%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE037+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 : n003.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 01:52:14 PM UTC 2026
% Result : Theorem 3.87s 1.26s
% Output : CNFRefutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 27 unt; 1 def)
% Number of atoms : 44 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 6 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 42 !; 1 ?; 18 :)
% 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(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
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(f17,conjecture,
! [X0] : leq(one,star(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0] : leq(one,star(X0)),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f21,plain,
? [X0] : ~ leq(one,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(one,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(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(f38,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f41,plain,
~ leq(one,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_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_63,plain,
! [X0: $i] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_66,negated_conjecture,
~ leq(one,star(sK0)),
inference(cnf_transformation,[],[f41]) ).
tcf(c_183,definition,
iPr_def_10 = star(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_184,negated_conjecture,
~ leq(one,iPr_def_10),
inference(demodulation,[status(thm)],[c_66,c_183]) ).
tcf(c_492,plain,
! [X0: $i] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_63,c_61]) ).
tcf(c_493,plain,
! [X0: $i] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(theory_normalisation,[status(thm)],[c_492,c_50,c_49]) ).
tcf(c_558,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_739,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_558,c_60]) ).
tcf(c_762,plain,
! [X0: $i] : leq(one,star(X0)),
inference(superposition,[status(thm)],[c_493,c_739]) ).
tcf(c_769,plain,
leq(one,iPr_def_10),
inference(superposition,[status(thm)],[c_183,c_762]) ).
tcf(c_771,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_769,c_184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE037+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 18:45:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 3.87/1.26 % SZS status Started for theBenchmark.p
% 3.87/1.26 % SZS status Theorem for theBenchmark.p
% 3.87/1.26
% 3.87/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.87/1.26
% 3.87/1.26 % ------ iProver source info
% 3.87/1.26
% 3.87/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 3.87/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.87/1.26 % git: non_committed_changes: false
% 3.87/1.26
% 3.87/1.26 % ------ Parsing...
% 3.87/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.87/1.26
% 3.87/1.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.87/1.26
% 3.87/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.87/1.26
% 3.87/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.87/1.26 % ------ Proving...
% 3.87/1.26 % ------ Problem Properties
% 3.87/1.26
% 3.87/1.26 %
% 3.87/1.26 % clauses 19
% 3.87/1.26 % conjectures 1
% 3.87/1.26 % EPR 1
% 3.87/1.26 % Horn 19
% 3.87/1.26 % unary 15
% 3.87/1.26 % binary 4
% 3.87/1.26 % lits 23
% 3.87/1.26 % lits eq 14
% 3.87/1.26 % fd_pure 0
% 3.87/1.26 % fd_pseudo 0
% 3.87/1.26 % fd_cond 0
% 3.87/1.26 % fd_pseudo_cond 0
% 3.87/1.26 % AC symbols 1
% 3.87/1.26
% 3.87/1.26 % ------ Schedule dynamic 5 is on
% 3.87/1.26
% 3.87/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.87/1.26
% 3.87/1.26
% 3.87/1.26 % ------
% 3.87/1.26 % Current options:
% 3.87/1.26 % ------
% 3.87/1.26
% 3.87/1.26
% 3.87/1.26 %
% 3.87/1.26
% 3.87/1.26 % ------ Proving...
% 3.87/1.26 %
% 3.87/1.26
% 3.87/1.26 % SZS status Theorem for theBenchmark.p
% 3.87/1.26
% 3.87/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.87/1.26
% 3.87/1.26
%------------------------------------------------------------------------------