%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE023+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 : n005.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 01:52:11 PM UTC 2026
% Result : Theorem 15.00s 2.86s
% Output : CNFRefutation 15.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 23
% Syntax : Number of formulae : 180 ( 141 unt; 8 def)
% Number of atoms : 455 ( 174 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 130 ( 53 ~; 45 |; 23 &)
% ( 4 <=>; 5 =>; 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 : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 159 ( 0 sgn 150 !; 9 ?; 71 :)
% 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(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox/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/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)
& test(X1) )
=> ( addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
=> addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
=> addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) ) ),
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)
& addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
& multiplication(c(X1),X0) != addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
? [X0,X1,X2] :
( test(X2)
& test(X1)
& addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
& multiplication(c(X1),X0) != addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) ),
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(sK3)
& test(sK2)
& multiplication(sK1,sK3) = addition(multiplication(sK2,sK1),multiplication(sK1,sK3))
& multiplication(c(sK2),sK1) != addition(multiplication(sK1,c(sK3)),multiplication(c(sK2),sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[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(f39,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
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(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(sK3),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
test(sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
multiplication(sK1,sK3) = addition(multiplication(sK2,sK1),multiplication(sK1,sK3)),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
multiplication(c(sK2),sK1) != addition(multiplication(sK1,c(sK3)),multiplication(c(sK2),sK1)),
inference(cnf_transformation,[],[f29]) ).
fof(f54,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_58,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f39]) ).
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_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,[],[f54]) ).
tcf(c_69,negated_conjecture,
addition(multiplication(sK1,c(sK3)),multiplication(c(sK2),sK1)) != multiplication(c(sK2),sK1),
inference(cnf_transformation,[],[f53]) ).
tcf(c_70,negated_conjecture,
addition(multiplication(sK2,sK1),multiplication(sK1,sK3)) = multiplication(sK1,sK3),
inference(cnf_transformation,[],[f52]) ).
tcf(c_71,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f51]) ).
tcf(c_72,negated_conjecture,
test(sK3),
inference(cnf_transformation,[],[f50]) ).
tcf(c_89,negated_conjecture,
addition(multiplication(sK1,sK3),multiplication(sK2,sK1)) = multiplication(sK1,sK3),
inference(theory_normalisation,[status(thm)],[c_70,c_50,c_49]) ).
tcf(c_473,definition,
iPr_def_10 = multiplication(sK1,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_474,definition,
iPr_def_11 = multiplication(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_475,definition,
iPr_def_12 = addition(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_476,definition,
iPr_def_13 = c(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_477,definition,
iPr_def_14 = multiplication(sK1,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_478,definition,
iPr_def_15 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_479,definition,
iPr_def_16 = multiplication(iPr_def_15,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_480,definition,
iPr_def_17 = addition(iPr_def_14,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_481,negated_conjecture,
iPr_def_12 = iPr_def_10,
inference(demodulation,[status(thm)],[c_89,c_474,c_473,c_475]) ).
tcf(c_482,negated_conjecture,
test(sK3),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_483,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_484,negated_conjecture,
iPr_def_17 != iPr_def_16,
inference(demodulation,[status(thm)],[c_69,c_478,c_479,c_476,c_477,c_480]) ).
tcf(c_751,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_756,plain,
addition(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_475,c_481]) ).
tcf(c_766,plain,
( complement(sK2,iPr_def_15)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_478,c_67]) ).
tcf(c_767,plain,
( complement(sK3,iPr_def_13)
| ~ test(sK3) ),
inference(superposition,[status(thm)],[c_476,c_67]) ).
tcf(c_771,plain,
complement(sK3,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_767,c_482]) ).
tcf(c_772,plain,
complement(sK2,iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_766,c_483]) ).
tcf(c_774,plain,
test(iPr_def_15),
inference(superposition,[status(thm)],[c_772,c_60]) ).
tcf(c_798,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_808,plain,
multiplication(iPr_def_15,sK2) = zero,
inference(superposition,[status(thm)],[c_772,c_63]) ).
tcf(c_818,plain,
! [X0: $i] :
( ( multiplication(sK0(X0),X0) = zero )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_61,c_64]) ).
tcf(c_820,plain,
multiplication(sK2,iPr_def_15) = zero,
inference(superposition,[status(thm)],[c_772,c_64]) ).
tcf(c_821,plain,
multiplication(sK3,iPr_def_13) = zero,
inference(superposition,[status(thm)],[c_771,c_64]) ).
tcf(c_914,plain,
! [X0: $i] :
( ( addition(X0,sK0(X0)) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_61,c_65]) ).
tcf(c_915,plain,
! [X0: $i] :
( ( addition(c(X0),X0) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_67,c_65]) ).
tcf(c_916,plain,
addition(iPr_def_15,sK2) = one,
inference(superposition,[status(thm)],[c_772,c_65]) ).
tcf(c_917,plain,
addition(iPr_def_13,sK3) = one,
inference(superposition,[status(thm)],[c_771,c_65]) ).
tcf(c_918,plain,
! [X0: $i] :
( ( addition(X0,c(X0)) = one )
| ~ test(X0) ),
inference(theory_normalisation,[status(thm)],[c_915,c_50,c_49]) ).
tcf(c_977,plain,
! [X0: $i] : multiplication(sK1,multiplication(sK3,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_473,c_53]) ).
tcf(c_978,plain,
! [X0: $i] : multiplication(sK2,multiplication(sK1,X0)) = multiplication(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_474,c_53]) ).
tcf(c_980,plain,
! [X0: $i] : multiplication(iPr_def_15,multiplication(sK1,X0)) = multiplication(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_479,c_53]) ).
tcf(c_981,plain,
! [X0: $i] : multiplication(iPr_def_15,multiplication(sK2,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_808,c_53]) ).
tcf(c_990,plain,
! [X0: $i] : multiplication(iPr_def_15,multiplication(sK2,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_981,c_59]) ).
tcf(c_1042,plain,
! [X0: $i] : addition(iPr_def_15,addition(sK2,X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_916,c_50]) ).
tcf(c_1043,plain,
! [X0: $i] : addition(iPr_def_15,addition(X0,sK2)) = addition(X0,one),
inference(superposition,[status(thm)],[c_916,c_751]) ).
tcf(c_1047,plain,
! [X0: $i] : addition(iPr_def_13,addition(sK3,X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_917,c_50]) ).
tcf(c_1048,plain,
! [X0: $i] : addition(iPr_def_13,addition(X0,sK3)) = addition(X0,one),
inference(superposition,[status(thm)],[c_917,c_751]) ).
tcf(c_1060,plain,
addition(one,sK2) = addition(iPr_def_15,sK2),
inference(superposition,[status(thm)],[c_52,c_1042]) ).
tcf(c_1067,plain,
addition(one,sK2) = one,
inference(light_normalisation,[status(thm)],[c_1060,c_916]) ).
tcf(c_1106,plain,
addition(one,one) = addition(iPr_def_15,one),
inference(superposition,[status(thm)],[c_1067,c_1043]) ).
tcf(c_1124,plain,
addition(one,sK3) = addition(iPr_def_13,sK3),
inference(superposition,[status(thm)],[c_52,c_1047]) ).
tcf(c_1131,plain,
addition(one,sK3) = one,
inference(light_normalisation,[status(thm)],[c_1124,c_917]) ).
tcf(c_1155,plain,
addition(one,one) = addition(iPr_def_13,one),
inference(superposition,[status(thm)],[c_1131,c_1048]) ).
tcf(c_1191,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_15),multiplication(X0,sK2)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_916,c_56]) ).
tcf(c_1192,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),multiplication(X0,sK3)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_917,c_56]) ).
tcf(c_1209,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),multiplication(X0,sK3)) = X0,
inference(light_normalisation,[status(thm)],[c_1192,c_54]) ).
tcf(c_1210,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_15),multiplication(X0,sK2)) = X0,
inference(light_normalisation,[status(thm)],[c_1191,c_54]) ).
tcf(c_1282,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_11,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_756,c_57]) ).
tcf(c_1283,plain,
! [X0: $i] : addition(multiplication(iPr_def_14,X0),multiplication(iPr_def_16,X0)) = multiplication(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_480,c_57]) ).
tcf(c_1533,plain,
multiplication(iPr_def_15,iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_474,c_990]) ).
tcf(c_1545,plain,
multiplication(sK3,iPr_def_13) = multiplication(iPr_def_15,iPr_def_11),
inference(demodulation,[status(thm)],[c_821,c_1533]) ).
tcf(c_1546,plain,
multiplication(sK2,iPr_def_15) = multiplication(iPr_def_15,iPr_def_11),
inference(demodulation,[status(thm)],[c_820,c_1533]) ).
tcf(c_1549,plain,
! [X0: $i] : addition(multiplication(iPr_def_15,iPr_def_11),X0) = X0,
inference(demodulation,[status(thm)],[c_798,c_1533]) ).
tcf(c_1554,plain,
! [X0: $i] : multiplication(X0,multiplication(iPr_def_15,iPr_def_11)) = multiplication(iPr_def_15,iPr_def_11),
inference(demodulation,[status(thm)],[c_58,c_1533]) ).
tcf(c_1864,plain,
addition(iPr_def_13,one) = addition(iPr_def_15,one),
inference(light_normalisation,[status(thm)],[c_1106,c_1155]) ).
tcf(c_1900,plain,
addition(iPr_def_13,one) = one,
inference(demodulation,[status(thm)],[c_1155,c_52]) ).
tcf(c_1901,plain,
addition(iPr_def_15,one) = one,
inference(demodulation,[status(thm)],[c_1864,c_1900]) ).
tcf(c_1903,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),multiplication(X0,one)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_1900,c_56]) ).
tcf(c_1909,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_13),X0) = X0,
inference(light_normalisation,[status(thm)],[c_1903,c_54]) ).
tcf(c_1910,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_13)) = X0,
inference(theory_normalisation,[status(thm)],[c_1909,c_50,c_49]) ).
tcf(c_1963,plain,
! [X0: $i] : addition(multiplication(iPr_def_15,X0),multiplication(one,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_1901,c_57]) ).
tcf(c_1965,plain,
! [X0: $i] : addition(multiplication(iPr_def_15,X0),X0) = X0,
inference(light_normalisation,[status(thm)],[c_1963,c_55]) ).
tcf(c_1966,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_15,X0)) = X0,
inference(theory_normalisation,[status(thm)],[c_1965,c_50,c_49]) ).
tcf(c_3327,plain,
addition(sK1,iPr_def_16) = sK1,
inference(superposition,[status(thm)],[c_479,c_1966]) ).
tcf(c_3342,plain,
addition(iPr_def_16,sK1) = sK1,
inference(theory_normalisation,[status(thm)],[c_3327,c_50,c_49]) ).
tcf(c_4177,plain,
! [X0: $i] :
( ( multiplication(sK0(X0),X0) = multiplication(iPr_def_15,iPr_def_11) )
| ~ test(X0) ),
inference(light_normalisation,[status(thm)],[c_818,c_1533]) ).
tcf(c_4185,plain,
multiplication(sK0(sK2),sK2) = multiplication(iPr_def_15,iPr_def_11),
inference(superposition,[status(thm)],[c_483,c_4177]) ).
tcf(c_4513,plain,
addition(sK2,sK0(sK2)) = one,
inference(superposition,[status(thm)],[c_483,c_914]) ).
tcf(c_4538,plain,
! [X0: $i] : addition(multiplication(sK2,X0),multiplication(sK0(sK2),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_4513,c_57]) ).
tcf(c_4542,plain,
! [X0: $i] : addition(multiplication(sK2,X0),multiplication(sK0(sK2),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_4538,c_55]) ).
tcf(c_4922,plain,
addition(iPr_def_15,c(iPr_def_15)) = one,
inference(superposition,[status(thm)],[c_774,c_918]) ).
tcf(c_5378,plain,
! [X0: $i] : addition(multiplication(iPr_def_15,X0),multiplication(c(iPr_def_15),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_4922,c_57]) ).
tcf(c_5380,plain,
! [X0: $i] : addition(multiplication(iPr_def_15,X0),multiplication(c(iPr_def_15),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_5378,c_55]) ).
tcf(c_6384,plain,
multiplication(sK1,multiplication(iPr_def_15,iPr_def_11)) = multiplication(iPr_def_10,iPr_def_13),
inference(superposition,[status(thm)],[c_1545,c_977]) ).
tcf(c_6395,plain,
multiplication(sK2,iPr_def_14) = multiplication(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_477,c_978]) ).
tcf(c_6468,plain,
addition(multiplication(iPr_def_15,iPr_def_11),multiplication(sK0(sK2),iPr_def_15)) = iPr_def_15,
inference(superposition,[status(thm)],[c_1546,c_4542]) ).
tcf(c_7630,plain,
multiplication(iPr_def_15,iPr_def_14) = multiplication(iPr_def_16,iPr_def_13),
inference(superposition,[status(thm)],[c_477,c_980]) ).
tcf(c_7655,plain,
addition(iPr_def_16,multiplication(iPr_def_15,iPr_def_14)) = iPr_def_16,
inference(superposition,[status(thm)],[c_7630,c_1910]) ).
tcf(c_8991,plain,
addition(multiplication(sK1,iPr_def_13),iPr_def_10) = sK1,
inference(superposition,[status(thm)],[c_473,c_1209]) ).
tcf(c_9010,plain,
addition(iPr_def_10,multiplication(sK1,iPr_def_13)) = sK1,
inference(theory_normalisation,[status(thm)],[c_8991,c_50,c_49]) ).
tcf(c_9011,plain,
addition(iPr_def_10,iPr_def_14) = sK1,
inference(light_normalisation,[status(thm)],[c_9010,c_477]) ).
tcf(c_9035,plain,
addition(iPr_def_16,addition(iPr_def_10,iPr_def_14)) = addition(iPr_def_10,iPr_def_14),
inference(demodulation,[status(thm)],[c_3342,c_9011]) ).
tcf(c_9045,plain,
addition(iPr_def_10,addition(iPr_def_14,iPr_def_16)) = addition(iPr_def_10,iPr_def_14),
inference(theory_normalisation,[status(thm)],[c_9035,c_50,c_49]) ).
tcf(c_9046,plain,
addition(iPr_def_10,iPr_def_14) = addition(iPr_def_10,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_9045,c_480]) ).
tcf(c_9791,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(iPr_def_17,X0)) = multiplication(addition(iPr_def_10,iPr_def_14),X0),
inference(superposition,[status(thm)],[c_9046,c_57]) ).
tcf(c_9798,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),addition(multiplication(iPr_def_14,X0),multiplication(iPr_def_16,X0))) = multiplication(addition(iPr_def_10,iPr_def_14),X0),
inference(light_normalisation,[status(thm)],[c_9791,c_1283]) ).
tcf(c_10686,plain,
addition(multiplication(sK0(sK2),iPr_def_15),multiplication(iPr_def_15,iPr_def_11)) = sK0(sK2),
inference(superposition,[status(thm)],[c_4185,c_1210]) ).
tcf(c_10701,plain,
addition(multiplication(iPr_def_15,iPr_def_11),multiplication(sK0(sK2),iPr_def_15)) = sK0(sK2),
inference(theory_normalisation,[status(thm)],[c_10686,c_50,c_49]) ).
tcf(c_10702,plain,
sK0(sK2) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_10701,c_6468]) ).
tcf(c_10754,plain,
( complement(iPr_def_15,sK2)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_10702,c_61]) ).
tcf(c_10755,plain,
complement(iPr_def_15,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_10754,c_483]) ).
tcf(c_10756,plain,
( ( c(iPr_def_15) = sK2 )
| ~ test(iPr_def_15) ),
inference(superposition,[status(thm)],[c_10755,c_66]) ).
tcf(c_10759,plain,
c(iPr_def_15) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_10756,c_774]) ).
tcf(c_10777,plain,
multiplication(c(iPr_def_15),iPr_def_14) = multiplication(iPr_def_11,iPr_def_13),
inference(demodulation,[status(thm)],[c_6395,c_10759]) ).
tcf(c_16035,plain,
multiplication(addition(iPr_def_10,iPr_def_14),multiplication(iPr_def_15,iPr_def_11)) = multiplication(iPr_def_10,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_6384,c_9011]) ).
tcf(c_16036,plain,
multiplication(iPr_def_10,iPr_def_13) = multiplication(iPr_def_15,iPr_def_11),
inference(demodulation,[status(thm)],[c_16035,c_1549,c_1554,c_9798]) ).
tcf(c_16056,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,iPr_def_13),X0) = X0,
inference(demodulation,[status(thm)],[c_1549,c_16036]) ).
tcf(c_16571,plain,
multiplication(iPr_def_10,iPr_def_13) = multiplication(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_16056,c_1282]) ).
tcf(c_16662,plain,
multiplication(c(iPr_def_15),iPr_def_14) = multiplication(iPr_def_10,iPr_def_13),
inference(demodulation,[status(thm)],[c_10777,c_16571]) ).
tcf(c_21741,plain,
addition(multiplication(iPr_def_15,iPr_def_14),multiplication(iPr_def_10,iPr_def_13)) = iPr_def_14,
inference(superposition,[status(thm)],[c_16662,c_5380]) ).
tcf(c_21757,plain,
addition(multiplication(iPr_def_10,iPr_def_13),multiplication(iPr_def_15,iPr_def_14)) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_21741,c_50,c_49]) ).
tcf(c_25612,plain,
multiplication(iPr_def_15,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_21757,c_16056]) ).
tcf(c_25614,plain,
addition(iPr_def_16,iPr_def_14) = iPr_def_16,
inference(demodulation,[status(thm)],[c_7655,c_25612]) ).
tcf(c_25616,plain,
addition(iPr_def_14,iPr_def_16) = iPr_def_16,
inference(theory_normalisation,[status(thm)],[c_25614,c_50,c_49]) ).
tcf(c_25618,plain,
iPr_def_16 = iPr_def_17,
inference(demodulation,[status(thm)],[c_480,c_25616]) ).
tcf(c_25629,plain,
iPr_def_16 != iPr_def_16,
inference(demodulation,[status(thm)],[c_484,c_25618]) ).
tcf(c_25630,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_25629]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE023+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.41 % Computer : n005.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Wed Sep 23 18:39:02 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 0.13/0.46
% 0.13/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.46
% 0.13/0.46 % Detected problem language: tptp
% 0.20/0.47 % Proving...
% 15.00/2.86 % SZS status Started for theBenchmark.p
% 15.00/2.86 % SZS status Theorem for theBenchmark.p
% 15.00/2.86
% 15.00/2.86 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.00/2.86
% 15.00/2.86 % ------ iProver source info
% 15.00/2.86
% 15.00/2.86 % git: date: 2026-07-19 20:42:38 +0200
% 15.00/2.86 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.00/2.86 % git: non_committed_changes: false
% 15.00/2.86
% 15.00/2.86 % ------ Parsing...
% 15.00/2.86 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.00/2.86
% 15.00/2.86 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 15.00/2.86
% 15.00/2.86 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.00/2.86
% 15.00/2.86 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 15.00/2.86 % ------ Proving...
% 15.00/2.86 % ------ Problem Properties
% 15.00/2.86
% 15.00/2.86 %
% 15.00/2.86 % clauses 32
% 15.00/2.86 % conjectures 4
% 15.00/2.86 % EPR 5
% 15.00/2.86 % Horn 31
% 15.00/2.86 % unary 23
% 15.00/2.86 % binary 7
% 15.00/2.86 % lits 44
% 15.00/2.86 % lits eq 29
% 15.00/2.86 % fd_pure 0
% 15.00/2.86 % fd_pseudo 0
% 15.00/2.86 % fd_cond 0
% 15.00/2.86 % fd_pseudo_cond 1
% 15.00/2.86 % AC symbols 1
% 15.00/2.86
% 15.00/2.86 % ------ Schedule dynamic 5 is on
% 15.00/2.86
% 15.00/2.86 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 15.00/2.86
% 15.00/2.86
% 15.00/2.86 % ------
% 15.00/2.86 % Current options:
% 15.00/2.86 % ------
% 15.00/2.86
% 15.00/2.86
% 15.00/2.86 %
% 15.00/2.86
% 15.00/2.86 % ------ Proving...
% 15.00/2.86 %
% 15.00/2.86
% 15.00/2.86 % SZS status Theorem for theBenchmark.p
% 15.00/2.86
% 15.00/2.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.00/2.87
% 15.00/2.87
%------------------------------------------------------------------------------