%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE004+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 : n009.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 01:52:06 PM UTC 2026
% Result : Theorem 3.06s 1.32s
% Output : CNFRefutation 3.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 30 unt; 1 def)
% Number of atoms : 164 ( 71 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 114 ( 48 ~; 48 |; 12 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 62 !; 3 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
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(f16,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_4) ).
fof(f17,conjecture,
c(zero) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
c(zero) != one,
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
one != c(zero),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
! [X0] :
( test(X0)
| c(X0) = zero ),
inference(ennf_transformation,[],[f16]) ).
fof(f22,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X0] :
( ( ~ test(X0)
| ? [X2] : complement(X2,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(rectify,[],[f22]) ).
fof(f24,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))],[f23]) ).
fof(f25,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(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(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f28,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f30,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f37,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f38,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f40,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| test(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f26]) ).
fof(f44,plain,
! [X0,X1] :
( addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| complement(X1,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f45,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0] :
( test(X0)
| zero = c(X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f48,plain,
one != c(zero),
inference(cnf_transformation,[],[f19]) ).
fof(f49,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f45]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f28]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f30]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f37]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f38]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( test(X1)
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( complement(X1,X0)
| ( multiplication(X1,X0) != zero )
| ( multiplication(X0,X1) != zero )
| ( addition(X0,X1) != one ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_67,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_68,plain,
! [X0: $i] :
( test(X0)
| ( c(X0) = zero ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_69,negated_conjecture,
c(zero) != one,
inference(cnf_transformation,[],[f48]) ).
tcf(c_416,definition,
iPr_def_10 = c(zero),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_417,negated_conjecture,
iPr_def_10 != one,
inference(demodulation,[status(thm)],[c_69,c_416]) ).
tcf(c_658,plain,
( complement(zero,iPr_def_10)
| ~ test(zero) ),
inference(superposition,[status(thm)],[c_416,c_67]) ).
tcf(c_672,plain,
( complement(zero,iPr_def_10)
| ( c(zero) = zero ) ),
inference(superposition,[status(thm)],[c_68,c_658]) ).
tcf(c_673,plain,
( complement(zero,iPr_def_10)
| ( zero = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_672,c_416]) ).
tcf(c_700,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_742,plain,
( ( zero = iPr_def_10 )
| ( addition(iPr_def_10,zero) = one ) ),
inference(superposition,[status(thm)],[c_673,c_65]) ).
tcf(c_953,plain,
( ( one = iPr_def_10 )
| ( zero = iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_742,c_51]) ).
tcf(c_962,plain,
zero = iPr_def_10,
inference(superposition,[status(thm)],[c_953,c_417]) ).
tcf(c_969,plain,
! [X0: $i] : addition(iPr_def_10,X0) = X0,
inference(demodulation,[status(thm)],[c_700,c_962]) ).
tcf(c_971,plain,
( complement(iPr_def_10,iPr_def_10)
| ~ test(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_658,c_962]) ).
tcf(c_973,plain,
! [X0: $i] : multiplication(iPr_def_10,X0) = iPr_def_10,
inference(demodulation,[status(thm)],[c_59,c_962]) ).
tcf(c_974,plain,
! [X0: $i] : multiplication(X0,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_58,c_962]) ).
tcf(c_1052,plain,
! [X0: $i,X1: $i] :
( complement(X1,X0)
| ( multiplication(X1,X0) != iPr_def_10 )
| ( multiplication(X0,X1) != iPr_def_10 )
| ( addition(X0,X1) != one ) ),
inference(light_normalisation,[status(thm)],[c_62,c_962]) ).
tcf(c_1072,plain,
! [X0: $i] :
( complement(X0,iPr_def_10)
| ( X0 != one )
| ( multiplication(iPr_def_10,X0) != iPr_def_10 )
| ( multiplication(X0,iPr_def_10) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_969,c_1052]) ).
tcf(c_1076,plain,
! [X0: $i] :
( complement(X0,iPr_def_10)
| ( X0 != one ) ),
inference(ground_joinability,[status(thm)],[c_1072,c_973,c_974]) ).
tcf(c_1182,plain,
complement(one,iPr_def_10),
inference(equality_resolution,[status(thm)],[c_1076]) ).
tcf(c_1185,plain,
test(iPr_def_10),
inference(superposition,[status(thm)],[c_1182,c_60]) ).
tcf(c_1188,plain,
complement(iPr_def_10,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_971,c_1185]) ).
tcf(c_1285,plain,
addition(iPr_def_10,iPr_def_10) = one,
inference(superposition,[status(thm)],[c_1188,c_65]) ).
tcf(c_1294,plain,
addition(iPr_def_10,iPr_def_10) != iPr_def_10,
inference(demodulation,[status(thm)],[c_417,c_1285]) ).
tcf(c_1295,plain,
$false,
inference(ground_joinability,[status(thm)],[c_1294,c_969]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE004+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.38 % Computer : n009.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Sep 23 18:34:14 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.13/0.43
% 0.13/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.43
% 0.13/0.43 % Detected problem language: tptp
% 0.13/0.45 % Proving...
% 3.06/1.32 % SZS status Started for theBenchmark.p
% 3.06/1.32 % SZS status Theorem for theBenchmark.p
% 3.06/1.32
% 3.06/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.06/1.32
% 3.06/1.32 % ------ iProver source info
% 3.06/1.32
% 3.06/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 3.06/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.06/1.32 % git: non_committed_changes: false
% 3.06/1.32
% 3.06/1.32 % ------ Parsing...
% 3.06/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.06/1.32
% 3.06/1.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.06/1.32
% 3.06/1.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.06/1.32
% 3.06/1.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.06/1.32 % ------ Proving...
% 3.06/1.32 % ------ Problem Properties
% 3.06/1.32
% 3.06/1.32 %
% 3.06/1.32 % clauses 22
% 3.06/1.32 % conjectures 1
% 3.06/1.32 % EPR 2
% 3.06/1.32 % Horn 21
% 3.06/1.32 % unary 13
% 3.06/1.32 % binary 7
% 3.06/1.32 % lits 34
% 3.06/1.32 % lits eq 21
% 3.06/1.32 % fd_pure 0
% 3.06/1.32 % fd_pseudo 0
% 3.06/1.32 % fd_cond 0
% 3.06/1.32 % fd_pseudo_cond 1
% 3.06/1.32 % AC symbols 1
% 3.06/1.32
% 3.06/1.32 % ------ Schedule dynamic 5 is on
% 3.06/1.32
% 3.06/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.06/1.32
% 3.06/1.32
% 3.06/1.32 % ------
% 3.06/1.32 % Current options:
% 3.06/1.32 % ------
% 3.06/1.32
% 3.06/1.32
% 3.06/1.32 %
% 3.06/1.32
% 3.06/1.32 % ------ Proving...
% 3.06/1.32 %
% 3.06/1.32
% 3.06/1.32 % SZS status Theorem for theBenchmark.p
% 3.06/1.32
% 3.06/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.06/1.32
% 3.06/1.32
%------------------------------------------------------------------------------