%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL486+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 02:06:45 PM UTC 2026
% Result : Theorem 111.94s 26.10s
% Output : CNFRefutation 111.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 25 unt; 0 def)
% Number of atoms : 105 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 86 ( 39 ~; 34 |; 2 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 92 !; 3 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
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/sandbox/benchmark/Axioms/LCL006+0.ax',implies_3) ).
fof(f25,axiom,
( r4
<=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r4) ).
fof(f26,axiom,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r5) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r4) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
fof(f45,conjecture,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f46,negated_conjecture,
~ implies_3,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ implies_3,
inference(flattening,[],[f46]) ).
fof(f48,plain,
( r5
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f26]) ).
fof(f49,plain,
( r4
=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f25]) ).
fof(f53,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
=> implies_3 ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f55,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f56,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f57,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f56]) ).
fof(f59,plain,
( ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| implies_3 ),
inference(ennf_transformation,[],[f53]) ).
fof(f63,plain,
( ~ r4
| ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f64,plain,
( ~ r5
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(ennf_transformation,[],[f48]) ).
fof(f68,plain,
( ~ op_implies_or
| ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f70,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| implies_3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f59]) ).
fof(f71,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f73,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| implies_3 ),
inference(cnf_transformation,[],[f70]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ r4
| is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(cnf_transformation,[],[f63]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ r5
| is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f82,plain,
! [X0,X1] :
( ~ op_implies_or
| implies(X0,X1) = or(not(X0),X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f84,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f87,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f91,plain,
r4,
inference(cnf_transformation,[],[f39]) ).
fof(f92,plain,
r5,
inference(cnf_transformation,[],[f40]) ).
fof(f97,plain,
~ implies_3,
inference(cnf_transformation,[],[f47]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_51,plain,
( implies_3
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))
| ~ r5 ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( or(not(X0),X1) = implies(X0,X1) )
| ~ op_implies_or ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_62,plain,
op_implies_or,
inference(cnf_transformation,[],[f84]) ).
tcf(c_65,plain,
modus_ponens,
inference(cnf_transformation,[],[f87]) ).
tcf(c_69,plain,
r4,
inference(cnf_transformation,[],[f91]) ).
tcf(c_70,plain,
r5,
inference(cnf_transformation,[],[f92]) ).
tcf(c_75,negated_conjecture,
~ implies_3,
inference(cnf_transformation,[],[f97]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] : or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_60,c_62,c_60]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_65,c_49]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_105]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(global_subsumption_just,[status(thm)],[c_56,c_70,c_56]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(global_subsumption_just,[status(thm)],[c_55,c_69,c_55]) ).
tcf(c_122,plain,
~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))),
inference(global_subsumption_just,[status(thm)],[c_51,c_75,c_51]) ).
tcf(c_5591,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(or(not(X2),X0),implies(X2,X1)))),
inference(superposition,[status(thm)],[c_96,c_116]) ).
tcf(c_5593,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(demodulation,[status(thm)],[c_5591,c_96]) ).
tcf(c_5601,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,or(X0,X2)))
| ~ is_a_theorem(or(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[c_119,c_106]) ).
tcf(c_5653,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(not(X1),or(X0,X2)))
| ~ is_a_theorem(or(X0,implies(X1,X2))) ),
inference(superposition,[status(thm)],[c_96,c_5601]) ).
tcf(c_5654,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X1,or(X0,X2)))
| ~ is_a_theorem(or(X0,implies(X1,X2))) ),
inference(demodulation,[status(thm)],[c_5653,c_96]) ).
tcf(c_5881,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X1,or(not(X0),X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(superposition,[status(thm)],[c_96,c_5654]) ).
tcf(c_5884,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(demodulation,[status(thm)],[c_5881,c_96]) ).
tcf(c_6998,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(superposition,[status(thm)],[c_5593,c_5884]) ).
tcf(c_7037,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_122,c_6998]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL486+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.38 % Computer : n005.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Sep 23 23:32:02 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 111.94/26.10 % SZS status Started for theBenchmark.p
% 111.94/26.10 % SZS status Theorem for theBenchmark.p
% 111.94/26.10
% 111.94/26.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 111.94/26.10
% 111.94/26.10 % ------ iProver source info
% 111.94/26.10
% 111.94/26.10 % git: date: 2026-07-19 20:42:38 +0200
% 111.94/26.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 111.94/26.10 % git: non_committed_changes: false
% 111.94/26.10
% 111.94/26.10 % ------ Parsing...
% 111.94/26.10 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 111.94/26.10
% 111.94/26.10 % ------ Preprocessing... sup_sim: 0 sf_s rm: 14 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 111.94/26.10
% 111.94/26.10 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 111.94/26.10
% 111.94/26.10 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 111.94/26.10 % ------ Proving...
% 111.94/26.10 % ------ Problem Properties
% 111.94/26.10
% 111.94/26.10 %
% 111.94/26.10 % clauses 13
% 111.94/26.10 % conjectures 0
% 111.94/26.10 % EPR 0
% 111.94/26.10 % Horn 13
% 111.94/26.10 % unary 11
% 111.94/26.10 % binary 1
% 111.94/26.10 % lits 16
% 111.94/26.10 % lits eq 6
% 111.94/26.10 % fd_pure 0
% 111.94/26.10 % fd_pseudo 0
% 111.94/26.10 % fd_cond 0
% 111.94/26.10 % fd_pseudo_cond 1
% 111.94/26.10 % AC symbols 0
% 111.94/26.10
% 111.94/26.10 % ------ Input Options Time Limit: Unbounded
% 111.94/26.10
% 111.94/26.10
% 111.94/26.10 % ------
% 111.94/26.10 % Current options:
% 111.94/26.10 % ------
% 111.94/26.10
% 111.94/26.10
% 111.94/26.10 %
% 111.94/26.10
% 111.94/26.10 % ------ Proving...
% 111.94/26.10 %
% 111.94/26.10
% 111.94/26.10 % SZS status Theorem for theBenchmark.p
% 111.94/26.10
% 111.94/26.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 111.94/26.10
% 111.94/26.10
%------------------------------------------------------------------------------