%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE036+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 : n016.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 01:52:14 PM UTC 2026
% Result : Theorem 89.19s 13.19s
% Output : CNFRefutation 89.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 19
% Syntax : Number of formulae : 120 ( 101 unt; 3 def)
% Number of atoms : 283 ( 82 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 69 ( 36 ~; 30 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 141 ( 0 sgn 140 !; 1 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+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/KLE002+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+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/KLE002+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/KLE002+0.ax',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).
fof(f13,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(f14,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X0)
=> leq(multiplication(X2,star(X1)),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_induction_right) ).
fof(f17,conjecture,
! [X0] : leq(star(X0),addition(one,multiplication(X0,star(X0)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0] : leq(star(X0),addition(one,multiplication(X0,star(X0)))),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f21,plain,
? [X0] : ~ leq(star(X0),addition(one,multiplication(X0,star(X0)))),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f23,plain,
~ leq(star(sK0),addition(one,multiplication(sK0,star(sK0)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f21]) ).
fof(f24,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f25,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f28,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f29,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f35,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f38,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f41,plain,
~ leq(star(sK0),addition(one,multiplication(sK0,star(sK0)))),
inference(cnf_transformation,[],[f23]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f27]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f29]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f30]) ).
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,[],[f31]) ).
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,[],[f32]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_62,plain,
! [X0: $i] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_63,plain,
! [X0: $i] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_66,negated_conjecture,
~ leq(star(sK0),addition(one,multiplication(sK0,star(sK0)))),
inference(cnf_transformation,[],[f41]) ).
tcf(c_183,definition,
iPr_def_10 = star(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_184,definition,
iPr_def_11 = multiplication(sK0,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_185,definition,
iPr_def_12 = addition(one,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_186,negated_conjecture,
~ leq(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_66,c_184,c_185,c_183]) ).
tcf(c_187,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_189,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leq(X0,X2)
| ~ leq(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_587,plain,
! [X0: $i,X1: $i] :
( leq(iPr_def_10,iPr_def_12)
| ~ leq(X0,X1)
| ( iPr_def_12 != X1 )
| ( iPr_def_10 != X0 ) ),
inference(instantiation,[status(thm)],[c_192]) ).
tcf(c_625,plain,
iPr_def_10 = iPr_def_10,
inference(instantiation,[status(thm)],[c_187]) ).
tcf(c_627,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_10 = X0 )
| ( iPr_def_10 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_189]) ).
tcf(c_920,plain,
iPr_def_12 = iPr_def_12,
inference(instantiation,[status(thm)],[c_187]) ).
tcf(c_928,plain,
! [X0: $i] :
( ( iPr_def_10 = X0 )
| ( iPr_def_10 != iPr_def_10 )
| ( X0 != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_627]) ).
tcf(c_1487,plain,
( ( iPr_def_10 = multiplication(one,iPr_def_10) )
| ( iPr_def_10 != iPr_def_10 )
| ( multiplication(one,iPr_def_10) != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_928]) ).
tcf(c_1488,plain,
multiplication(one,iPr_def_10) = iPr_def_10,
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_4741,plain,
! [X0: $i] :
( leq(iPr_def_10,iPr_def_12)
| ~ leq(multiplication(one,iPr_def_10),X0)
| ( iPr_def_12 != X0 )
| ( iPr_def_10 != multiplication(one,iPr_def_10) ) ),
inference(instantiation,[status(thm)],[c_587]) ).
tcf(c_19409,plain,
( leq(iPr_def_10,iPr_def_12)
| ~ leq(multiplication(one,iPr_def_10),iPr_def_12)
| ( iPr_def_12 != iPr_def_12 )
| ( iPr_def_10 != multiplication(one,iPr_def_10) ) ),
inference(instantiation,[status(thm)],[c_4741]) ).
tcf(c_169210,plain,
addition(iPr_def_11,one) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_185,c_50,c_49]) ).
tcf(c_169213,plain,
leq(addition(one,multiplication(sK0,iPr_def_10)),iPr_def_10),
inference(superposition,[status(thm)],[c_183,c_62]) ).
tcf(c_169216,plain,
leq(addition(one,iPr_def_11),iPr_def_10),
inference(light_normalisation,[status(thm)],[c_169213,c_184]) ).
tcf(c_169217,plain,
leq(addition(iPr_def_11,one),iPr_def_10),
inference(theory_normalisation,[status(thm)],[c_169216,c_50,c_49]) ).
tcf(c_169218,plain,
leq(iPr_def_12,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_169217,c_169210]) ).
tcf(c_169226,plain,
leq(addition(one,multiplication(iPr_def_10,sK0)),iPr_def_10),
inference(superposition,[status(thm)],[c_183,c_63]) ).
tcf(c_169260,plain,
addition(iPr_def_12,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_169218,c_61]) ).
tcf(c_169261,plain,
addition(addition(one,multiplication(iPr_def_10,sK0)),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_169226,c_61]) ).
tcf(c_169264,plain,
addition(iPr_def_10,iPr_def_12) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_169260,c_50,c_49]) ).
tcf(c_169265,plain,
addition(iPr_def_10,addition(one,multiplication(iPr_def_10,sK0))) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_169261,c_50,c_49]) ).
tcf(c_169274,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_169276,plain,
! [X0: $i] : addition(iPr_def_11,addition(one,X0)) = addition(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_169210,c_50]) ).
tcf(c_169289,plain,
! [X0: $i] : multiplication(sK0,multiplication(iPr_def_10,X0)) = multiplication(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_184,c_53]) ).
tcf(c_169297,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(one,X1)),
inference(superposition,[status(thm)],[c_54,c_56]) ).
tcf(c_169354,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_169514,plain,
addition(iPr_def_11,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_169210,c_169274]) ).
tcf(c_169519,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_169274,c_60]) ).
tcf(c_169532,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_169519]) ).
tcf(c_169534,plain,
! [X0: $i,X1: $i,X2: $i] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(superposition,[status(thm)],[c_50,c_169519]) ).
tcf(c_169537,plain,
! [X0: $i,X1: $i,X2: $i] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(superposition,[status(thm)],[c_56,c_169519]) ).
tcf(c_169564,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X2,X0))),
inference(superposition,[status(thm)],[c_50,c_169532]) ).
tcf(c_169570,plain,
leq(one,iPr_def_12),
inference(superposition,[status(thm)],[c_169210,c_169532]) ).
tcf(c_169576,plain,
addition(one,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_169570,c_61]) ).
tcf(c_169577,plain,
addition(iPr_def_12,one) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_169576,c_50,c_49]) ).
tcf(c_169621,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(multiplication(X0,star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_49,c_65]) ).
tcf(c_169722,plain,
leq(multiplication(iPr_def_10,sK0),iPr_def_10),
inference(superposition,[status(thm)],[c_169265,c_169564]) ).
tcf(c_169729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(superposition,[status(thm)],[c_56,c_169564]) ).
tcf(c_169737,plain,
! [X0: $i] : leq(one,addition(X0,iPr_def_12)),
inference(superposition,[status(thm)],[c_169577,c_169564]) ).
tcf(c_169777,plain,
addition(multiplication(iPr_def_10,sK0),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_169722,c_61]) ).
tcf(c_169778,plain,
addition(iPr_def_10,multiplication(iPr_def_10,sK0)) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_169777,c_50,c_49]) ).
tcf(c_169794,plain,
leq(one,iPr_def_10),
inference(superposition,[status(thm)],[c_169264,c_169737]) ).
tcf(c_169803,plain,
addition(one,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_169794,c_61]) ).
tcf(c_169804,plain,
addition(iPr_def_10,one) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_169803,c_50,c_49]) ).
tcf(c_170216,plain,
multiplication(iPr_def_10,addition(one,sK0)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_169778,c_169297]) ).
tcf(c_170328,plain,
! [X0: $i,X1: $i,X2: $i] : leq(addition(X0,X1),addition(X0,addition(X2,X1))),
inference(superposition,[status(thm)],[c_49,c_169534]) ).
tcf(c_170982,plain,
! [X0: $i,X1: $i] : leq(X0,multiplication(X0,addition(one,X1))),
inference(superposition,[status(thm)],[c_54,c_169537]) ).
tcf(c_171047,plain,
! [X0: $i,X1: $i] : leq(X0,multiplication(X0,addition(X1,one))),
inference(superposition,[status(thm)],[c_49,c_170982]) ).
tcf(c_171133,plain,
! [X0: $i] : leq(X0,multiplication(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_169804,c_171047]) ).
tcf(c_171151,plain,
leq(sK0,iPr_def_11),
inference(superposition,[status(thm)],[c_184,c_171133]) ).
tcf(c_171173,plain,
addition(sK0,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_171151,c_61]) ).
tcf(c_171174,plain,
addition(iPr_def_11,sK0) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_171173,c_50,c_49]) ).
tcf(c_173012,plain,
! [X0: $i] : leq(addition(X0,sK0),addition(X0,iPr_def_11)),
inference(superposition,[status(thm)],[c_171174,c_170328]) ).
tcf(c_173470,plain,
! [X0: $i] : leq(addition(X0,sK0),addition(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_49,c_173012]) ).
tcf(c_175552,plain,
! [X0: $i] : leq(addition(addition(one,X0),sK0),addition(iPr_def_12,X0)),
inference(superposition,[status(thm)],[c_169276,c_173470]) ).
tcf(c_175683,plain,
! [X0: $i] : leq(addition(one,addition(X0,sK0)),addition(iPr_def_12,X0)),
inference(theory_normalisation,[status(thm)],[c_175552,c_50,c_49]) ).
tcf(c_179735,plain,
multiplication(iPr_def_11,addition(one,sK0)) = multiplication(sK0,iPr_def_10),
inference(superposition,[status(thm)],[c_170216,c_169289]) ).
tcf(c_179773,plain,
multiplication(iPr_def_11,addition(one,sK0)) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_179735,c_184]) ).
tcf(c_182196,plain,
! [X0: $i] : leq(multiplication(iPr_def_11,sK0),addition(X0,iPr_def_11)),
inference(superposition,[status(thm)],[c_179773,c_169729]) ).
tcf(c_182377,plain,
! [X0: $i] : leq(multiplication(iPr_def_11,sK0),addition(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_49,c_182196]) ).
tcf(c_182473,plain,
leq(multiplication(iPr_def_11,sK0),iPr_def_12),
inference(superposition,[status(thm)],[c_169514,c_182377]) ).
tcf(c_182478,plain,
addition(multiplication(iPr_def_11,sK0),iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_182473,c_61]) ).
tcf(c_182479,plain,
addition(iPr_def_12,multiplication(iPr_def_11,sK0)) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_182478,c_50,c_49]) ).
tcf(c_183744,plain,
leq(addition(one,addition(multiplication(iPr_def_11,sK0),sK0)),iPr_def_12),
inference(superposition,[status(thm)],[c_182479,c_175683]) ).
tcf(c_183797,plain,
leq(addition(one,addition(sK0,multiplication(iPr_def_11,sK0))),iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_183744,c_50,c_49]) ).
tcf(c_193516,plain,
leq(addition(one,multiplication(iPr_def_12,sK0)),iPr_def_12),
inference(demodulation,[status(thm)],[c_183797,c_49,c_169210,c_169354]) ).
tcf(c_193518,plain,
leq(multiplication(one,star(sK0)),iPr_def_12),
inference(superposition,[status(thm)],[c_193516,c_169621]) ).
tcf(c_193519,plain,
leq(multiplication(one,iPr_def_10),iPr_def_12),
inference(light_normalisation,[status(thm)],[c_193518,c_183]) ).
tcf(c_193521,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_193519,c_19409,c_1488,c_1487,c_920,c_625,c_186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE036+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 18:48:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.44
% 0.14/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.44
% 0.14/0.44 % Detected problem language: tptp
% 0.14/0.45 % Proving...
% 89.19/13.19 % SZS status Started for theBenchmark.p
% 89.19/13.19 ERROR - "ProverProcess:heur/445550:16.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clause.get_demod_eqs: not a demod/lightnorm conclusion ( leq(zero,addition(one,one)) )")
% 89.19/13.19 Fatal error: exception Failure("Clause.get_demod_eqs: not a demod/lightnorm conclusion ( leq(zero,addition(one,one)) )")
% 89.19/13.19 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode time_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 1.6084091637003026 --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd false --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red true --prep_gs_sim false --prep_res_sim true --prep_sem_filter neg --prep_sup_sim_all true --prep_sup_sim_sup true --prep_unflatten true --prep_upred false --preprocessing_flag true --prolific_symb_bound 32768 --prop_solver_per_cl 4096 --pure_diseq_elim false --res_backward_subs subset_subsumption --res_backward_subs_resolution false --res_forward_subs subset_subsumption --res_forward_subs_resolution false --res_lit_sel adaptive --res_lit_sel_side num_var --res_ordering kbo --res_passive_queue_type stack --res_passive_queues "[[-num_lits;+conj_symb;-num_symb];[-num_lits;+min_def_symb]]" --res_passive_queues_freq "[1;3]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input false --res_time_limit 202.19 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl true --splitting_grd true --splitting_mode input --splitting_nvd 16 --stats_out none --sub_typing false --subs_bck_mult 1 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[DemodLightNormLoopTriv;ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 640 --sup_share_score_frac 0.1 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.9903106699302947 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 5.33" --time_out_real 16.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_08yvx3cf/e147wg4k 2>> /export/starexec/sandbox/tmp/iprover_out_08yvx3cf/e147wg4k_error
% 89.19/13.19 % SZS status Theorem for theBenchmark.p
% 89.19/13.19
% 89.19/13.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 89.19/13.19
% 89.19/13.19 % ------ iProver source info
% 89.19/13.19
% 89.19/13.19 % git: date: 2026-07-19 20:42:38 +0200
% 89.19/13.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 89.19/13.19 % git: non_committed_changes: false
% 89.19/13.19
% 89.19/13.19 % ------ Parsing...
% 89.19/13.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 89.19/13.19
% 89.19/13.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 89.19/13.19
% 89.19/13.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 89.19/13.19
% 89.19/13.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 89.19/13.19 % ------ Proving...
% 89.19/13.19 % ------ Problem Properties
% 89.19/13.19
% 89.19/13.19 %
% 89.19/13.19 % clauses 21
% 89.19/13.19 % conjectures 1
% 89.19/13.19 % EPR 1
% 89.19/13.19 % Horn 21
% 89.19/13.19 % unary 17
% 89.19/13.19 % binary 4
% 89.19/13.19 % lits 25
% 89.19/13.19 % lits eq 16
% 89.19/13.19 % fd_pure 0
% 89.19/13.19 % fd_pseudo 0
% 89.19/13.19 % fd_cond 0
% 89.19/13.19 % fd_pseudo_cond 0
% 89.19/13.19 % AC symbols 1
% 89.19/13.19
% 89.19/13.19 % ------ Schedule dynamic 5 is on
% 89.19/13.19
% 89.19/13.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 89.19/13.19
% 89.19/13.19
% 89.19/13.19 % ------
% 89.19/13.19 % Current options:
% 89.19/13.19 % ------
% 89.19/13.19
% 89.19/13.19
% 89.19/13.19 %
% 89.19/13.19
% 89.19/13.19 % ------ Proving...
% 89.19/13.19 % Proof_search_loop: time out after: 3715 full_loop iterations
% 89.19/13.19
% 89.19/13.19 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 89.19/13.19
% 89.19/13.19
% 89.19/13.19 % ------
% 89.19/13.19 % Current options:
% 89.19/13.19 % ------
% 89.19/13.19
% 89.19/13.19
% 89.19/13.19 %
% 89.19/13.19
% 89.19/13.19 % ------ Proving...
% 89.19/13.19 %
% 89.19/13.19
% 89.19/13.19 % SZS status Theorem for theBenchmark.p
% 89.19/13.19
% 89.19/13.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 89.19/13.20
% 89.19/13.20
%------------------------------------------------------------------------------