%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL490+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 : 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 02:06:45 PM UTC 2026
% Result : Theorem 20.88s 4.27s
% Output : CNFRefutation 20.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 84 ( 34 unt; 0 def)
% Number of atoms : 165 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 151 ( 70 ~; 66 |; 2 &)
% ( 5 <=>; 8 =>; 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 : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 105 !; 2 ?; 57 :)
% 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(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_1) ).
fof(f23,axiom,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r2) ).
fof(f24,axiom,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r3) ).
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(f37,axiom,
r2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
fof(f45,conjecture,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f46,negated_conjecture,
~ or_1,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ or_1,
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(f50,plain,
( r3
=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f51,plain,
( r2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f53,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
=> or_1 ),
inference(unused_predicate_definition_removal,[],[f10]) ).
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] : ~ is_a_theorem(implies(X0,or(X0,X1)))
| or_1 ),
inference(ennf_transformation,[],[f53]) ).
fof(f61,plain,
( ~ r2
| ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(ennf_transformation,[],[f51]) ).
fof(f62,plain,
( ~ r3
| ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(ennf_transformation,[],[f50]) ).
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(sK0,or(sK0,sK1)))
| or_1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[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(sK0,or(sK0,sK1)))
| or_1 ),
inference(cnf_transformation,[],[f70]) ).
fof(f75,plain,
! [X0,X1] :
( ~ r2
| is_a_theorem(implies(X1,or(X0,X1))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f76,plain,
! [X0,X1] :
( ~ r3
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(cnf_transformation,[],[f62]) ).
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(f89,plain,
r2,
inference(cnf_transformation,[],[f37]) ).
fof(f90,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f92,plain,
r5,
inference(cnf_transformation,[],[f40]) ).
fof(f97,plain,
~ or_1,
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,
( or_1
| ~ is_a_theorem(implies(sK0,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ r2 ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f76]) ).
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_67,plain,
r2,
inference(cnf_transformation,[],[f89]) ).
tcf(c_68,plain,
r3,
inference(cnf_transformation,[],[f90]) ).
tcf(c_70,plain,
r5,
inference(cnf_transformation,[],[f92]) ).
tcf(c_75,negated_conjecture,
~ or_1,
inference(cnf_transformation,[],[f97]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_53,c_67,c_53]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_54,c_68,c_54]) ).
tcf(c_98,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_107,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_108,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_107]) ).
tcf(c_118,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_234,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_236,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_237,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_386,plain,
! [X0: $i] :
( is_a_theorem(implies(sK0,or(sK0,sK1)))
| ~ is_a_theorem(X0)
| ( implies(sK0,or(sK0,sK1)) != X0 ) ),
inference(instantiation,[status(thm)],[c_237]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ is_a_theorem(implies(implies(or(X0,X1),or(X1,X0)),X2)) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_440,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,or(X2,X1)))
| ( X0 != implies(X1,or(X2,X1)) ) ),
inference(instantiation,[status(thm)],[c_237]) ).
tcf(c_464,plain,
! [X0: $i,X1: $i] :
( ( implies(sK0,or(sK0,sK1)) = X1 )
| ( X1 != X0 )
| ( implies(sK0,or(sK0,sK1)) != X0 ) ),
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_494,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(or(X2,or(X0,X1)),or(X2,or(X1,X0))))
| ~ is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ is_a_theorem(implies(implies(or(X0,X1),or(X1,X0)),implies(or(X2,or(X0,X1)),or(X2,or(X1,X0))))) ),
inference(instantiation,[status(thm)],[c_414]) ).
tcf(c_524,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(not(X0),or(X1,X0)))
| ~ is_a_theorem(implies(X0,or(X1,X0)))
| ( or(not(X0),or(X1,X0)) != implies(X0,or(X1,X0)) ) ),
inference(instantiation,[status(thm)],[c_440]) ).
tcf(c_612,plain,
! [X0: $i] :
( ( implies(sK0,or(sK0,sK1)) = X0 )
| ( X0 != implies(sK0,or(sK0,sK1)) )
| ( implies(sK0,or(sK0,sK1)) != implies(sK0,or(sK0,sK1)) ) ),
inference(instantiation,[status(thm)],[c_464]) ).
tcf(c_623,plain,
implies(sK0,or(sK0,sK1)) = implies(sK0,or(sK0,sK1)),
inference(instantiation,[status(thm)],[c_234]) ).
tcf(c_767,plain,
! [X0: $i,X1: $i] : or(not(X0),or(X1,X0)) = implies(X0,or(X1,X0)),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_801,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(or(X0,X1),or(X1,X0)),implies(or(X2,or(X0,X1)),or(X2,or(X1,X0))))),
inference(instantiation,[status(thm)],[c_118]) ).
tcf(c_889,plain,
( ( implies(sK0,or(sK0,sK1)) = or(not(sK0),or(sK0,sK1)) )
| ( implies(sK0,or(sK0,sK1)) != implies(sK0,or(sK0,sK1)) )
| ( or(not(sK0),or(sK0,sK1)) != implies(sK0,or(sK0,sK1)) ) ),
inference(instantiation,[status(thm)],[c_612]) ).
tcf(c_1216,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(or(not(X0),or(X1,X0)))
| ~ is_a_theorem(implies(or(not(X0),or(X1,X0)),X2)) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_1521,plain,
or(not(sK0),or(sK0,sK1)) = implies(sK0,or(sK0,sK1)),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_2047,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(not(X0),or(X0,X1)))
| ~ is_a_theorem(or(not(X0),or(X1,X0)))
| ~ is_a_theorem(implies(or(not(X0),or(X1,X0)),or(not(X0),or(X0,X1)))) ),
inference(instantiation,[status(thm)],[c_1216]) ).
tcf(c_5958,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(sK0,or(sK0,sK1)))
| ~ is_a_theorem(or(not(X0),or(X0,X1)))
| ( implies(sK0,or(sK0,sK1)) != or(not(X0),or(X0,X1)) ) ),
inference(instantiation,[status(thm)],[c_386]) ).
tcf(c_12971,plain,
( is_a_theorem(implies(sK0,or(sK0,sK1)))
| ~ is_a_theorem(or(not(sK0),or(sK0,sK1)))
| ( implies(sK0,or(sK0,sK1)) != or(not(sK0),or(sK0,sK1)) ) ),
inference(instantiation,[status(thm)],[c_5958]) ).
tcf(c_16341,plain,
is_a_theorem(implies(sK0,or(sK1,sK0))),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_18057,plain,
( is_a_theorem(or(not(sK0),or(sK0,sK1)))
| ~ is_a_theorem(or(not(sK0),or(sK1,sK0)))
| ~ is_a_theorem(implies(or(not(sK0),or(sK1,sK0)),or(not(sK0),or(sK0,sK1)))) ),
inference(instantiation,[status(thm)],[c_2047]) ).
tcf(c_25916,plain,
( is_a_theorem(or(not(sK0),or(sK1,sK0)))
| ~ is_a_theorem(implies(sK0,or(sK1,sK0)))
| ( or(not(sK0),or(sK1,sK0)) != implies(sK0,or(sK1,sK0)) ) ),
inference(instantiation,[status(thm)],[c_524]) ).
tcf(c_35419,plain,
or(not(sK0),or(sK1,sK0)) = implies(sK0,or(sK1,sK0)),
inference(instantiation,[status(thm)],[c_767]) ).
tcf(c_43637,plain,
( is_a_theorem(implies(or(not(sK0),or(sK1,sK0)),or(not(sK0),or(sK0,sK1))))
| ~ is_a_theorem(implies(or(sK1,sK0),or(sK0,sK1)))
| ~ is_a_theorem(implies(implies(or(sK1,sK0),or(sK0,sK1)),implies(or(not(sK0),or(sK1,sK0)),or(not(sK0),or(sK0,sK1))))) ),
inference(instantiation,[status(thm)],[c_494]) ).
tcf(c_43763,plain,
is_a_theorem(implies(or(sK1,sK0),or(sK0,sK1))),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_56426,plain,
is_a_theorem(implies(implies(or(sK1,sK0),or(sK0,sK1)),implies(or(not(sK0),or(sK1,sK0)),or(not(sK0),or(sK0,sK1))))),
inference(instantiation,[status(thm)],[c_801]) ).
tcf(c_56427,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_56426,c_43763,c_43637,c_35419,c_25916,c_18057,c_16341,c_12971,c_1521,c_889,c_623,c_51,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL490+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 23:34:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 20.88/4.27 % SZS status Started for theBenchmark.p
% 20.88/4.27 % SZS status Theorem for theBenchmark.p
% 20.88/4.27
% 20.88/4.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 20.88/4.27
% 20.88/4.27 % ------ iProver source info
% 20.88/4.27
% 20.88/4.27 % git: date: 2026-07-19 20:42:38 +0200
% 20.88/4.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 20.88/4.27 % git: non_committed_changes: false
% 20.88/4.27
% 20.88/4.27 % ------ Parsing...
% 20.88/4.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 20.88/4.27
% 20.88/4.27 % ------ Preprocessing... sup_sim: 2 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 %
% 20.88/4.27
% 20.88/4.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 20.88/4.27
% 20.88/4.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 20.88/4.27 % ------ Proving...
% 20.88/4.27 % ------ Problem Properties
% 20.88/4.27
% 20.88/4.27 %
% 20.88/4.27 % clauses 13
% 20.88/4.27 % conjectures 0
% 20.88/4.27 % EPR 0
% 20.88/4.27 % Horn 13
% 20.88/4.27 % unary 11
% 20.88/4.27 % binary 1
% 20.88/4.27 % lits 16
% 20.88/4.27 % lits eq 6
% 20.88/4.27 % fd_pure 0
% 20.88/4.27 % fd_pseudo 0
% 20.88/4.27 % fd_cond 0
% 20.88/4.27 % fd_pseudo_cond 1
% 20.88/4.27 % AC symbols 0
% 20.88/4.27
% 20.88/4.27 % ------ Input Options Time Limit: Unbounded
% 20.88/4.27
% 20.88/4.27
% 20.88/4.27 % ------
% 20.88/4.27 % Current options:
% 20.88/4.27 % ------
% 20.88/4.27
% 20.88/4.27
% 20.88/4.27 %
% 20.88/4.27
% 20.88/4.27 % ------ Proving...
% 20.88/4.27 %
% 20.88/4.27
% 20.88/4.27 % SZS status Theorem for theBenchmark.p
% 20.88/4.27
% 20.88/4.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.88/4.27
% 20.88/4.27
%------------------------------------------------------------------------------