%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE006+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 0.29s 1.07s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 20 unt; 2 def)
% Number of atoms : 84 ( 41 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 62 ( 26 ~; 19 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 37 !; 1 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f17,conjecture,
! [X0] :
( test(X0)
=> one = addition(X0,c(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0] :
( test(X0)
=> one = addition(X0,c(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] :
( test(X0)
& one != addition(X0,c(X0)) ),
inference(ennf_transformation,[],[f18]) ).
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,[],[f19]) ).
fof(f28,plain,
( test(sK1)
& one != addition(sK1,c(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f21]) ).
fof(f29,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f30,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f42,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
test(sK1),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
one != addition(sK1,c(sK1)),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f46]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f29]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_67,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_69,negated_conjecture,
addition(sK1,c(sK1)) != one,
inference(cnf_transformation,[],[f50]) ).
tcf(c_70,negated_conjecture,
test(sK1),
inference(cnf_transformation,[],[f49]) ).
tcf(c_443,definition,
iPr_def_10 = c(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_444,definition,
iPr_def_11 = addition(sK1,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_445,negated_conjecture,
test(sK1),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_446,negated_conjecture,
iPr_def_11 != one,
inference(demodulation,[status(thm)],[c_69,c_443,c_444]) ).
tcf(c_684,plain,
addition(iPr_def_10,sK1) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_444,c_50,c_49]) ).
tcf(c_696,plain,
( complement(sK1,iPr_def_10)
| ~ test(sK1) ),
inference(superposition,[status(thm)],[c_443,c_67]) ).
tcf(c_700,plain,
complement(sK1,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_696,c_445]) ).
tcf(c_747,plain,
addition(iPr_def_10,sK1) = one,
inference(superposition,[status(thm)],[c_700,c_65]) ).
tcf(c_748,plain,
one = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_747,c_684]) ).
tcf(c_757,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_446,c_748]) ).
tcf(c_758,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_757]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE006+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 18:34:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 0.29/1.07 % SZS status Started for theBenchmark.p
% 0.29/1.07 % SZS status Theorem for theBenchmark.p
% 0.29/1.07
% 0.29/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.29/1.07
% 0.29/1.07 % ------ iProver source info
% 0.29/1.07
% 0.29/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 0.29/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.29/1.07 % git: non_committed_changes: false
% 0.29/1.07
% 0.29/1.07 % ------ Parsing...
% 0.29/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.29/1.07
% 0.29/1.07 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.29/1.07
% 0.29/1.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.29/1.07
% 0.29/1.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.29/1.07 % ------ Proving...
% 0.29/1.07 % ------ Problem Properties
% 0.29/1.07
% 0.29/1.07 %
% 0.29/1.07 % clauses 24
% 0.29/1.07 % conjectures 2
% 0.29/1.07 % EPR 3
% 0.29/1.07 % Horn 23
% 0.29/1.07 % unary 15
% 0.29/1.07 % binary 7
% 0.29/1.07 % lits 36
% 0.29/1.07 % lits eq 22
% 0.29/1.07 % fd_pure 0
% 0.29/1.07 % fd_pseudo 0
% 0.29/1.07 % fd_cond 0
% 0.29/1.07 % fd_pseudo_cond 1
% 0.29/1.07 % AC symbols 1
% 0.29/1.07
% 0.29/1.07 % ------ Schedule dynamic 5 is on
% 0.29/1.07
% 0.29/1.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.29/1.07
% 0.29/1.07
% 0.29/1.07 % ------
% 0.29/1.07 % Current options:
% 0.29/1.07 % ------
% 0.29/1.07
% 0.29/1.07
% 0.29/1.07 %
% 0.29/1.07
% 0.29/1.07 % ------ Proving...
% 0.29/1.07 %
% 0.29/1.07
% 0.29/1.07 % SZS status Theorem for theBenchmark.p
% 0.29/1.07
% 0.29/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.29/1.08
% 0.29/1.08
%------------------------------------------------------------------------------