%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 02:06:41 PM UTC 2026
% Result : Theorem 1.25s 1.16s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 7 |; 0 &)
% ( 2 <=>; 2 =>; 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 : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 24 !; 3 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_3) ).
fof(f19,axiom,
( cn1
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn1) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
fof(f53,conjecture,
cn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn1) ).
fof(f54,negated_conjecture,
~ cn1,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ cn1,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
=> cn1 ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f66,plain,
( implies_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f81,plain,
( ~ implies_3
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(ennf_transformation,[],[f66]) ).
fof(f91,plain,
( ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| cn1 ),
inference(ennf_transformation,[],[f56]) ).
fof(f95,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| cn1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f91]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ implies_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(cnf_transformation,[],[f81]) ).
fof(f111,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| cn1 ),
inference(cnf_transformation,[],[f95]) ).
fof(f122,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f135,plain,
~ cn1,
inference(cnf_transformation,[],[f55]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_64,plain,
( cn1
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_75,plain,
implies_3,
inference(cnf_transformation,[],[f122]) ).
tcf(c_88,negated_conjecture,
~ cn1,
inference(cnf_transformation,[],[f135]) ).
tcf(c_147,plain,
~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))),
inference(global_subsumption_just,[status(thm)],[c_64,c_88,c_64]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(global_subsumption_just,[status(thm)],[c_54,c_75,c_54]) ).
tcf(c_226,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_147,c_152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.34 % Computer : n015.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Wed Sep 23 23:29:55 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.39 % Detected problem language: tptp
% 0.13/0.40 % Proving...
% 1.25/1.16 % SZS status Started for theBenchmark.p
% 1.25/1.16 % SZS status Theorem for theBenchmark.p
% 1.25/1.16
% 1.25/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.25/1.16
% 1.25/1.16 % ------ iProver source info
% 1.25/1.16
% 1.25/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 1.25/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.25/1.16 % git: non_committed_changes: false
% 1.25/1.16
% 1.25/1.16 % ------ Parsing...
% 1.25/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.25/1.16
% 1.25/1.16 % ------ Preprocessing...%
% 1.25/1.16
% 1.25/1.16 % SZS status Theorem for theBenchmark.p
% 1.25/1.16
% 1.25/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.25/1.16
% 1.25/1.16
%------------------------------------------------------------------------------