%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE141+2 : 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 : 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 01:52:29 PM UTC 2026
% Result : Theorem 1.03s 6.30s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 21 unt; 2 def)
% Number of atoms : 70 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 14 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 52 !; 1 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(X2,addition(multiplication(X0,X2),X1))
=> leq(X2,multiplication(strong_iteration(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(f19,conjecture,
! [X0] :
( leq(strong_iteration(one),multiplication(strong_iteration(one),X0))
& leq(multiplication(strong_iteration(one),X0),strong_iteration(one)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(one),multiplication(strong_iteration(one),X0))
& leq(multiplication(strong_iteration(one),X0),strong_iteration(one)) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f24,plain,
? [X0] :
( ~ leq(strong_iteration(one),multiplication(strong_iteration(one),X0))
| ~ leq(multiplication(strong_iteration(one),X0),strong_iteration(one)) ),
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(strong_iteration(one),multiplication(strong_iteration(one),sK0))
| ~ leq(multiplication(strong_iteration(one),sK0),strong_iteration(one)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f24]) ).
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(f32,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( ~ leq(strong_iteration(one),multiplication(strong_iteration(one),sK0))
| ~ leq(multiplication(strong_iteration(one),sK0),strong_iteration(one)) ),
inference(cnf_transformation,[],[f26]) ).
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_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f32]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(X0,multiplication(strong_iteration(X1),X2))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(cnf_transformation,[],[f42]) ).
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(one),multiplication(strong_iteration(one),sK0))
| ~ leq(multiplication(strong_iteration(one),sK0),strong_iteration(one)) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_217,definition,
iPr_def_10 = strong_iteration(one),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_218,definition,
iPr_def_11 = multiplication(iPr_def_10,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_219,negated_conjecture,
( ~ leq(iPr_def_11,iPr_def_10)
| ~ leq(iPr_def_10,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_68,c_217,c_218]) ).
tcf(c_9148,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_9320,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_9148,c_66]) ).
tcf(c_9459,plain,
! [X0: $i,X1: $i] :
( leq(X0,multiplication(strong_iteration(one),X1))
| ~ leq(X0,addition(X0,X1)) ),
inference(superposition,[status(thm)],[c_55,c_64]) ).
tcf(c_9469,plain,
! [X0: $i,X1: $i] :
( leq(X0,multiplication(iPr_def_10,X1))
| ~ leq(X0,addition(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_9459,c_217]) ).
tcf(c_9470,plain,
! [X0: $i,X1: $i] : leq(X0,multiplication(iPr_def_10,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_9469,c_9320]) ).
tcf(c_9532,plain,
! [X0: $i] : leq(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_54,c_9470]) ).
tcf(c_9534,plain,
! [X0: $i] : leq(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_218,c_9470]) ).
tcf(c_9538,plain,
~ leq(iPr_def_10,iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_219,c_9532]) ).
tcf(c_9539,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9538,c_9534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE141+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n009.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Wed Sep 23 19:03:48 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 1.03/6.30 % SZS status Started for theBenchmark.p
% 1.03/6.30 % SZS status Theorem for theBenchmark.p
% 1.03/6.30
% 1.03/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.03/6.30
% 1.03/6.30 % ------ iProver source info
% 1.03/6.30
% 1.03/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 1.03/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.03/6.30 % git: non_committed_changes: false
% 1.03/6.30
% 1.03/6.30 % ------ Parsing...
% 1.03/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.03/6.30
% 1.03/6.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.03/6.30
% 1.03/6.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.03/6.30
% 1.03/6.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.03/6.30 % ------ Proving...
% 1.03/6.30 % ------ Problem Properties
% 1.03/6.30
% 1.03/6.30 %
% 1.03/6.30 % clauses 22
% 1.03/6.30 % conjectures 1
% 1.03/6.30 % EPR 1
% 1.03/6.30 % Horn 22
% 1.03/6.30 % unary 16
% 1.03/6.30 % binary 6
% 1.03/6.30 % lits 28
% 1.03/6.30 % lits eq 18
% 1.03/6.30 % fd_pure 0
% 1.03/6.30 % fd_pseudo 0
% 1.03/6.30 % fd_cond 0
% 1.03/6.30 % fd_pseudo_cond 0
% 1.03/6.30 % AC symbols 1
% 1.03/6.30
% 1.03/6.30 % ------ Schedule dynamic 5 is on
% 1.03/6.30
% 1.03/6.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.03/6.30
% 1.03/6.30
% 1.03/6.30 % ------
% 1.03/6.30 % Current options:
% 1.03/6.30 % ------
% 1.03/6.30
% 1.03/6.30
% 1.03/6.30 %
% 1.03/6.30
% 1.03/6.30 % ------ Proving...
% 1.03/6.30 %
% 1.03/6.30
% 1.03/6.30 % SZS status Theorem for theBenchmark.p
% 1.03/6.30
% 1.03/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.03/6.30
% 1.03/6.30
%------------------------------------------------------------------------------