication(iPr_def_10,iPr_def_14) = c(X0) ) ),
inference(light_normalisation,[status(thm)],[c_810,c_985]) ).
tcf(c_1830,plain,
( test(iPr_def_12)
| ( multiplication(iPr_def_10,iPr_def_14) = c(iPr_def_17) ) ),
inference(superposition,[status(thm)],[c_1814,c_1220]) ).
tcf(c_1831,plain,
( test(iPr_def_12)
| ( multiplication(iPr_def_10,iPr_def_14) = iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_1830,c_1198]) ).
tcf(c_1918,plain,
! [X0: $i] :
( ( multiplication(X0,sK0(X0)) = multiplication(iPr_def_10,iPr_def_14) )
| ~ test(X0) ),
inference(light_normalisation,[status(thm)],[c_743,c_991]) ).
tcf(c_1929,plain,
multiplication(iPr_def_16,sK0(iPr_def_16)) = multiplication(iPr_def_10,iPr_def_14),
inference(superposition,[status(thm)],[c_804,c_1918]) ).
tcf(c_1941,plain,
( test(iPr_def_17)
| ( multiplication(iPr_def_10,iPr_def_14) = c(iPr_def_12) ) ),
inference(superposition,[status(thm)],[c_1814,c_1771]) ).
tcf(c_1942,plain,
( test(iPr_def_17)
| ( multiplication(iPr_def_10,iPr_def_14) = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_1941,c_1745]) ).
tcf(c_2138,plain,
( test(iPr_def_17)
| ( multiplication(iPr_def_10,iPr_def_14) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_1831,c_1771]) ).
tcf(c_2223,plain,
! [X0: $i] :
( ( multiplication(sK0(X0),X0) = multiplication(iPr_def_10,iPr_def_14) )
| ~ test(X0) ),
inference(light_normalisation,[status(thm)],[c_755,c_991]) ).
tcf(c_2234,plain,
multiplication(sK0(iPr_def_16),iPr_def_16) = multiplication(iPr_def_10,iPr_def_14),
inference(superposition,[status(thm)],[c_804,c_2223]) ).
tcf(c_2563,plain,
( complement(iPr_def_16,sK0(iPr_def_16))
| ( multiplication(iPr_def_16,sK0(iPr_def_16)) != multiplication(iPr_def_10,iPr_def_14) )
| ( addition(sK0(iPr_def_16),iPr_def_16) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2234,c_1103]) ).
tcf(c_2566,plain,
( complement(iPr_def_16,sK0(iPr_def_16))
| ( multiplication(iPr_def_16,sK0(iPr_def_16)) != multiplication(iPr_def_10,iPr_def_14) )
| ( addition(iPr_def_16,sK0(iPr_def_16)) != iPr_def_13 ) ),
inference(theory_normalisation,[status(thm)],[c_2563,c_50,c_49]) ).
tcf(c_2567,plain,
( complement(iPr_def_16,sK0(iPr_def_16))
| ( addition(iPr_def_16,sK0(iPr_def_16)) != iPr_def_13 ) ),
inference(ground_joinability,[status(thm)],[c_2566,c_1929]) ).
tcf(c_2624,plain,
! [X0: $i] :
( ( addition(X0,sK0(X0)) = iPr_def_13 )
| ~ test(X0) ),
inference(demodulation,[status(thm)],[c_783,c_788]) ).
tcf(c_2634,plain,
addition(iPr_def_11,sK0(iPr_def_11)) = iPr_def_13,
inference(superposition,[status(thm)],[c_705,c_2624]) ).
tcf(c_2635,plain,
addition(iPr_def_16,sK0(iPr_def_16)) = iPr_def_13,
inference(superposition,[status(thm)],[c_804,c_2624]) ).
tcf(c_2656,plain,
complement(iPr_def_16,sK0(iPr_def_16)),
inference(backward_subsumption_resolution,[status(thm)],[c_2567,c_2635]) ).
tcf(c_2662,plain,
! [X0: $i] :
( ( addition(X0,c(X0)) = iPr_def_13 )
| ~ test(X0) ),
inference(demodulation,[status(thm)],[c_789,c_788]) ).
tcf(c_2677,plain,
( ( multiplication(iPr_def_10,iPr_def_14) = iPr_def_12 )
| ( addition(iPr_def_17,c(iPr_def_17)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2138,c_2662]) ).
tcf(c_2678,plain,
( ( multiplication(iPr_def_10,iPr_def_14) = iPr_def_17 )
| ( addition(iPr_def_17,c(iPr_def_17)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1942,c_2662]) ).
tcf(c_2688,plain,
( ( multiplication(iPr_def_10,iPr_def_14) = iPr_def_17 )
| ( addition(iPr_def_17,iPr_def_12) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2678,c_1198]) ).
tcf(c_2689,plain,
( ( multiplication(iPr_def_10,iPr_def_14) = iPr_def_17 )
| ( addition(iPr_def_12,iPr_def_17) = iPr_def_13 ) ),
inference(theory_normalisation,[status(thm)],[c_2688,c_50,c_49]) ).
tcf(c_2690,plain,
( ( iPr_def_13 = iPr_def_18 )
| ( multiplication(iPr_def_10,iPr_def_14) = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2689,c_387]) ).
tcf(c_2691,plain,
multiplication(iPr_def_10,iPr_def_14) = iPr_def_17,
inference(forward_subsumption_resolution,[status(thm)],[c_2690,c_834]) ).
tcf(c_2692,plain,
( ( multiplication(iPr_def_10,iPr_def_14) = iPr_def_12 )
| ( addition(iPr_def_17,iPr_def_12) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2677,c_1198]) ).
tcf(c_2693,plain,
( ( multiplication(iPr_def_10,iPr_def_14) = iPr_def_12 )
| ( addition(iPr_def_12,iPr_def_17) = iPr_def_13 ) ),
inference(theory_normalisation,[status(thm)],[c_2692,c_50,c_49]) ).
tcf(c_2694,plain,
( ( iPr_def_13 = iPr_def_18 )
| ( multiplication(iPr_def_10,iPr_def_14) = iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_2693,c_387]) ).
tcf(c_2695,plain,
multiplication(iPr_def_10,iPr_def_14) = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_2694,c_834]) ).
tcf(c_2717,plain,
! [X0: $i] : addition(X0,iPr_def_17) = X0,
inference(demodulation,[status(thm)],[c_1370,c_2691]) ).
tcf(c_2721,plain,
! [X0: $i] : addition(iPr_def_17,X0) = X0,
inference(demodulation,[status(thm)],[c_1363,c_2691]) ).
tcf(c_2731,plain,
iPr_def_12 = iPr_def_18,
inference(demodulation,[status(thm)],[c_387,c_2717]) ).
tcf(c_2733,plain,
iPr_def_12 != iPr_def_13,
inference(demodulation,[status(thm)],[c_834,c_2731]) ).
tcf(c_2850,plain,
( ( sK0(iPr_def_16) = c(iPr_def_16) )
| ~ test(iPr_def_16) ),
inference(superposition,[status(thm)],[c_2656,c_66]) ).
tcf(c_2853,plain,
( ( sK0(iPr_def_16) = iPr_def_11 )
| ~ test(iPr_def_16) ),
inference(light_normalisation,[status(thm)],[c_2850,c_803]) ).
tcf(c_2854,plain,
sK0(iPr_def_16) = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_2853,c_804]) ).
tcf(c_2870,plain,
iPr_def_12 = iPr_def_17,
inference(demodulation,[status(thm)],[c_2691,c_2695]) ).
tcf(c_2878,plain,
c(iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1198,c_2870]) ).
tcf(c_2879,plain,
addition(iPr_def_14,iPr_def_16) = iPr_def_12,
inference(demodulation,[status(thm)],[c_386,c_2870]) ).
tcf(c_2919,plain,
! [X0: $i] : addition(iPr_def_14,addition(iPr_def_16,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_887,c_2721]) ).
tcf(c_2926,plain,
! [X0: $i] : addition(iPr_def_14,X0) = X0,
inference(superposition,[status(thm)],[c_2919,c_886]) ).
tcf(c_3201,plain,
! [X0: $i] : addition(X0,iPr_def_12) = X0,
inference(light_normalisation,[status(thm)],[c_2717,c_2870]) ).
tcf(c_3210,plain,
! [X0: $i] : addition(iPr_def_12,X0) = X0,
inference(superposition,[status(thm)],[c_3201,c_49]) ).
tcf(c_3359,plain,
iPr_def_12 = iPr_def_16,
inference(demodulation,[status(thm)],[c_2879,c_2926]) ).
tcf(c_3363,plain,
sK0(iPr_def_12) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2854,c_3359]) ).
tcf(c_3374,plain,
c(iPr_def_12) = iPr_def_11,
inference(demodulation,[status(thm)],[c_803,c_3359]) ).
tcf(c_3383,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_2878,c_3374]) ).
tcf(c_3386,plain,
! [X0: $i] : addition(iPr_def_11,X0) = X0,
inference(demodulation,[status(thm)],[c_3210,c_3383]) ).
tcf(c_3402,plain,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_2733,c_3383]) ).
tcf(c_3410,plain,
sK0(iPr_def_11) = iPr_def_13,
inference(demodulation,[status(thm)],[c_2634,c_3386]) ).
tcf(c_3425,plain,
iPr_def_11 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_3363,c_3383,c_3410]) ).
tcf(c_3449,plain,
$false,
inference(ground_joinability,[status(thm)],[c_3402,c_3425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE011+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 18:38:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 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...
% 3.74/1.20 % SZS status Started for theBenchmark.p
% 3.74/1.20 % SZS status Theorem for theBenchmark.p
% 3.74/1.20
% 3.74/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.74/1.20
% 3.74/1.20 % ------ iProver source info
% 3.74/1.20
% 3.74/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.74/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.74/1.20 % git: non_committed_changes: false
% 3.74/1.20
% 3.74/1.20 % ------ Parsing...
% 3.74/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.74/1.20
% 3.74/1.20 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.74/1.20
% 3.74/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.74/1.20
% 3.74/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.74/1.20 % ------ Proving...
% 3.74/1.20 % ------ Problem Properties
% 3.74/1.20
% 3.74/1.20 %
% 3.74/1.20 % clauses 34
% 3.74/1.20 % conjectures 3
% 3.74/1.20 % EPR 4
% 3.74/1.20 % Horn 33
% 3.74/1.20 % unary 23
% 3.74/1.20 % binary 7
% 3.74/1.20 % lits 50
% 3.74/1.20 % lits eq 31
% 3.74/1.20 % fd_pure 0
% 3.74/1.20 % fd_pseudo 0
% 3.74/1.20 % fd_cond 0
% 3.74/1.20 % fd_pseudo_cond 1
% 3.74/1.20 % AC symbols 1
% 3.74/1.20
% 3.74/1.20 % ------ Schedule dynamic 5 is on
% 3.74/1.20
% 3.74/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.74/1.20
% 3.74/1.20
% 3.74/1.20 % ------
% 3.74/1.20 % Current options:
% 3.74/1.20 % ------
% 3.74/1.20
% 3.74/1.20
% 3.74/1.20 %
% 3.74/1.20
% 3.74/1.20 % ------ Proving...
% 3.74/1.20 %
% 3.74/1.20
% 3.74/1.20 % SZS status Theorem for theBenchmark.p
% 3.74/1.20
% 3.74/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.89/1.21
%------------------------------------------------------------------------------