%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE142+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 : n016.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 01:52:30 PM UTC 2026
% Result : Theorem 2.13s 1.10s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 86 ( 64 unt; 3 def)
% Number of atoms : 185 ( 55 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 50 ( 26 ~; 19 |; 3 &)
% ( 1 <=>; 1 =>; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn 102 !; 1 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/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/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(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
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(f10,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
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(f17,axiom,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',isolation) ).
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),strong_iteration(strong_iteration(X0)))
& leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(one),strong_iteration(strong_iteration(X0)))
& leq(strong_iteration(strong_iteration(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),strong_iteration(strong_iteration(X0)))
| ~ leq(strong_iteration(strong_iteration(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),strong_iteration(strong_iteration(sK0)))
| ~ leq(strong_iteration(strong_iteration(sK0)),strong_iteration(one)) ),
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(f32,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
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(f42,plain,
! [X2,X0,X1] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[],[f17]) ).
fof(f44,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( ~ leq(strong_iteration(one),strong_iteration(strong_iteration(sK0)))
| ~ leq(strong_iteration(strong_iteration(sK0)),strong_iteration(one)) ),
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_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_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_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_65,plain,
! [X0: $i] : addition(star(X0),multiplication(strong_iteration(X0),zero)) = strong_iteration(X0),
inference(cnf_transformation,[],[f43]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_68,negated_conjecture,
( ~ leq(strong_iteration(one),strong_iteration(strong_iteration(sK0)))
| ~ leq(strong_iteration(strong_iteration(sK0)),strong_iteration(one)) ),
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 = strong_iteration(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_218,definition,
iPr_def_11 = strong_iteration(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_219,definition,
iPr_def_12 = strong_iteration(one),
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_607,plain,
addition(one,multiplication(iPr_def_10,iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_218,c_86]) ).
tcf(c_610,plain,
addition(multiplication(iPr_def_10,iPr_def_11),one) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_607,c_50,c_49]) ).
tcf(c_619,plain,
! [X0: $i] : addition(multiplication(strong_iteration(X0),zero),star(X0)) = strong_iteration(X0),
inference(theory_normalisation,[status(thm)],[c_65,c_50,c_49]) ).
tcf(c_622,plain,
addition(multiplication(iPr_def_11,zero),star(iPr_def_10)) = iPr_def_11,
inference(superposition,[status(thm)],[c_218,c_619]) ).
tcf(c_633,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_1009,plain,
addition(multiplication(iPr_def_11,zero),iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_622,c_633]) ).
tcf(c_1012,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_633,c_66]) ).
tcf(c_1017,plain,
addition(iPr_def_11,multiplication(iPr_def_11,zero)) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_1009,c_50,c_49]) ).
tcf(c_1055,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_1012]) ).
tcf(c_1062,plain,
! [X0: $i] : leq(one,strong_iteration(X0)),
inference(superposition,[status(thm)],[c_86,c_1012]) ).
tcf(c_1323,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_1333,plain,
! [X0: $i,X1: $i] :
( leq(X0,multiplication(iPr_def_12,X1))
| ~ leq(X0,addition(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_1323,c_219]) ).
tcf(c_1334,plain,
! [X0: $i,X1: $i] : leq(X0,multiplication(iPr_def_12,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_1333,c_1012]) ).
tcf(c_1379,plain,
leq(one,iPr_def_11),
inference(superposition,[status(thm)],[c_218,c_1062]) ).
tcf(c_1382,plain,
addition(one,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_1379,c_67]) ).
tcf(c_1383,plain,
addition(iPr_def_11,one) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_1382,c_50,c_49]) ).
tcf(c_1400,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X2,X0))),
inference(superposition,[status(thm)],[c_50,c_1055]) ).
tcf(c_1551,plain,
! [X0: $i] : leq(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_54,c_1334]) ).
tcf(c_1556,plain,
~ leq(iPr_def_12,iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_220,c_1551]) ).
tcf(c_1568,plain,
! [X0: $i] : addition(X0,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_1551,c_67]) ).
tcf(c_1728,plain,
! [X0: $i,X1: $i] :
( leq(X0,multiplication(strong_iteration(X1),iPr_def_12))
| ~ leq(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_1568,c_64]) ).
tcf(c_1732,plain,
! [X0: $i,X1: $i] : leq(X0,multiplication(strong_iteration(X1),iPr_def_12)),
inference(forward_subsumption_resolution,[status(thm)],[c_1728,c_1551]) ).
tcf(c_1774,plain,
! [X0: $i] : leq(X0,multiplication(iPr_def_11,iPr_def_12)),
inference(superposition,[status(thm)],[c_218,c_1732]) ).
tcf(c_1827,plain,
! [X0: $i] : leq(one,addition(X0,iPr_def_11)),
inference(superposition,[status(thm)],[c_1383,c_1400]) ).
tcf(c_1913,plain,
! [X0: $i] : leq(one,multiplication(strong_iteration(X0),iPr_def_11)),
inference(superposition,[status(thm)],[c_1827,c_64]) ).
tcf(c_2060,plain,
leq(one,multiplication(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_217,c_1913]) ).
tcf(c_2066,plain,
addition(one,multiplication(iPr_def_10,iPr_def_11)) = multiplication(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_2060,c_67]) ).
tcf(c_2067,plain,
addition(multiplication(iPr_def_10,iPr_def_11),one) = multiplication(iPr_def_10,iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_2066,c_50,c_49]) ).
tcf(c_2068,plain,
multiplication(iPr_def_10,iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_2067,c_610]) ).
tcf(c_2100,plain,
! [X0: $i] :
( leq(iPr_def_11,multiplication(strong_iteration(iPr_def_10),X0))
| ~ leq(iPr_def_11,addition(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_2068,c_64]) ).
tcf(c_2102,plain,
! [X0: $i] :
( leq(iPr_def_11,multiplication(iPr_def_11,X0))
| ~ leq(iPr_def_11,addition(iPr_def_11,X0)) ),
inference(light_normalisation,[status(thm)],[c_2100,c_218]) ).
tcf(c_2103,plain,
! [X0: $i] : leq(iPr_def_11,multiplication(iPr_def_11,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2102,c_1012]) ).
tcf(c_2114,plain,
! [X0: $i] : addition(iPr_def_11,multiplication(iPr_def_11,X0)) = multiplication(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_2103,c_67]) ).
tcf(c_3313,plain,
multiplication(iPr_def_11,zero) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1017,c_2114]) ).
tcf(c_3323,plain,
! [X0: $i] : multiplication(iPr_def_11,multiplication(zero,X0)) = multiplication(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_3313,c_53]) ).
tcf(c_3327,plain,
! [X0: $i] : multiplication(iPr_def_11,X0) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_3323,c_58,c_3313]) ).
tcf(c_3336,plain,
! [X0: $i] : leq(X0,iPr_def_11),
inference(demodulation,[status(thm)],[c_1774,c_3327]) ).
tcf(c_3337,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1556,c_3336]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE142+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.37 % Computer : n016.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Wed Sep 23 19:08:11 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 2.13/1.10 % SZS status Started for theBenchmark.p
% 2.13/1.10 % SZS status Theorem for theBenchmark.p
% 2.13/1.10
% 2.13/1.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.13/1.10
% 2.13/1.10 % ------ iProver source info
% 2.13/1.10
% 2.13/1.10 % git: date: 2026-07-19 20:42:38 +0200
% 2.13/1.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.13/1.10 % git: non_committed_changes: false
% 2.13/1.10
% 2.13/1.10 % ------ Parsing...
% 2.13/1.10 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.13/1.10
% 2.13/1.10 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.13/1.10
% 2.13/1.10 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.13/1.10
% 2.13/1.10 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.13/1.10 % ------ Proving...
% 2.13/1.10 % ------ Problem Properties
% 2.13/1.10
% 2.13/1.10 %
% 2.13/1.10 % clauses 23
% 2.13/1.10 % conjectures 1
% 2.13/1.10 % EPR 1
% 2.13/1.10 % Horn 23
% 2.13/1.10 % unary 17
% 2.13/1.10 % binary 6
% 2.13/1.10 % lits 29
% 2.13/1.10 % lits eq 19
% 2.13/1.10 % fd_pure 0
% 2.13/1.10 % fd_pseudo 0
% 2.13/1.10 % fd_cond 0
% 2.13/1.10 % fd_pseudo_cond 0
% 2.13/1.10 % AC symbols 1
% 2.13/1.10
% 2.13/1.10 % ------ Schedule dynamic 5 is on
% 2.13/1.10
% 2.13/1.10 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.13/1.10
% 2.13/1.10
% 2.13/1.10 % ------
% 2.13/1.10 % Current options:
% 2.13/1.10 % ------
% 2.13/1.10
% 2.13/1.10
% 2.13/1.10 %
% 2.13/1.10
% 2.13/1.10 % ------ Proving...
% 2.13/1.10 %
% 2.13/1.10
% 2.13/1.10 % SZS status Theorem for theBenchmark.p
% 2.13/1.10
% 2.13/1.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.13/1.10
% 2.13/1.10
%------------------------------------------------------------------------------