%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE018+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 : n012.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 7.84s 1.50s
% Output : CNFRefutation 7.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 20
% Syntax : Number of formulae : 134 ( 96 unt; 5 def)
% Number of atoms : 288 ( 122 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 137 ( 54 ~; 44 |; 29 &)
% ( 5 <=>; 5 =>; 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 : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 144 ( 0 sgn 135 !; 9 ?; 56 :)
% 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(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
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,X2] :
( ( test(X2)
& test(X1)
& test(X0) )
=> ( leq(multiplication(X0,c(X1)),X2)
=> leq(X0,addition(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1)
& test(X0) )
=> ( leq(multiplication(X0,c(X1)),X2)
=> leq(X0,addition(X1,X2)) ) ),
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,X2] :
( test(X2)
& test(X1)
& test(X0)
& leq(multiplication(X0,c(X1)),X2)
& ~ leq(X0,addition(X1,X2)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
? [X0,X1,X2] :
( test(X2)
& test(X1)
& test(X0)
& leq(multiplication(X0,c(X1)),X2)
& ~ leq(X0,addition(X1,X2)) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X0] :
( ( ~ test(X0)
| ? [X2] : complement(X2,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f26,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))],[f25]) ).
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(nnf_transformation,[],[f14]) ).
fof(f28,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,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f30,plain,
( test(sK3)
& test(sK2)
& test(sK1)
& leq(multiplication(sK1,c(sK2)),sK3)
& ~ leq(sK1,addition(sK2,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f22]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f41,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f42,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
! [X0] :
( ~ test(X0)
| complement(sK0(X0),X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
test(sK3),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
test(sK2),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
test(sK1),
inference(cnf_transformation,[],[f30]) ).
fof(f56,plain,
leq(multiplication(sK1,c(sK2)),sK3),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
~ leq(sK1,addition(sK2,sK3)),
inference(cnf_transformation,[],[f30]) ).
fof(f58,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f50]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f34]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f37]) ).
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,[],[f38]) ).
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,[],[f39]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f41]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_63,plain,
! [X0: $i] :
( complement(sK0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( multiplication(X0,X1) = zero )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_69,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_71,negated_conjecture,
~ leq(sK1,addition(sK2,sK3)),
inference(cnf_transformation,[],[f57]) ).
tcf(c_72,negated_conjecture,
leq(multiplication(sK1,c(sK2)),sK3),
inference(cnf_transformation,[],[f56]) ).
tcf(c_73,negated_conjecture,
test(sK1),
inference(cnf_transformation,[],[f55]) ).
tcf(c_74,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f54]) ).
tcf(c_75,negated_conjecture,
test(sK3),
inference(cnf_transformation,[],[f53]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) != X1 )
| leq(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(renaming,[status(thm)],[c_93]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i] :
( ( X0 != sK1 )
| ( addition(sK2,sK3) != X1 )
| ( addition(X0,X1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_94,c_71]) ).
tcf(c_304,plain,
addition(sK1,addition(sK2,sK3)) != addition(sK2,sK3),
inference(unflattening,[status(thm)],[c_303]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ( X1 != sK3 )
| ( multiplication(sK1,c(sK2)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_95,c_72]) ).
tcf(c_309,plain,
addition(multiplication(sK1,c(sK2)),sK3) = sK3,
inference(unflattening,[status(thm)],[c_308]) ).
tcf(c_610,plain,
addition(sK3,multiplication(sK1,c(sK2))) = sK3,
inference(theory_normalisation,[status(thm)],[c_309,c_50,c_49]) ).
tcf(c_1009,definition,
iPr_def_10 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1010,definition,
iPr_def_11 = multiplication(sK1,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1011,definition,
iPr_def_12 = addition(sK3,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1012,definition,
iPr_def_13 = addition(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1013,definition,
iPr_def_14 = addition(sK1,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1014,plain,
iPr_def_12 = sK3,
inference(demodulation,[status(thm)],[c_610,c_1009,c_1010,c_1011]) ).
tcf(c_1016,plain,
iPr_def_14 != iPr_def_13,
inference(demodulation,[status(thm)],[c_304,c_1013]) ).
tcf(c_1017,negated_conjecture,
test(sK3),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_1018,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_1019,negated_conjecture,
test(sK1),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_1289,plain,
test(iPr_def_12),
inference(light_normalisation,[status(thm)],[c_1017,c_1014]) ).
tcf(c_1293,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_1301,plain,
addition(iPr_def_11,sK3) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_1011,c_50,c_49]) ).
tcf(c_1302,plain,
addition(iPr_def_11,iPr_def_12) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_1301,c_1014]) ).
tcf(c_1303,plain,
addition(sK2,iPr_def_12) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_1012,c_1014]) ).
tcf(c_1304,plain,
addition(iPr_def_12,sK2) = iPr_def_13,
inference(demodulation,[status(thm)],[c_1303,c_49]) ).
tcf(c_1305,plain,
addition(iPr_def_13,sK1) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_1013,c_50,c_49]) ).
tcf(c_1319,plain,
( complement(sK2,iPr_def_10)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_1009,c_69]) ).
tcf(c_1323,plain,
complement(sK2,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1319,c_1018]) ).
tcf(c_1333,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_1335,plain,
! [X0: $i] : addition(iPr_def_11,addition(iPr_def_12,X0)) = addition(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_1302,c_50]) ).
tcf(c_1364,plain,
! [X0: $i] :
( ( multiplication(sK0(X0),X0) = zero )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_63,c_66]) ).
tcf(c_1375,plain,
! [X0: $i] :
( ( addition(X0,sK0(X0)) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_63,c_67]) ).
tcf(c_1377,plain,
addition(iPr_def_10,sK2) = one,
inference(superposition,[status(thm)],[c_1323,c_67]) ).
tcf(c_1384,plain,
! [X0: $i] : addition(iPr_def_10,addition(sK2,X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_1377,c_50]) ).
tcf(c_1386,plain,
! [X0: $i] : addition(iPr_def_10,addition(X0,sK2)) = addition(one,X0),
inference(superposition,[status(thm)],[c_49,c_1384]) ).
tcf(c_1403,plain,
addition(one,iPr_def_12) = addition(iPr_def_10,iPr_def_13),
inference(superposition,[status(thm)],[c_1304,c_1386]) ).
tcf(c_1412,plain,
addition(iPr_def_10,iPr_def_13) = addition(iPr_def_12,one),
inference(theory_normalisation,[status(thm)],[c_1403,c_50,c_49]) ).
tcf(c_1435,plain,
addition(iPr_def_11,iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_1304,c_1335]) ).
tcf(c_1794,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_13)) = multiplication(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_1435,c_56]) ).
tcf(c_4478,plain,
multiplication(sK0(sK1),sK1) = zero,
inference(superposition,[status(thm)],[c_1019,c_1364]) ).
tcf(c_4492,plain,
! [X0: $i] : multiplication(sK0(sK1),multiplication(sK1,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_4478,c_53]) ).
tcf(c_4494,plain,
! [X0: $i] : multiplication(sK0(sK1),multiplication(sK1,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_4492,c_59]) ).
tcf(c_4619,plain,
multiplication(sK0(sK1),iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_1010,c_4494]) ).
tcf(c_5134,plain,
addition(sK1,sK0(sK1)) = one,
inference(superposition,[status(thm)],[c_1019,c_1375]) ).
tcf(c_5138,plain,
addition(iPr_def_12,sK0(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_1289,c_1375]) ).
tcf(c_5147,plain,
addition(sK1,one) = one,
inference(superposition,[status(thm)],[c_5134,c_1333]) ).
tcf(c_5153,plain,
! [X0: $i] : addition(multiplication(sK1,X0),multiplication(sK0(sK1),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_5134,c_57]) ).
tcf(c_5155,plain,
addition(one,sK1) = one,
inference(theory_normalisation,[status(thm)],[c_5147,c_50,c_49]) ).
tcf(c_5157,plain,
! [X0: $i] : addition(multiplication(sK1,X0),multiplication(sK0(sK1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_5153,c_55]) ).
tcf(c_5250,plain,
! [X0: $i] : addition(multiplication(one,X0),multiplication(sK1,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_5155,c_57]) ).
tcf(c_5254,plain,
! [X0: $i] : addition(X0,multiplication(sK1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_5250,c_55]) ).
tcf(c_5381,plain,
addition(iPr_def_12,one) = one,
inference(superposition,[status(thm)],[c_5138,c_1333]) ).
tcf(c_5389,plain,
addition(iPr_def_10,iPr_def_13) = one,
inference(light_normalisation,[status(thm)],[c_5381,c_1412]) ).
tcf(c_5432,plain,
! [X0: $i] : multiplication(X0,addition(iPr_def_10,iPr_def_13)) = X0,
inference(demodulation,[status(thm)],[c_54,c_5389]) ).
tcf(c_6236,plain,
addition(multiplication(sK1,iPr_def_11),zero) = iPr_def_11,
inference(superposition,[status(thm)],[c_4619,c_5157]) ).
tcf(c_6245,plain,
addition(zero,multiplication(sK1,iPr_def_11)) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_6236,c_50,c_49]) ).
tcf(c_7314,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,iPr_def_13)) = X0,
inference(demodulation,[status(thm)],[c_5432,c_56]) ).
tcf(c_7318,plain,
addition(iPr_def_11,multiplication(sK1,iPr_def_13)) = sK1,
inference(superposition,[status(thm)],[c_1010,c_7314]) ).
tcf(c_7879,plain,
multiplication(sK1,iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_6245,c_1293]) ).
tcf(c_12400,plain,
addition(iPr_def_11,multiplication(sK1,iPr_def_13)) = multiplication(sK1,iPr_def_13),
inference(superposition,[status(thm)],[c_7879,c_1794]) ).
tcf(c_12414,plain,
multiplication(sK1,iPr_def_13) = sK1,
inference(light_normalisation,[status(thm)],[c_12400,c_7318]) ).
tcf(c_12477,plain,
addition(iPr_def_13,sK1) = iPr_def_13,
inference(superposition,[status(thm)],[c_12414,c_5254]) ).
tcf(c_12491,plain,
iPr_def_13 = iPr_def_14,
inference(demodulation,[status(thm)],[c_1305,c_12477]) ).
tcf(c_12526,plain,
iPr_def_13 != iPr_def_13,
inference(demodulation,[status(thm)],[c_1016,c_12491]) ).
tcf(c_12527,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_12526]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE018+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 18:37:42 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.06/0.33
% 0.06/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.06/0.33
% 0.06/0.33 % Detected problem language: tptp
% 0.06/0.33 % Proving...
% 7.84/1.50 % SZS status Started for theBenchmark.p
% 7.84/1.50 % SZS status Theorem for theBenchmark.p
% 7.84/1.50
% 7.84/1.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.84/1.50
% 7.84/1.50 % ------ iProver source info
% 7.84/1.50
% 7.84/1.50 % git: date: 2026-07-19 20:42:38 +0200
% 7.84/1.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.84/1.50 % git: non_committed_changes: false
% 7.84/1.50
% 7.84/1.50 % ------ Parsing...
% 7.84/1.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.84/1.50
% 7.84/1.50 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 7.84/1.50
% 7.84/1.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.84/1.50
% 7.84/1.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.84/1.50 % ------ Proving...
% 7.84/1.50 % ------ Problem Properties
% 7.84/1.50
% 7.84/1.50 %
% 7.84/1.50 % clauses 31
% 7.84/1.50 % conjectures 3
% 7.84/1.50 % EPR 7
% 7.84/1.50 % Horn 30
% 7.84/1.50 % unary 21
% 7.84/1.50 % binary 8
% 7.84/1.50 % lits 44
% 7.84/1.50 % lits eq 28
% 7.84/1.50 % fd_pure 0
% 7.84/1.50 % fd_pseudo 0
% 7.84/1.50 % fd_cond 0
% 7.84/1.50 % fd_pseudo_cond 1
% 7.84/1.50 % AC symbols 1
% 7.84/1.50
% 7.84/1.50 % ------ Schedule dynamic 5 is on
% 7.84/1.50
% 7.84/1.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.84/1.50
% 7.84/1.50
% 7.84/1.50 % ------
% 7.84/1.50 % Current options:
% 7.84/1.50 % ------
% 7.84/1.50
% 7.84/1.50
% 7.84/1.50 %
% 7.84/1.50
% 7.84/1.50 % ------ Proving...
% 7.84/1.50 %
% 7.84/1.50
% 7.84/1.50 % SZS status Theorem for theBenchmark.p
% 7.84/1.50
% 7.84/1.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.84/1.51
% 7.84/1.51
%------------------------------------------------------------------------------