%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE041+1 : 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 : 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 01:52:15 PM UTC 2026
% Result : Theorem 5.80s 1.75s
% Output : CNFRefutation 5.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 58 unt; 2 def)
% Number of atoms : 134 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 16 ~; 10 |; 3 &)
% ( 1 <=>; 3 =>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 91 !; 2 ?; 48 :)
% 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(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_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(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,X1] :
( leq(X0,X1)
=> leq(star(X0),star(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,X1)
=> leq(star(X0),star(X1)) ),
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,X1] :
( leq(X0,X1)
& ~ leq(star(X0),star(X1)) ),
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(sK0,sK1)
& ~ leq(star(sK0),star(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[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(f29,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
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(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(sK0,sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
~ leq(star(sK0),star(sK1)),
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_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f29]) ).
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_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),star(sK1)),
inference(cnf_transformation,[],[f42]) ).
tcf(c_67,negated_conjecture,
leq(sK0,sK1),
inference(cnf_transformation,[],[f41]) ).
tcf(c_186,definition,
iPr_def_10 = star(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_187,definition,
iPr_def_11 = star(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_188,negated_conjecture,
leq(sK0,sK1),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_189,negated_conjecture,
~ leq(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_66,c_187,c_186]) ).
tcf(c_486,plain,
leq(addition(one,multiplication(sK1,iPr_def_11)),iPr_def_11),
inference(superposition,[status(thm)],[c_187,c_62]) ).
tcf(c_523,plain,
addition(sK0,sK1) = sK1,
inference(superposition,[status(thm)],[c_188,c_61]) ).
tcf(c_527,plain,
addition(addition(one,multiplication(sK1,iPr_def_11)),iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_486,c_61]) ).
tcf(c_534,plain,
addition(iPr_def_11,addition(one,multiplication(sK1,iPr_def_11))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_527,c_50,c_49]) ).
tcf(c_545,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_626,plain,
! [X0: $i] : addition(multiplication(sK0,X0),multiplication(sK1,X0)) = multiplication(sK1,X0),
inference(superposition,[status(thm)],[c_523,c_57]) ).
tcf(c_763,plain,
! [X0: $i,X1: $i] : addition(multiplication(sK0,X0),addition(multiplication(sK1,X0),X1)) = addition(multiplication(sK1,X0),X1),
inference(superposition,[status(thm)],[c_626,c_50]) ).
tcf(c_960,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_1643,plain,
! [X0: $i,X1: $i] : leq(multiplication(sK0,X0),addition(multiplication(sK1,X0),X1)),
inference(superposition,[status(thm)],[c_763,c_60]) ).
tcf(c_1873,plain,
! [X0: $i,X1: $i] : leq(multiplication(sK0,X0),addition(X1,multiplication(sK1,X0))),
inference(superposition,[status(thm)],[c_49,c_1643]) ).
tcf(c_2931,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_545,c_60]) ).
tcf(c_2981,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_2931]) ).
tcf(c_2983,plain,
! [X0: $i,X1: $i,X2: $i] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(superposition,[status(thm)],[c_50,c_2931]) ).
tcf(c_3017,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X2,X0))),
inference(superposition,[status(thm)],[c_50,c_2981]) ).
tcf(c_3047,plain,
leq(multiplication(sK1,iPr_def_11),iPr_def_11),
inference(superposition,[status(thm)],[c_534,c_3017]) ).
tcf(c_3055,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X0,X2))),
inference(superposition,[status(thm)],[c_49,c_3017]) ).
tcf(c_3314,plain,
leq(one,iPr_def_11),
inference(superposition,[status(thm)],[c_534,c_3055]) ).
tcf(c_3529,plain,
! [X0: $i,X1: $i,X2: $i] : leq(addition(X0,X1),addition(X0,addition(X2,X1))),
inference(superposition,[status(thm)],[c_49,c_2983]) ).
tcf(c_3748,plain,
addition(one,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_3314,c_61]) ).
tcf(c_3749,plain,
addition(iPr_def_11,one) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_3748,c_50,c_49]) ).
tcf(c_3752,plain,
addition(multiplication(sK1,iPr_def_11),iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_3047,c_61]) ).
tcf(c_3753,plain,
addition(iPr_def_11,multiplication(sK1,iPr_def_11)) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_3752,c_50,c_49]) ).
tcf(c_4875,plain,
leq(multiplication(sK0,iPr_def_11),iPr_def_11),
inference(superposition,[status(thm)],[c_3753,c_1873]) ).
tcf(c_4943,plain,
addition(multiplication(sK0,iPr_def_11),iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_4875,c_61]) ).
tcf(c_4944,plain,
addition(iPr_def_11,multiplication(sK0,iPr_def_11)) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_4943,c_50,c_49]) ).
tcf(c_7420,plain,
! [X0: $i] : leq(addition(X0,one),addition(X0,iPr_def_11)),
inference(superposition,[status(thm)],[c_3749,c_3529]) ).
tcf(c_7452,plain,
! [X0: $i] : leq(addition(X0,one),addition(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_49,c_7420]) ).
tcf(c_7912,plain,
leq(addition(multiplication(sK0,iPr_def_11),one),iPr_def_11),
inference(superposition,[status(thm)],[c_4944,c_7452]) ).
tcf(c_7915,plain,
leq(addition(one,multiplication(sK0,iPr_def_11)),iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_7912,c_50,c_49]) ).
tcf(c_8393,plain,
leq(multiplication(star(sK0),one),iPr_def_11),
inference(superposition,[status(thm)],[c_7915,c_960]) ).
tcf(c_8417,plain,
leq(multiplication(iPr_def_10,one),iPr_def_11),
inference(light_normalisation,[status(thm)],[c_8393,c_186]) ).
tcf(c_9596,plain,
leq(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_8417,c_54]) ).
tcf(c_9597,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9596,c_189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE041+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 18:44:49 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 5.80/1.75 % SZS status Started for theBenchmark.p
% 5.80/1.75 % SZS status Theorem for theBenchmark.p
% 5.80/1.75
% 5.80/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.80/1.75
% 5.80/1.75 % ------ iProver source info
% 5.80/1.75
% 5.80/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 5.80/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.80/1.75 % git: non_committed_changes: false
% 5.80/1.75
% 5.80/1.75 % ------ Parsing...
% 5.80/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.80/1.75
% 5.80/1.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 5.80/1.75
% 5.80/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.80/1.75
% 5.80/1.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.80/1.75 % ------ Proving...
% 5.80/1.75 % ------ Problem Properties
% 5.80/1.75
% 5.80/1.75 %
% 5.80/1.75 % clauses 21
% 5.80/1.75 % conjectures 2
% 5.80/1.75 % EPR 2
% 5.80/1.75 % Horn 21
% 5.80/1.75 % unary 17
% 5.80/1.75 % binary 4
% 5.80/1.75 % lits 25
% 5.80/1.75 % lits eq 15
% 5.80/1.75 % fd_pure 0
% 5.80/1.75 % fd_pseudo 0
% 5.80/1.75 % fd_cond 0
% 5.80/1.75 % fd_pseudo_cond 0
% 5.80/1.75 % AC symbols 1
% 5.80/1.75
% 5.80/1.75 % ------ Schedule dynamic 5 is on
% 5.80/1.75
% 5.80/1.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.80/1.75
% 5.80/1.75
% 5.80/1.75 % ------
% 5.80/1.75 % Current options:
% 5.80/1.75 % ------
% 5.80/1.75
% 5.80/1.75
% 5.80/1.75 %
% 5.80/1.75
% 5.80/1.75 % ------ Proving...
% 5.80/1.75 %
% 5.80/1.75
% 5.80/1.75 % SZS status Theorem for theBenchmark.p
% 5.80/1.75
% 5.80/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.80/1.76
% 5.80/1.76
%------------------------------------------------------------------------------