%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE150+2 : 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 : n019.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 01:52:32 PM UTC 2026
% Result : Theorem 4.30s 1.27s
% Output : CNFRefutation 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 31 unt; 3 def)
% Number of atoms : 77 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 9 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 47 !; 1 ?; 17 :)
% 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(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(f10,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
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(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
& leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
& leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f24,plain,
? [X0] :
( ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
| ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
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(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
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(f31,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f36,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
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(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
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_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f31]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f36]) ).
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(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero)))
| ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero))) ),
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_217,definition,
iPr_def_10 = multiplication(sK0,zero),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_218,definition,
iPr_def_11 = addition(one,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_219,definition,
iPr_def_12 = strong_iteration(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_220,negated_conjecture,
( ~ leq(iPr_def_12,iPr_def_11)
| ~ leq(iPr_def_11,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_68,c_219,c_217,c_218]) ).
tcf(c_554,plain,
addition(iPr_def_10,one) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_218,c_50,c_49]) ).
tcf(c_566,plain,
! [X0: $i] : leq(X0,X0),
inference(superposition,[status(thm)],[c_52,c_66]) ).
tcf(c_658,plain,
! [X0: $i] : multiplication(sK0,multiplication(zero,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_217,c_53]) ).
tcf(c_662,plain,
! [X0: $i] : multiplication(iPr_def_10,X0) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_658,c_58,c_217]) ).
tcf(c_791,plain,
addition(one,iPr_def_10) = strong_iteration(iPr_def_10),
inference(superposition,[status(thm)],[c_662,c_86]) ).
tcf(c_792,plain,
addition(iPr_def_10,one) = strong_iteration(iPr_def_10),
inference(theory_normalisation,[status(thm)],[c_791,c_50,c_49]) ).
tcf(c_793,plain,
iPr_def_11 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_792,c_219,c_554]) ).
tcf(c_799,plain,
~ leq(iPr_def_11,iPr_def_11),
inference(demodulation,[status(thm)],[c_220,c_793]) ).
tcf(c_800,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_799,c_566]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.36 % Computer : n019.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Wed Sep 23 19:06:37 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.40 Running first-order theorem proving
% 0.07/0.40 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
% 0.07/0.41
% 0.07/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.41
% 0.07/0.41 % Detected problem language: tptp
% 0.07/0.42 % Proving...
% 4.30/1.27 % SZS status Started for theBenchmark.p
% 4.30/1.27 % SZS status Theorem for theBenchmark.p
% 4.30/1.27
% 4.30/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.30/1.27
% 4.30/1.27 % ------ iProver source info
% 4.30/1.27
% 4.30/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 4.30/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.30/1.27 % git: non_committed_changes: false
% 4.30/1.27
% 4.30/1.27 % ------ Parsing...
% 4.30/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.30/1.27
% 4.30/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.30/1.27
% 4.30/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.30/1.27
% 4.30/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.30/1.27 % ------ Proving...
% 4.30/1.27 % ------ Problem Properties
% 4.30/1.27
% 4.30/1.27 %
% 4.30/1.27 % clauses 23
% 4.30/1.27 % conjectures 1
% 4.30/1.27 % EPR 1
% 4.30/1.27 % Horn 23
% 4.30/1.27 % unary 17
% 4.30/1.27 % binary 6
% 4.30/1.27 % lits 29
% 4.30/1.27 % lits eq 19
% 4.30/1.27 % fd_pure 0
% 4.30/1.27 % fd_pseudo 0
% 4.30/1.27 % fd_cond 0
% 4.30/1.27 % fd_pseudo_cond 0
% 4.30/1.27 % AC symbols 1
% 4.30/1.27
% 4.30/1.27 % ------ Schedule dynamic 5 is on
% 4.30/1.27
% 4.30/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.30/1.27
% 4.30/1.27
% 4.30/1.27 % ------
% 4.30/1.27 % Current options:
% 4.30/1.27 % ------
% 4.30/1.27
% 4.30/1.27
% 4.30/1.27 %
% 4.30/1.27
% 4.30/1.27 % ------ Proving...
% 4.30/1.27 %
% 4.30/1.27
% 4.30/1.27 % SZS status Theorem for theBenchmark.p
% 4.30/1.27
% 4.30/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.30/1.27
% 4.30/1.27
%------------------------------------------------------------------------------