%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE040+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 : n020.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 01:52:15 PM UTC 2026
% Result : Theorem 0.75s 1.29s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 68 ( 48 unt; 2 def)
% Number of atoms : 146 ( 36 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 46 ( 24 ~; 17 |; 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 82 !; 1 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+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/KLE002+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
fof(f13,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(f14,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
fof(f15,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X1)
=> leq(multiplication(star(X0),X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_induction_left) ).
fof(f17,conjecture,
! [X0] :
( leq(star(X0),multiplication(star(X0),star(X0)))
& leq(multiplication(star(X0),star(X0)),star(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0] :
( leq(star(X0),multiplication(star(X0),star(X0)))
& leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
? [X0] :
( ~ leq(star(X0),multiplication(star(X0),star(X0)))
| ~ leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f23,plain,
( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
| ~ leq(multiplication(star(sK0),star(sK0)),star(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f21]) ).
fof(f24,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f25,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f35,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f38,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
| ~ leq(multiplication(star(sK0),star(sK0)),star(sK0)) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f30]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f32]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_62,plain,
! [X0: $i] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_63,plain,
! [X0: $i] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_66,negated_conjecture,
( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
| ~ leq(multiplication(star(sK0),star(sK0)),star(sK0)) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_195,definition,
iPr_def_10 = star(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_196,definition,
iPr_def_11 = multiplication(iPr_def_10,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_197,negated_conjecture,
( ~ leq(iPr_def_11,iPr_def_10)
| ~ leq(iPr_def_10,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_66,c_195,c_196]) ).
tcf(c_518,plain,
leq(addition(one,multiplication(sK0,iPr_def_10)),iPr_def_10),
inference(superposition,[status(thm)],[c_195,c_62]) ).
tcf(c_524,plain,
leq(addition(one,multiplication(iPr_def_10,sK0)),iPr_def_10),
inference(superposition,[status(thm)],[c_195,c_63]) ).
tcf(c_539,plain,
! [X0: $i] : leq(X0,X0),
inference(superposition,[status(thm)],[c_52,c_60]) ).
tcf(c_561,plain,
addition(addition(one,multiplication(sK0,iPr_def_10)),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_518,c_61]) ).
tcf(c_562,plain,
addition(addition(one,multiplication(iPr_def_10,sK0)),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_524,c_61]) ).
tcf(c_565,plain,
addition(iPr_def_10,addition(one,multiplication(iPr_def_10,sK0))) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_562,c_50,c_49]) ).
tcf(c_566,plain,
addition(iPr_def_10,addition(one,multiplication(sK0,iPr_def_10))) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_561,c_50,c_49]) ).
tcf(c_619,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_751,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(multiplication(star(X1),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_49,c_64]) ).
tcf(c_893,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_619,c_60]) ).
tcf(c_1008,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_893]) ).
tcf(c_1024,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X2,X0))),
inference(superposition,[status(thm)],[c_50,c_1008]) ).
tcf(c_1042,plain,
leq(multiplication(sK0,iPr_def_10),iPr_def_10),
inference(superposition,[status(thm)],[c_566,c_1024]) ).
tcf(c_1044,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X0,X2))),
inference(superposition,[status(thm)],[c_49,c_1024]) ).
tcf(c_1096,plain,
addition(multiplication(sK0,iPr_def_10),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_1042,c_61]) ).
tcf(c_1097,plain,
addition(iPr_def_10,multiplication(sK0,iPr_def_10)) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_1096,c_50,c_49]) ).
tcf(c_1103,plain,
leq(one,iPr_def_10),
inference(superposition,[status(thm)],[c_565,c_1044]) ).
tcf(c_1129,plain,
addition(one,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_1103,c_61]) ).
tcf(c_1130,plain,
addition(iPr_def_10,one) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_1129,c_50,c_49]) ).
tcf(c_1165,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),multiplication(one,X0)) = multiplication(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_1130,c_57]) ).
tcf(c_1169,plain,
! [X0: $i] : addition(multiplication(iPr_def_10,X0),X0) = multiplication(iPr_def_10,X0),
inference(light_normalisation,[status(thm)],[c_1165,c_55]) ).
tcf(c_1170,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_10,X0)) = multiplication(iPr_def_10,X0),
inference(theory_normalisation,[status(thm)],[c_1169,c_50,c_49]) ).
tcf(c_4286,plain,
! [X0: $i] : leq(X0,multiplication(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_1170,c_60]) ).
tcf(c_4567,plain,
leq(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_196,c_4286]) ).
tcf(c_4569,plain,
~ leq(iPr_def_11,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_197,c_4567]) ).
tcf(c_6902,plain,
( leq(multiplication(star(sK0),iPr_def_10),iPr_def_10)
| ~ leq(iPr_def_10,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1097,c_751]) ).
tcf(c_6925,plain,
( leq(iPr_def_11,iPr_def_10)
| ~ leq(iPr_def_10,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_6902,c_195,c_196]) ).
tcf(c_6926,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6925,c_4569,c_539]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE040+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 18:45:33 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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...
% 0.75/1.29 % SZS status Started for theBenchmark.p
% 0.75/1.29 % SZS status Theorem for theBenchmark.p
% 0.75/1.29
% 0.75/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.75/1.29
% 0.75/1.29 % ------ iProver source info
% 0.75/1.29
% 0.75/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.75/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.75/1.29 % git: non_committed_changes: false
% 0.75/1.29
% 0.75/1.29 % ------ Parsing...
% 0.75/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.75/1.29
% 0.75/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.75/1.29
% 0.75/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.75/1.29
% 0.75/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.75/1.29 % ------ Proving...
% 0.75/1.29 % ------ Problem Properties
% 0.75/1.29
% 0.75/1.29 %
% 0.75/1.29 % clauses 20
% 0.75/1.29 % conjectures 1
% 0.75/1.29 % EPR 1
% 0.75/1.29 % Horn 20
% 0.75/1.29 % unary 15
% 0.75/1.29 % binary 5
% 0.75/1.29 % lits 25
% 0.75/1.29 % lits eq 15
% 0.75/1.29 % fd_pure 0
% 0.75/1.29 % fd_pseudo 0
% 0.75/1.29 % fd_cond 0
% 0.75/1.29 % fd_pseudo_cond 0
% 0.75/1.29 % AC symbols 1
% 0.75/1.29
% 0.75/1.29 % ------ Schedule dynamic 5 is on
% 0.75/1.29
% 0.75/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.75/1.29
% 0.75/1.29
% 0.75/1.29 % ------
% 0.75/1.29 % Current options:
% 0.75/1.29 % ------
% 0.75/1.29
% 0.75/1.29
% 0.75/1.29 %
% 0.75/1.29
% 0.75/1.29 % ------ Proving...
% 0.75/1.29 %
% 0.75/1.29
% 0.75/1.29 % SZS status Theorem for theBenchmark.p
% 0.75/1.29
% 0.75/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.75/1.29
% 0.75/1.29
%------------------------------------------------------------------------------