%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE015+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 : 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 01:52:09 PM UTC 2026
% Result : Theorem 10.06s 7.27s
% Output : CNFRefutation 10.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 19
% Syntax : Number of formulae : 190 ( 148 unt; 5 def)
% Number of atoms : 529 ( 185 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 146 ( 64 ~; 55 |; 20 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 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 : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 161 ( 0 sgn 154 !; 7 ?; 77 :)
% 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(multiplication(addition(X0,X1),c(X0)),c(X1)) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) = zero ),
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)
& zero != multiplication(multiplication(addition(X0,X1),c(X0)),c(X1)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& zero != multiplication(multiplication(addition(X0,X1),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)
& zero != multiplication(multiplication(addition(sK1,sK2),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(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(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,
zero != multiplication(multiplication(addition(sK1,sK2),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_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_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,
multiplication(multiplication(addition(sK1,sK2),c(sK1)),c(sK2)) != zero,
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_190,plain,
multiplication(addition(sK1,sK2),multiplication(c(sK1),c(sK2))) != zero,
inference(demodulation,[status(thm)],[c_69,c_53]) ).
tcf(c_470,definition,
iPr_def_10 = addition(sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_471,definition,
iPr_def_11 = c(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_472,definition,
iPr_def_12 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_473,definition,
iPr_def_13 = multiplication(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_474,definition,
iPr_def_14 = multiplication(iPr_def_10,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_475,plain,
iPr_def_14 != zero,
inference(demodulation,[status(thm)],[c_190,c_472,c_471,c_473,c_470,c_474]) ).
tcf(c_476,negated_conjecture,
test(sK1),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_477,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_742,plain,
( complement(sK1,iPr_def_11)
| ~ test(sK1) ),
inference(superposition,[status(thm)],[c_471,c_67]) ).
tcf(c_743,plain,
( complement(sK2,iPr_def_12)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_472,c_67]) ).
tcf(c_747,plain,
complement(sK2,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_743,c_477]) ).
tcf(c_748,plain,
complement(sK1,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_742,c_476]) ).
tcf(c_749,plain,
test(iPr_def_12),
inference(superposition,[status(thm)],[c_747,c_60]) ).
tcf(c_761,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_779,plain,
! [X0: $i] : addition(sK1,addition(X0,sK2)) = addition(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_470,c_728]) ).
tcf(c_796,plain,
! [X0: $i] :
( ( multiplication(X0,sK0(X0)) = zero )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_61,c_63]) ).
tcf(c_797,plain,
! [X0: $i] :
( ( multiplication(c(X0),X0) = zero )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_67,c_63]) ).
tcf(c_799,plain,
multiplication(iPr_def_12,sK2) = zero,
inference(superposition,[status(thm)],[c_747,c_63]) ).
tcf(c_808,plain,
! [X0: $i] :
( ( multiplication(sK0(X0),X0) = zero )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_61,c_64]) ).
tcf(c_810,plain,
multiplication(sK1,iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_748,c_64]) ).
tcf(c_811,plain,
multiplication(sK2,iPr_def_12) = zero,
inference(superposition,[status(thm)],[c_747,c_64]) ).
tcf(c_822,plain,
addition(iPr_def_11,sK1) = one,
inference(superposition,[status(thm)],[c_748,c_65]) ).
tcf(c_823,plain,
addition(iPr_def_12,sK2) = one,
inference(superposition,[status(thm)],[c_747,c_65]) ).
tcf(c_833,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_839,plain,
! [X0: $i] : addition(iPr_def_11,addition(sK1,X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_822,c_50]) ).
tcf(c_844,plain,
! [X0: $i] : addition(iPr_def_12,addition(sK2,X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_823,c_50]) ).
tcf(c_853,plain,
addition(one,sK1) = addition(iPr_def_11,sK1),
inference(superposition,[status(thm)],[c_52,c_839]) ).
tcf(c_854,plain,
addition(one,sK2) = addition(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_470,c_839]) ).
tcf(c_859,plain,
addition(one,sK2) = addition(iPr_def_10,iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_854,c_50,c_49]) ).
tcf(c_860,plain,
addition(one,sK1) = one,
inference(light_normalisation,[status(thm)],[c_853,c_822]) ).
tcf(c_903,plain,
! [X0: $i] : addition(iPr_def_12,addition(X0,sK2)) = addition(one,X0),
inference(superposition,[status(thm)],[c_49,c_844]) ).
tcf(c_907,plain,
addition(one,sK2) = addition(iPr_def_12,sK2),
inference(superposition,[status(thm)],[c_52,c_844]) ).
tcf(c_912,plain,
addition(iPr_def_10,iPr_def_11) = one,
inference(light_normalisation,[status(thm)],[c_907,c_823,c_859]) ).
tcf(c_918,plain,
addition(addition(iPr_def_10,iPr_def_11),sK1) = addition(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_860,c_912]) ).
tcf(c_920,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_12,sK2),
inference(demodulation,[status(thm)],[c_823,c_912]) ).
tcf(c_922,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = addition(iPr_def_10,iPr_def_11) )
| ~ complement(X0,X1) ),
inference(demodulation,[status(thm)],[c_65,c_912]) ).
tcf(c_923,plain,
! [X0: $i] : multiplication(addition(iPr_def_10,iPr_def_11),X0) = X0,
inference(demodulation,[status(thm)],[c_55,c_912]) ).
tcf(c_924,plain,
! [X0: $i] : multiplication(X0,addition(iPr_def_10,iPr_def_11)) = X0,
inference(demodulation,[status(thm)],[c_54,c_912]) ).
tcf(c_928,plain,
addition(iPr_def_10,addition(iPr_def_11,sK1)) = addition(iPr_def_10,iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_918,c_50,c_49]) ).
tcf(c_946,plain,
! [X0: $i] : addition(X0,addition(iPr_def_10,iPr_def_11)) = addition(iPr_def_12,addition(X0,sK2)),
inference(superposition,[status(thm)],[c_920,c_728]) ).
tcf(c_957,plain,
! [X0: $i] : multiplication(iPr_def_12,multiplication(sK2,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_799,c_53]) ).
tcf(c_958,plain,
! [X0: $i] : multiplication(sK1,multiplication(iPr_def_11,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_810,c_53]) ).
tcf(c_962,plain,
! [X0: $i] : multiplication(sK1,multiplication(iPr_def_11,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_958,c_59]) ).
tcf(c_963,plain,
! [X0: $i] : multiplication(iPr_def_12,multiplication(sK2,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_957,c_59]) ).
tcf(c_1011,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,sK2)) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_920,c_56]) ).
tcf(c_1019,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,sK2)) = X0,
inference(light_normalisation,[status(thm)],[c_1011,c_924]) ).
tcf(c_1040,plain,
! [X0: $i] : addition(multiplication(sK1,X0),multiplication(sK2,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_470,c_57]) ).
tcf(c_1077,plain,
addition(addition(iPr_def_10,iPr_def_11),sK2) = addition(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_859,c_912]) ).
tcf(c_1078,plain,
addition(iPr_def_10,addition(iPr_def_11,sK2)) = addition(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_1077,c_50]) ).
tcf(c_1080,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,addition(iPr_def_11,sK2))) = multiplication(X0,addition(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_1078,c_56]) ).
tcf(c_1086,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,addition(iPr_def_11,sK2))) = X0,
inference(light_normalisation,[status(thm)],[c_1080,c_924]) ).
tcf(c_1103,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_11,X0)) = X0,
inference(demodulation,[status(thm)],[c_923,c_57]) ).
tcf(c_1109,plain,
addition(multiplication(iPr_def_10,iPr_def_12),iPr_def_13) = iPr_def_12,
inference(superposition,[status(thm)],[c_473,c_1103]) ).
tcf(c_1117,plain,
addition(iPr_def_13,multiplication(iPr_def_10,iPr_def_12)) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_1109,c_50,c_49]) ).
tcf(c_1141,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,iPr_def_11)) = X0,
inference(demodulation,[status(thm)],[c_924,c_56]) ).
tcf(c_1149,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,iPr_def_10),addition(multiplication(X0,iPr_def_11),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_1141,c_50]) ).
tcf(c_1197,plain,
multiplication(sK1,iPr_def_13) = zero,
inference(superposition,[status(thm)],[c_473,c_962]) ).
tcf(c_1237,plain,
! [X0: $i,X1: $i] :
( complement(X1,X0)
| ( multiplication(X1,X0) != zero )
| ( multiplication(X0,X1) != zero )
| ( addition(X0,X1) != addition(iPr_def_10,iPr_def_11) ) ),
inference(light_normalisation,[status(thm)],[c_62,c_912]) ).
tcf(c_1527,plain,
! [X0: $i] : addition(addition(iPr_def_10,iPr_def_11),X0) = addition(iPr_def_12,addition(X0,sK2)),
inference(light_normalisation,[status(thm)],[c_903,c_912,c_946]) ).
tcf(c_1528,plain,
! [X0: $i] : addition(iPr_def_10,addition(iPr_def_11,X0)) = addition(iPr_def_12,addition(X0,sK2)),
inference(demodulation,[status(thm)],[c_1527,c_50]) ).
tcf(c_1535,plain,
addition(iPr_def_10,addition(iPr_def_11,sK1)) = addition(iPr_def_12,iPr_def_10),
inference(superposition,[status(thm)],[c_470,c_1528]) ).
tcf(c_1547,plain,
addition(iPr_def_10,addition(iPr_def_11,sK1)) = addition(iPr_def_10,iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_1535,c_50,c_49]) ).
tcf(c_1548,plain,
addition(iPr_def_10,iPr_def_11) = addition(iPr_def_10,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_1547,c_928]) ).
tcf(c_1627,plain,
addition(sK1,sK2) = addition(sK2,iPr_def_10),
inference(superposition,[status(thm)],[c_52,c_779]) ).
tcf(c_1640,plain,
addition(sK1,sK2) = addition(iPr_def_10,sK2),
inference(theory_normalisation,[status(thm)],[c_1627,c_50,c_49]) ).
tcf(c_1641,plain,
addition(iPr_def_10,sK2) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1640,c_470]) ).
tcf(c_1668,plain,
addition(sK1,iPr_def_10) = addition(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_1641,c_779]) ).
tcf(c_1670,plain,
addition(iPr_def_10,sK1) = addition(iPr_def_10,iPr_def_10),
inference(theory_normalisation,[status(thm)],[c_1668,c_50,c_49]) ).
tcf(c_1704,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_12,X0)) = multiplication(addition(iPr_def_10,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_1548,c_57]) ).
tcf(c_1731,plain,
addition(iPr_def_10,sK1) = iPr_def_10,
inference(demodulation,[status(thm)],[c_1670,c_52]) ).
tcf(c_1736,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(sK1,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_1731,c_57]) ).
tcf(c_1755,plain,
multiplication(sK2,sK0(sK2)) = zero,
inference(superposition,[status(thm)],[c_477,c_796]) ).
tcf(c_1820,plain,
! [X0: $i] :
( ( addition(X0,sK0(X0)) = addition(iPr_def_10,iPr_def_11) )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_61,c_922]) ).
tcf(c_1894,plain,
multiplication(c(iPr_def_12),iPr_def_12) = zero,
inference(superposition,[status(thm)],[c_749,c_797]) ).
tcf(c_1915,plain,
multiplication(sK0(sK2),sK2) = zero,
inference(superposition,[status(thm)],[c_477,c_808]) ).
tcf(c_2058,plain,
addition(iPr_def_13,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_1117,c_833]) ).
tcf(c_2074,plain,
addition(iPr_def_12,iPr_def_13) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_2058,c_50,c_49]) ).
tcf(c_2199,plain,
! [X0: $i] : addition(iPr_def_12,addition(iPr_def_13,X0)) = addition(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_2074,c_50]) ).
tcf(c_2200,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_12),multiplication(X0,iPr_def_13)) = multiplication(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_2074,c_56]) ).
tcf(c_2595,plain,
addition(multiplication(iPr_def_12,iPr_def_12),zero) = iPr_def_12,
inference(superposition,[status(thm)],[c_799,c_1019]) ).
tcf(c_2596,plain,
addition(multiplication(sK0(sK2),iPr_def_12),zero) = sK0(sK2),
inference(superposition,[status(thm)],[c_1915,c_1019]) ).
tcf(c_2606,plain,
addition(zero,multiplication(sK0(sK2),iPr_def_12)) = sK0(sK2),
inference(theory_normalisation,[status(thm)],[c_2596,c_50,c_49]) ).
tcf(c_2664,plain,
multiplication(iPr_def_12,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2595,c_51]) ).
tcf(c_2805,plain,
multiplication(sK0(sK2),iPr_def_12) = sK0(sK2),
inference(demodulation,[status(thm)],[c_2606,c_761]) ).
tcf(c_3883,plain,
addition(iPr_def_12,multiplication(iPr_def_10,iPr_def_12)) = addition(iPr_def_12,iPr_def_12),
inference(superposition,[status(thm)],[c_1117,c_2199]) ).
tcf(c_4295,plain,
! [X0: $i] : addition(X0,multiplication(X0,sK2)) = X0,
inference(demodulation,[status(thm)],[c_1086,c_56,c_1149]) ).
tcf(c_5780,plain,
addition(sK2,sK0(sK2)) = addition(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_477,c_1820]) ).
tcf(c_5809,plain,
( complement(sK0(sK2),sK2)
| ( multiplication(sK2,sK0(sK2)) != zero )
| ( multiplication(sK0(sK2),sK2) != zero ) ),
inference(superposition,[status(thm)],[c_5780,c_1237]) ).
tcf(c_5813,plain,
! [X0: $i] : addition(multiplication(sK2,X0),multiplication(sK0(sK2),X0)) = multiplication(addition(iPr_def_10,iPr_def_11),X0),
inference(superposition,[status(thm)],[c_5780,c_57]) ).
tcf(c_5824,plain,
! [X0: $i] : addition(multiplication(sK2,X0),multiplication(sK0(sK2),X0)) = addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_12,X0)),
inference(light_normalisation,[status(thm)],[c_5813,c_1704]) ).
tcf(c_5826,plain,
complement(sK0(sK2),sK2),
inference(ground_joinability,[status(thm)],[c_5809,c_1755,c_1915]) ).
tcf(c_6408,plain,
addition(zero,multiplication(sK2,iPr_def_11)) = multiplication(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_810,c_1040]) ).
tcf(c_6411,plain,
addition(zero,multiplication(sK2,iPr_def_13)) = multiplication(iPr_def_10,iPr_def_13),
inference(superposition,[status(thm)],[c_1197,c_1040]) ).
tcf(c_6441,plain,
addition(zero,multiplication(sK2,iPr_def_13)) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_6411,c_474]) ).
tcf(c_6751,plain,
multiplication(sK2,iPr_def_11) = multiplication(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_6408,c_761]) ).
tcf(c_6759,plain,
multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_11)) = zero,
inference(superposition,[status(thm)],[c_6751,c_963]) ).
tcf(c_6810,plain,
multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_11)) = multiplication(sK0(sK2),sK2),
inference(demodulation,[status(thm)],[c_1915,c_6759]) ).
tcf(c_6812,plain,
multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_11)) = multiplication(c(iPr_def_12),iPr_def_12),
inference(demodulation,[status(thm)],[c_1894,c_6759]) ).
tcf(c_6824,plain,
multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_11)) = multiplication(sK1,iPr_def_13),
inference(demodulation,[status(thm)],[c_1197,c_6759]) ).
tcf(c_6830,plain,
multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_11)) = multiplication(sK2,iPr_def_12),
inference(demodulation,[status(thm)],[c_811,c_6759]) ).
tcf(c_6836,plain,
! [X0: $i] : addition(multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_11)),X0) = X0,
inference(demodulation,[status(thm)],[c_761,c_6759]) ).
tcf(c_6841,plain,
multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_11)) != iPr_def_14,
inference(demodulation,[status(thm)],[c_475,c_6759]) ).
tcf(c_6919,plain,
addition(sK0(sK2),multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_11))) = sK0(sK2),
inference(superposition,[status(thm)],[c_6810,c_4295]) ).
tcf(c_6921,plain,
addition(multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_11)),sK0(sK2)) = sK0(sK2),
inference(theory_normalisation,[status(thm)],[c_6919,c_50,c_49]) ).
tcf(c_7840,plain,
addition(iPr_def_14,multiplication(sK1,iPr_def_13)) = iPr_def_14,
inference(superposition,[status(thm)],[c_474,c_1736]) ).
tcf(c_7861,plain,
addition(iPr_def_14,multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_11))) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_7840,c_6824]) ).
tcf(c_8075,plain,
addition(multiplication(iPr_def_10,iPr_def_12),multiplication(iPr_def_12,iPr_def_12)) = addition(multiplication(sK2,iPr_def_12),sK0(sK2)),
inference(superposition,[status(thm)],[c_2805,c_5824]) ).
tcf(c_8083,plain,
addition(multiplication(iPr_def_10,iPr_def_12),iPr_def_12) = sK0(sK2),
inference(light_normalisation,[status(thm)],[c_8075,c_2664,c_6830,c_6921]) ).
tcf(c_8084,plain,
addition(iPr_def_12,multiplication(iPr_def_10,iPr_def_12)) = sK0(sK2),
inference(theory_normalisation,[status(thm)],[c_8083,c_50,c_49]) ).
tcf(c_8085,plain,
addition(iPr_def_12,iPr_def_12) = sK0(sK2),
inference(light_normalisation,[status(thm)],[c_8084,c_3883]) ).
tcf(c_8125,plain,
complement(addition(iPr_def_12,iPr_def_12),sK2),
inference(demodulation,[status(thm)],[c_5826,c_8085]) ).
tcf(c_8165,plain,
complement(iPr_def_12,sK2),
inference(demodulation,[status(thm)],[c_8125,c_52]) ).
tcf(c_8167,plain,
( ( c(iPr_def_12) = sK2 )
| ~ test(iPr_def_12) ),
inference(superposition,[status(thm)],[c_8165,c_66]) ).
tcf(c_8169,plain,
c(iPr_def_12) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_8167,c_749]) ).
tcf(c_9460,plain,
addition(multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_11)),multiplication(c(iPr_def_12),iPr_def_13)) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_6441,c_6759,c_8169]) ).
tcf(c_9461,plain,
multiplication(c(iPr_def_12),iPr_def_13) = iPr_def_14,
inference(demodulation,[status(thm)],[c_9460,c_6836]) ).
tcf(c_11362,plain,
addition(multiplication(c(iPr_def_12),iPr_def_12),iPr_def_14) = multiplication(c(iPr_def_12),iPr_def_12),
inference(superposition,[status(thm)],[c_9461,c_2200]) ).
tcf(c_11376,plain,
addition(iPr_def_14,multiplication(c(iPr_def_12),iPr_def_12)) = multiplication(c(iPr_def_12),iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_11362,c_50,c_49]) ).
tcf(c_11377,plain,
multiplication(iPr_def_12,multiplication(iPr_def_10,iPr_def_11)) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_11376,c_6812,c_7861]) ).
tcf(c_11378,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11377,c_6841]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE015+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.36 % Computer : n026.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Wed Sep 23 18:38:59 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.42 % Detected problem language: tptp
% 0.14/5.43 % Proving...
% 10.06/7.27 % SZS status Started for theBenchmark.p
% 10.06/7.27 % SZS status Theorem for theBenchmark.p
% 10.06/7.27
% 10.06/7.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.06/7.27
% 10.06/7.27 % ------ iProver source info
% 10.06/7.27
% 10.06/7.27 % git: date: 2026-07-19 20:42:38 +0200
% 10.06/7.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.06/7.27 % git: non_committed_changes: false
% 10.06/7.27
% 10.06/7.27 % ------ Parsing...
% 10.06/7.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.06/7.27
% 10.06/7.27 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 10.06/7.27
% 10.06/7.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.06/7.27
% 10.06/7.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.06/7.27 % ------ Proving...
% 10.06/7.27 % ------ Problem Properties
% 10.06/7.27
% 10.06/7.27 %
% 10.06/7.27 % clauses 28
% 10.06/7.27 % conjectures 2
% 10.06/7.27 % EPR 4
% 10.06/7.27 % Horn 27
% 10.06/7.27 % unary 19
% 10.06/7.27 % binary 7
% 10.06/7.27 % lits 40
% 10.06/7.27 % lits eq 25
% 10.06/7.27 % fd_pure 0
% 10.06/7.27 % fd_pseudo 0
% 10.06/7.27 % fd_cond 0
% 10.06/7.27 % fd_pseudo_cond 1
% 10.06/7.27 % AC symbols 1
% 10.06/7.27
% 10.06/7.27 % ------ Schedule dynamic 5 is on
% 10.06/7.27
% 10.06/7.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.06/7.27
% 10.06/7.27
% 10.06/7.27 % ------
% 10.06/7.27 % Current options:
% 10.06/7.27 % ------
% 10.06/7.27
% 10.06/7.27
% 10.06/7.27 %
% 10.06/7.27
% 10.06/7.27 % ------ Proving...
% 10.06/7.27 %
% 10.06/7.27
% 10.06/7.27 % SZS status Theorem for theBenchmark.p
% 10.06/7.27
% 10.06/7.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.06/7.28
% 10.06/7.28
%------------------------------------------------------------------------------