%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE146+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 01:52:31 PM UTC 2026
% Result : Theorem 3.31s 1.29s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 26 unt; 1 def)
% Number of atoms : 41 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 4 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 36 !; 1 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+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/KLE004+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(f19,conjecture,
! [X0] : leq(one,strong_iteration(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] : leq(one,strong_iteration(X0)),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f24,plain,
? [X0] : ~ leq(one,strong_iteration(X0)),
inference(ennf_transformation,[],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f26,plain,
~ leq(one,strong_iteration(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f24]) ).
fof(f27,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f30,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
~ leq(one,strong_iteration(sK0)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f27]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f30]) ).
tcf(c_63,plain,
! [X0: $i] : addition(multiplication(X0,strong_iteration(X0)),one) = strong_iteration(X0),
inference(cnf_transformation,[],[f41]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_68,negated_conjecture,
~ leq(one,strong_iteration(sK0)),
inference(cnf_transformation,[],[f46]) ).
tcf(c_86,plain,
! [X0: $i] : addition(one,multiplication(X0,strong_iteration(X0))) = strong_iteration(X0),
inference(theory_normalisation,[status(thm)],[c_63,c_50,c_49]) ).
tcf(c_206,definition,
iPr_def_10 = strong_iteration(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_207,negated_conjecture,
~ leq(one,iPr_def_10),
inference(demodulation,[status(thm)],[c_68,c_206]) ).
tcf(c_544,plain,
addition(one,multiplication(sK0,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_206,c_86]) ).
tcf(c_590,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_849,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_590,c_66]) ).
tcf(c_898,plain,
leq(one,iPr_def_10),
inference(superposition,[status(thm)],[c_544,c_849]) ).
tcf(c_902,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_898,c_207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE146+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 : n005.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 19:05:04 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...
% 3.31/1.29 % SZS status Started for theBenchmark.p
% 3.31/1.29 % SZS status Theorem for theBenchmark.p
% 3.31/1.29
% 3.31/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.31/1.29
% 3.31/1.29 % ------ iProver source info
% 3.31/1.29
% 3.31/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 3.31/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.31/1.29 % git: non_committed_changes: false
% 3.31/1.29
% 3.31/1.29 % ------ Parsing...
% 3.31/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.31/1.29
% 3.31/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.31/1.29
% 3.31/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.31/1.29
% 3.31/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.31/1.29 % ------ Proving...
% 3.31/1.29 % ------ Problem Properties
% 3.31/1.29
% 3.31/1.29 %
% 3.31/1.29 % clauses 21
% 3.31/1.29 % conjectures 1
% 3.31/1.29 % EPR 1
% 3.31/1.29 % Horn 21
% 3.31/1.29 % unary 16
% 3.31/1.29 % binary 5
% 3.31/1.29 % lits 26
% 3.31/1.29 % lits eq 17
% 3.31/1.29 % fd_pure 0
% 3.31/1.29 % fd_pseudo 0
% 3.31/1.29 % fd_cond 0
% 3.31/1.29 % fd_pseudo_cond 0
% 3.31/1.29 % AC symbols 1
% 3.31/1.29
% 3.31/1.29 % ------ Schedule dynamic 5 is on
% 3.31/1.29
% 3.31/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.31/1.29
% 3.31/1.29
% 3.31/1.29 % ------
% 3.31/1.29 % Current options:
% 3.31/1.29 % ------
% 3.31/1.29
% 3.31/1.29
% 3.31/1.29 %
% 3.31/1.29
% 3.31/1.29 % ------ Proving...
% 3.31/1.29 %
% 3.31/1.29
% 3.31/1.29 % SZS status Theorem for theBenchmark.p
% 3.31/1.29
% 3.31/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.31/1.29
% 3.31/1.29
%------------------------------------------------------------------------------