%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE008+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:52:07 PM UTC 2026
% Result : Theorem 134.59s 21.49s
% Output : CNFRefutation 134.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 19
% Syntax : Number of formulae : 176 ( 98 unt; 3 def)
% Number of atoms : 478 ( 163 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 218 ( 82 ~; 103 |; 23 &)
% ( 6 <=>; 3 =>; 0 <=; 1 <~>)
% 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 : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 181 ( 0 sgn 172 !; 9 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( test(X2)
=> ( leq(X0,multiplication(X2,X1))
<=> ( leq(multiplication(c(X2),X0),zero)
& leq(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( test(X2)
=> ( leq(X0,multiplication(X2,X1))
<=> ( leq(multiplication(c(X2),X0),zero)
& leq(X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
? [X0,X1,X2] :
( test(X2)
& ( leq(X0,multiplication(X2,X1))
<~> ( leq(multiplication(c(X2),X0),zero)
& leq(X0,X1) ) ) ),
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(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,
? [X0,X1,X2] :
( test(X2)
& ( leq(X0,multiplication(X2,X1))
| ( leq(multiplication(c(X2),X0),zero)
& leq(X0,X1) ) )
& ( ~ leq(X0,multiplication(X2,X1))
| ~ leq(multiplication(c(X2),X0),zero)
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f30,plain,
? [X0,X1,X2] :
( test(X2)
& ( leq(X0,multiplication(X2,X1))
| ( leq(multiplication(c(X2),X0),zero)
& leq(X0,X1) ) )
& ( ~ leq(X0,multiplication(X2,X1))
| ~ leq(multiplication(c(X2),X0),zero)
| ~ leq(X0,X1) ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
( test(sK3)
& ( leq(sK1,multiplication(sK3,sK2))
| ( leq(multiplication(c(sK3),sK1),zero)
& leq(sK1,sK2) ) )
& ( ~ leq(sK1,multiplication(sK3,sK2))
| ~ leq(multiplication(c(sK3),sK1),zero)
| ~ leq(sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f30]) ).
fof(f32,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f33,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f34,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f35,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f37,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f38,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f40,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(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f42,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f43,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f47,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f51,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f54,plain,
test(sK3),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
( leq(sK1,multiplication(sK3,sK2))
| leq(multiplication(c(sK3),sK1),zero) ),
inference(cnf_transformation,[],[f31]) ).
fof(f56,plain,
( leq(sK1,multiplication(sK3,sK2))
| leq(sK1,sK2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f57,plain,
( ~ leq(sK1,multiplication(sK3,sK2))
| ~ leq(multiplication(c(sK3),sK1),zero)
| ~ leq(sK1,sK2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f58,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f51]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f32]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f34]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f35]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f37]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f38]) ).
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,[],[f39]) ).
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,[],[f40]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f41]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f42]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( multiplication(X1,X0) = zero )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_69,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_71,negated_conjecture,
( ~ leq(sK1,sK2)
| ~ leq(sK1,multiplication(sK3,sK2))
| ~ leq(multiplication(c(sK3),sK1),zero) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_72,negated_conjecture,
( leq(sK1,sK2)
| leq(sK1,multiplication(sK3,sK2)) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_73,negated_conjecture,
( leq(sK1,multiplication(sK3,sK2))
| leq(multiplication(c(sK3),sK1),zero) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_74,negated_conjecture,
test(sK3),
inference(cnf_transformation,[],[f54]) ).
tcf(c_570,definition,
iPr_def_10 = c(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_571,definition,
iPr_def_11 = multiplication(iPr_def_10,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_572,definition,
iPr_def_12 = multiplication(sK3,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_573,negated_conjecture,
test(sK3),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_574,negated_conjecture,
( leq(iPr_def_11,zero)
| leq(sK1,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_73,c_572,c_570,c_571]) ).
tcf(c_575,negated_conjecture,
( leq(sK1,iPr_def_12)
| leq(sK1,sK2) ),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_576,negated_conjecture,
( ~ leq(iPr_def_11,zero)
| ~ leq(sK1,iPr_def_12)
| ~ leq(sK1,sK2) ),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_579,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1116,plain,
( complement(sK3,iPr_def_10)
| ~ test(sK3) ),
inference(superposition,[status(thm)],[c_570,c_69]) ).
tcf(c_1120,plain,
complement(sK3,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1116,c_573]) ).
tcf(c_1157,plain,
( leq(sK1,iPr_def_12)
| ( addition(sK1,sK2) = sK2 ) ),
inference(superposition,[status(thm)],[c_575,c_61]) ).
tcf(c_1159,plain,
( leq(iPr_def_11,zero)
| ( addition(sK1,iPr_def_12) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_574,c_61]) ).
tcf(c_1160,plain,
( leq(iPr_def_11,zero)
| ( addition(iPr_def_12,sK1) = iPr_def_12 ) ),
inference(theory_normalisation,[status(thm)],[c_1159,c_50,c_49]) ).
tcf(c_1171,plain,
multiplication(iPr_def_10,sK3) = zero,
inference(superposition,[status(thm)],[c_1120,c_65]) ).
tcf(c_1201,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(sK3,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_1171,c_53]) ).
tcf(c_1202,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(sK3,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_1201,c_59]) ).
tcf(c_1214,plain,
( ( addition(sK1,iPr_def_12) = iPr_def_12 )
| ( addition(sK1,sK2) = sK2 ) ),
inference(superposition,[status(thm)],[c_1157,c_61]) ).
tcf(c_1215,plain,
( ( addition(iPr_def_12,sK1) = iPr_def_12 )
| ( addition(sK1,sK2) = sK2 ) ),
inference(theory_normalisation,[status(thm)],[c_1214,c_50,c_49]) ).
tcf(c_1233,plain,
( leq(sK1,sK2)
| ( addition(iPr_def_12,sK1) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_1215,c_60]) ).
tcf(c_1249,plain,
multiplication(iPr_def_10,iPr_def_12) = zero,
inference(superposition,[status(thm)],[c_572,c_1202]) ).
tcf(c_1254,plain,
( leq(iPr_def_11,multiplication(iPr_def_10,iPr_def_12))
| ( addition(iPr_def_12,sK1) = iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_1160,c_1249]) ).
tcf(c_1265,plain,
( ~ leq(sK1,iPr_def_12)
| ~ leq(sK1,sK2)
| ~ leq(iPr_def_11,multiplication(iPr_def_10,iPr_def_12)) ),
inference(demodulation,[status(thm)],[c_576,c_1249]) ).
tcf(c_1469,plain,
( ( addition(iPr_def_12,sK1) = iPr_def_12 )
| ~ leq(sK1,iPr_def_12)
| ~ leq(sK1,sK2) ),
inference(superposition,[status(thm)],[c_1254,c_1265]) ).
tcf(c_1483,plain,
( ( addition(iPr_def_12,sK1) = iPr_def_12 )
| ~ leq(sK1,iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_1469,c_1233,c_1469]) ).
tcf(c_1804,plain,
( complement(sK3,iPr_def_10)
| ~ test(sK3) ),
inference(superposition,[status(thm)],[c_570,c_69]) ).
tcf(c_1808,plain,
complement(sK3,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1804,c_573]) ).
tcf(c_1816,plain,
! [X0: $i] :
( leq(sK1,X0)
| ( addition(sK1,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_2127,plain,
multiplication(iPr_def_10,sK3) = zero,
inference(superposition,[status(thm)],[c_1808,c_65]) ).
tcf(c_2380,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(sK3,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_2127,c_53]) ).
tcf(c_2381,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(sK3,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_2380,c_59]) ).
tcf(c_2565,plain,
multiplication(iPr_def_10,iPr_def_12) = zero,
inference(superposition,[status(thm)],[c_572,c_2381]) ).
tcf(c_26551,plain,
( leq(sK1,iPr_def_12)
| ( addition(sK1,iPr_def_12) != iPr_def_12 ) ),
inference(instantiation,[status(thm)],[c_1816]) ).
tcf(c_26574,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_12 )
| ( iPr_def_12 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_579]) ).
tcf(c_41993,plain,
! [X0: $i] :
( ( X0 = iPr_def_12 )
| ( iPr_def_12 != multiplication(sK3,sK2) )
| ( X0 != multiplication(sK3,sK2) ) ),
inference(instantiation,[status(thm)],[c_26574]) ).
tcf(c_59683,plain,
( ( iPr_def_12 = iPr_def_12 )
| ( iPr_def_12 != multiplication(sK3,sK2) ) ),
inference(instantiation,[status(thm)],[c_41993]) ).
tcf(c_141873,plain,
! [X0: $i,X1: $i] :
( ( addition(sK1,X0) = X0 )
| ( X0 != X1 )
| ( addition(sK1,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_579]) ).
tcf(c_142974,plain,
addition(sK1,iPr_def_12) = addition(iPr_def_12,sK1),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_143129,plain,
! [X0: $i] :
( ( addition(sK1,X0) = X0 )
| ( X0 != addition(X0,sK1) )
| ( addition(sK1,X0) != addition(X0,sK1) ) ),
inference(instantiation,[status(thm)],[c_141873]) ).
tcf(c_163217,plain,
( ( addition(sK1,iPr_def_12) = iPr_def_12 )
| ( iPr_def_12 != addition(iPr_def_12,sK1) )
| ( addition(sK1,iPr_def_12) != addition(iPr_def_12,sK1) ) ),
inference(instantiation,[status(thm)],[c_143129]) ).
tcf(c_195004,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(sK1,X0)) = multiplication(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_571,c_53]) ).
tcf(c_195019,plain,
( complement(sK3,iPr_def_10)
| ~ test(sK3) ),
inference(superposition,[status(thm)],[c_570,c_69]) ).
tcf(c_195023,plain,
complement(sK3,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_195019,c_573]) ).
tcf(c_195086,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_49,c_51]) ).
tcf(c_195108,plain,
( leq(sK1,iPr_def_12)
| ( addition(sK1,sK2) = sK2 ) ),
inference(superposition,[status(thm)],[c_575,c_61]) ).
tcf(c_195110,plain,
( leq(iPr_def_11,zero)
| ( addition(sK1,iPr_def_12) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_574,c_61]) ).
tcf(c_195111,plain,
( leq(iPr_def_11,zero)
| ( addition(iPr_def_12,sK1) = iPr_def_12 ) ),
inference(theory_normalisation,[status(thm)],[c_195110,c_50,c_49]) ).
tcf(c_195129,plain,
! [X0: $i] : leq(zero,X0),
inference(superposition,[status(thm)],[c_195086,c_60]) ).
tcf(c_195146,plain,
( ( addition(sK1,iPr_def_12) = iPr_def_12 )
| ( addition(sK1,sK2) = sK2 ) ),
inference(superposition,[status(thm)],[c_195108,c_61]) ).
tcf(c_195147,plain,
( ( addition(iPr_def_12,sK1) = iPr_def_12 )
| ( addition(sK1,sK2) = sK2 ) ),
inference(theory_normalisation,[status(thm)],[c_195146,c_50,c_49]) ).
tcf(c_195154,plain,
( ( addition(iPr_def_12,sK1) = iPr_def_12 )
| ( addition(iPr_def_11,zero) = zero ) ),
inference(superposition,[status(thm)],[c_195111,c_61]) ).
tcf(c_195162,plain,
( leq(sK1,sK2)
| ( addition(iPr_def_12,sK1) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_195147,c_60]) ).
tcf(c_195167,plain,
( ( zero = iPr_def_11 )
| ( addition(iPr_def_12,sK1) = iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_195154,c_51]) ).
tcf(c_195196,plain,
( ( addition(iPr_def_12,sK1) = iPr_def_12 )
| ~ leq(iPr_def_11,zero)
| ~ leq(sK1,iPr_def_12) ),
inference(superposition,[status(thm)],[c_195162,c_576]) ).
tcf(c_195200,plain,
( ( addition(iPr_def_12,sK1) = iPr_def_12 )
| ~ leq(sK1,iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_195196,c_1483]) ).
tcf(c_195368,plain,
addition(iPr_def_10,sK3) = one,
inference(superposition,[status(thm)],[c_195023,c_67]) ).
tcf(c_195377,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_195448,plain,
! [X0: $i] : addition(iPr_def_10,addition(sK3,X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_195368,c_50]) ).
tcf(c_195473,plain,
addition(one,sK3) = addition(iPr_def_10,sK3),
inference(superposition,[status(thm)],[c_52,c_195448]) ).
tcf(c_195476,plain,
addition(sK3,one) = addition(iPr_def_10,sK3),
inference(theory_normalisation,[status(thm)],[c_195473,c_50,c_49]) ).
tcf(c_195477,plain,
addition(sK3,one) = one,
inference(light_normalisation,[status(thm)],[c_195476,c_195368]) ).
tcf(c_198596,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_195377,c_60]) ).
tcf(c_198695,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_198596]) ).
tcf(c_198697,plain,
! [X0: $i,X1: $i,X2: $i] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(superposition,[status(thm)],[c_50,c_198596]) ).
tcf(c_198701,plain,
! [X0: $i,X1: $i,X2: $i] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(superposition,[status(thm)],[c_57,c_198596]) ).
tcf(c_198732,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X2,X0))),
inference(superposition,[status(thm)],[c_50,c_198695]) ).
tcf(c_199144,plain,
! [X0: $i] :
( leq(sK1,addition(X0,iPr_def_12))
| ( zero = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_195167,c_198732]) ).
tcf(c_200248,plain,
! [X0: $i,X1: $i,X2: $i] : leq(addition(X0,X1),addition(X0,addition(X2,X1))),
inference(superposition,[status(thm)],[c_49,c_198697]) ).
tcf(c_201726,plain,
! [X0: $i] : leq(multiplication(sK3,X0),multiplication(one,X0)),
inference(superposition,[status(thm)],[c_195477,c_198701]) ).
tcf(c_201736,plain,
! [X0: $i] : leq(multiplication(sK3,X0),X0),
inference(light_normalisation,[status(thm)],[c_201726,c_55]) ).
tcf(c_202517,plain,
leq(iPr_def_12,sK2),
inference(superposition,[status(thm)],[c_572,c_201736]) ).
tcf(c_202549,plain,
addition(iPr_def_12,sK2) = sK2,
inference(superposition,[status(thm)],[c_202517,c_61]) ).
tcf(c_207122,plain,
( leq(iPr_def_11,zero)
| ( addition(sK1,iPr_def_12) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_574,c_61]) ).
tcf(c_207123,plain,
( leq(iPr_def_11,zero)
| ( addition(iPr_def_12,sK1) = iPr_def_12 ) ),
inference(theory_normalisation,[status(thm)],[c_207122,c_50,c_49]) ).
tcf(c_207179,plain,
( ( addition(iPr_def_12,sK1) = iPr_def_12 )
| ( addition(iPr_def_11,zero) = zero ) ),
inference(superposition,[status(thm)],[c_207123,c_61]) ).
tcf(c_207196,plain,
( ( zero = iPr_def_11 )
| ( addition(iPr_def_12,sK1) = iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_207179,c_51]) ).
tcf(c_207460,plain,
! [X0: $i] : addition(zero,multiplication(iPr_def_10,X0)) = multiplication(iPr_def_10,addition(iPr_def_12,X0)),
inference(superposition,[status(thm)],[c_2565,c_56]) ).
tcf(c_207468,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,X1),zero) = multiplication(X0,addition(X1,zero)),
inference(superposition,[status(thm)],[c_58,c_56]) ).
tcf(c_207493,plain,
! [X0: $i,X1: $i] : addition(zero,multiplication(X0,X1)) = multiplication(X0,addition(X1,zero)),
inference(theory_normalisation,[status(thm)],[c_207468,c_50,c_49]) ).
tcf(c_207530,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,X1),zero) = multiplication(addition(X0,zero),X1),
inference(superposition,[status(thm)],[c_59,c_57]) ).
tcf(c_207555,plain,
! [X0: $i,X1: $i] : addition(zero,multiplication(X0,X1)) = multiplication(addition(X0,zero),X1),
inference(theory_normalisation,[status(thm)],[c_207530,c_50,c_49]) ).
tcf(c_207556,plain,
! [X0: $i,X1: $i] : multiplication(X0,addition(X1,zero)) = multiplication(X0,X1),
inference(light_normalisation,[status(thm)],[c_207555,c_51,c_207493]) ).
tcf(c_207666,plain,
! [X0: $i] : multiplication(iPr_def_10,addition(iPr_def_12,X0)) = multiplication(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_207460,c_207493,c_207556]) ).
tcf(c_207670,plain,
( ( zero = iPr_def_11 )
| ( multiplication(iPr_def_10,sK1) = multiplication(iPr_def_10,iPr_def_12) ) ),
inference(superposition,[status(thm)],[c_207196,c_207666]) ).
tcf(c_207678,plain,
zero = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_207670,c_571,c_2565]) ).
tcf(c_209094,plain,
zero = iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_199144,c_207678]) ).
tcf(c_209125,plain,
! [X0: $i] : leq(iPr_def_11,X0),
inference(demodulation,[status(thm)],[c_195129,c_209094]) ).
tcf(c_209126,plain,
! [X0: $i] : addition(iPr_def_11,X0) = X0,
inference(demodulation,[status(thm)],[c_195086,c_209094]) ).
tcf(c_209130,plain,
! [X0: $i] : multiplication(iPr_def_11,X0) = iPr_def_11,
inference(demodulation,[status(thm)],[c_59,c_209094]) ).
tcf(c_209134,plain,
( ~ leq(iPr_def_11,iPr_def_11)
| ~ leq(sK1,iPr_def_12)
| ~ leq(sK1,sK2) ),
inference(demodulation,[status(thm)],[c_576,c_209094]) ).
tcf(c_209160,plain,
( ~ leq(sK1,iPr_def_12)
| ~ leq(sK1,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_209134,c_209125]) ).
tcf(c_209180,plain,
! [X0: $i] : multiplication(iPr_def_10,multiplication(sK1,X0)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_195004,c_209130]) ).
tcf(c_210154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X0,X2),addition(X3,multiplication(X1,X2)))),
inference(superposition,[status(thm)],[c_57,c_200248]) ).
tcf(c_221854,plain,
multiplication(iPr_def_10,sK1) = iPr_def_11,
inference(superposition,[status(thm)],[c_54,c_209180]) ).
tcf(c_222255,plain,
! [X0: $i] :
( ( iPr_def_12 = addition(iPr_def_12,sK1) )
| ( iPr_def_12 != X0 )
| ( addition(iPr_def_12,sK1) != X0 ) ),
inference(instantiation,[status(thm)],[c_579]) ).
tcf(c_249410,plain,
( ( iPr_def_12 = addition(iPr_def_12,sK1) )
| ( iPr_def_12 != iPr_def_12 )
| ( addition(iPr_def_12,sK1) != iPr_def_12 ) ),
inference(instantiation,[status(thm)],[c_222255]) ).
tcf(c_448501,plain,
! [X0: $i,X1: $i] : leq(multiplication(one,X0),addition(multiplication(iPr_def_10,X0),addition(X1,multiplication(sK3,X0)))),
inference(superposition,[status(thm)],[c_195368,c_210154]) ).
tcf(c_448684,plain,
! [X0: $i,X1: $i] : leq(X0,addition(multiplication(iPr_def_10,X0),addition(X1,multiplication(sK3,X0)))),
inference(light_normalisation,[status(thm)],[c_448501,c_55]) ).
tcf(c_449422,plain,
! [X0: $i] : leq(sK1,addition(iPr_def_11,addition(X0,multiplication(sK3,sK1)))),
inference(superposition,[status(thm)],[c_221854,c_448684]) ).
tcf(c_449988,plain,
! [X0: $i] : leq(sK1,addition(X0,multiplication(sK3,sK1))),
inference(demodulation,[status(thm)],[c_449422,c_209126]) ).
tcf(c_449989,plain,
! [X0: $i] : leq(sK1,addition(multiplication(sK3,sK1),X0)),
inference(superposition,[status(thm)],[c_49,c_449988]) ).
tcf(c_450004,plain,
! [X0: $i] : leq(sK1,multiplication(sK3,addition(sK1,X0))),
inference(superposition,[status(thm)],[c_56,c_449989]) ).
tcf(c_451247,plain,
( leq(sK1,multiplication(sK3,sK2))
| ( addition(iPr_def_12,sK1) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_195147,c_450004]) ).
tcf(c_451259,plain,
( leq(sK1,iPr_def_12)
| ( addition(iPr_def_12,sK1) = iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_451247,c_572]) ).
tcf(c_451939,plain,
leq(sK1,iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_451259,c_572,c_26551,c_59683,c_142974,c_163217,c_249410,c_451259]) ).
tcf(c_451941,plain,
~ leq(sK1,sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_209160,c_451939]) ).
tcf(c_451942,plain,
addition(iPr_def_12,sK1) = iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_195200,c_451939]) ).
tcf(c_452291,plain,
! [X0: $i] : leq(sK1,addition(X0,iPr_def_12)),
inference(superposition,[status(thm)],[c_451942,c_198732]) ).
tcf(c_453141,plain,
! [X0: $i] : leq(sK1,addition(iPr_def_12,X0)),
inference(superposition,[status(thm)],[c_49,c_452291]) ).
tcf(c_453519,plain,
leq(sK1,sK2),
inference(superposition,[status(thm)],[c_202549,c_453141]) ).
tcf(c_453530,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_453519,c_451941]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE008+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n006.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 18:34:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 134.59/21.49 % SZS status Started for theBenchmark.p
% 134.59/21.49 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(X0,addition(X1,addition(X0,X1))) )")
% 134.59/21.49 Fatal error: exception Failure("Clause.get_demod_eqs: not a demod/lightnorm conclusion ( leq(X0,addition(X1,addition(X0,X1))) )")
% 134.59/21.49 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_g_uq6h1k/58ia4ub6 2>> /export/starexec/sandbox/tmp/iprover_out_g_uq6h1k/58ia4ub6_error
% 134.59/21.49 % SZS status Theorem for theBenchmark.p
% 134.59/21.49
% 134.59/21.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 134.59/21.49
% 134.59/21.49 % ------ iProver source info
% 134.59/21.49
% 134.59/21.49 % git: date: 2026-07-19 20:42:38 +0200
% 134.59/21.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 134.59/21.49 % git: non_committed_changes: false
% 134.59/21.49
% 134.59/21.49 % ------ Parsing...
% 134.59/21.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 134.59/21.49
% 134.59/21.49 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 134.59/21.49
% 134.59/21.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 134.59/21.49
% 134.59/21.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 134.59/21.49 % ------ Proving...
% 134.59/21.49 % ------ Problem Properties
% 134.59/21.49
% 134.59/21.49 %
% 134.59/21.49 % clauses 29
% 134.59/21.49 % conjectures 4
% 134.59/21.49 % EPR 5
% 134.59/21.49 % Horn 26
% 134.59/21.49 % unary 15
% 134.59/21.49 % binary 11
% 134.59/21.49 % lits 47
% 134.59/21.49 % lits eq 24
% 134.59/21.49 % fd_pure 0
% 134.59/21.49 % fd_pseudo 0
% 134.59/21.49 % fd_cond 0
% 134.59/21.49 % fd_pseudo_cond 1
% 134.59/21.49 % AC symbols 1
% 134.59/21.49
% 134.59/21.49 % ------ Schedule dynamic 5 is on
% 134.59/21.49
% 134.59/21.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 134.59/21.49
% 134.59/21.49
% 134.59/21.49 % ------
% 134.59/21.49 % Current options:
% 134.59/21.49 % ------
% 134.59/21.49
% 134.59/21.49
% 134.59/21.49 %
% 134.59/21.49
% 134.59/21.49 % ------ Proving...
% 134.59/21.49 % Proof_search_loop: time out after: 7544 full_loop iterations
% 134.59/21.49
% 134.59/21.49 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 134.59/21.49
% 134.59/21.49
% 134.59/21.49 % ------
% 134.59/21.49 % Current options:
% 134.59/21.49 % ------
% 134.59/21.49
% 134.59/21.49
% 134.59/21.49 %
% 134.59/21.49
% 134.59/21.49 % ------ Proving...
% 134.59/21.49 %
% 134.59/21.49
% 134.59/21.49 % SZS status Theorem for theBenchmark.p
% 134.59/21.49
% 134.59/21.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 134.59/21.49
% 134.59/21.49
%------------------------------------------------------------------------------