%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL494+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 : 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 02:06:46 PM UTC 2026
% Result : Theorem 4.11s 1.41s
% Output : CNFRefutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 91 ( 46 unt; 0 def)
% Number of atoms : 150 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 106 ( 47 ~; 42 |; 2 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 113 !; 2 ?; 53 :)
% 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/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',equivalence_2) ).
fof(f23,axiom,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(f33,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(f42,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f43,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f44,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f45,conjecture,
equivalence_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f46,negated_conjecture,
~ equivalence_2,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ equivalence_2,
inference(flattening,[],[f46]) ).
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(equiv(X0,X1),implies(X1,X0)))
=> equivalence_2 ),
inference(unused_predicate_definition_removal,[],[f14]) ).
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(equiv(X0,X1),implies(X1,X0)))
| equivalence_2 ),
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(f65,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f66,plain,
( ~ op_and
| ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f28]) ).
fof(f67,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f68,plain,
( ~ op_implies_or
| ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f69,plain,
( ~ op_equiv
| ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f70,plain,
( ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0)))
| equivalence_2 ),
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(equiv(sK0,sK1),implies(sK1,sK0)))
| equivalence_2 ),
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(f79,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f65]) ).
fof(f80,plain,
! [X0,X1] :
( ~ op_and
| and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f66]) ).
fof(f81,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f67]) ).
fof(f82,plain,
! [X0,X1] :
( ~ op_implies_or
| implies(X0,X1) = or(not(X0),X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f83,plain,
! [X0,X1] :
( ~ op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f84,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f85,plain,
op_and,
inference(cnf_transformation,[],[f33]) ).
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(f94,plain,
op_or,
inference(cnf_transformation,[],[f42]) ).
fof(f95,plain,
op_implies_and,
inference(cnf_transformation,[],[f43]) ).
fof(f96,plain,
op_equiv,
inference(cnf_transformation,[],[f44]) ).
fof(f97,plain,
~ equivalence_2,
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,
( equivalence_2
| ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))) ),
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_57,plain,
! [X0: $i,X1: $i] :
( ( not(and(not(X0),not(X1))) = or(X0,X1) )
| ~ op_or ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( not(or(not(X0),not(X1))) = and(X0,X1) )
| ~ op_and ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( or(not(X0),X1) = implies(X0,X1) )
| ~ op_implies_or ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) )
| ~ op_equiv ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_62,plain,
op_implies_or,
inference(cnf_transformation,[],[f84]) ).
tcf(c_63,plain,
op_and,
inference(cnf_transformation,[],[f85]) ).
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_72,plain,
op_or,
inference(cnf_transformation,[],[f94]) ).
tcf(c_73,plain,
op_implies_and,
inference(cnf_transformation,[],[f95]) ).
tcf(c_74,plain,
op_equiv,
inference(cnf_transformation,[],[f96]) ).
tcf(c_75,negated_conjecture,
~ equivalence_2,
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_93,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_96,plain,
~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_75,c_51]) ).
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_104,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_59,c_73,c_59]) ).
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_109,plain,
! [X0: $i,X1: $i] : not(or(not(X0),not(X1))) = and(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_58,c_63,c_58]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_57,c_72,c_57]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] : and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_61,c_74,c_61]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_112,c_104]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i] : not(implies(X0,not(X1))) = and(X0,X1),
inference(demodulation,[status(thm)],[c_109,c_98]) ).
tcf(c_420,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(superposition,[status(thm)],[c_98,c_87]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X1,not(X0)))),
inference(superposition,[status(thm)],[c_190,c_420]) ).
tcf(c_449,plain,
! [X0: $i,X1: $i,X2: $i] : or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_191,c_190]) ).
tcf(c_603,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_93,c_108]) ).
tcf(c_744,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,not(X1)),X1)),
inference(superposition,[status(thm)],[c_439,c_603]) ).
tcf(c_825,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X1)),
inference(demodulation,[status(thm)],[c_744,c_449]) ).
tcf(c_826,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(superposition,[status(thm)],[c_115,c_825]) ).
tcf(c_830,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_96,c_826]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL494+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n005.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 23:33:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 4.11/1.41 % SZS status Started for theBenchmark.p
% 4.11/1.41 % SZS status Theorem for theBenchmark.p
% 4.11/1.41
% 4.11/1.41 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.11/1.41
% 4.11/1.41 % ------ iProver source info
% 4.11/1.41
% 4.11/1.41 % git: date: 2026-07-19 20:42:38 +0200
% 4.11/1.41 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.11/1.41 % git: non_committed_changes: false
% 4.11/1.41
% 4.11/1.41 % ------ Parsing...
% 4.11/1.41 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.11/1.41
% 4.11/1.41 % ------ 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 %
% 4.11/1.41
% 4.11/1.41 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.11/1.41
% 4.11/1.41 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.11/1.41 % ------ Proving...
% 4.11/1.41 % ------ Problem Properties
% 4.11/1.41
% 4.11/1.41 %
% 4.11/1.41 % clauses 13
% 4.11/1.41 % conjectures 0
% 4.11/1.41 % EPR 0
% 4.11/1.41 % Horn 13
% 4.11/1.41 % unary 11
% 4.11/1.41 % binary 1
% 4.11/1.41 % lits 16
% 4.11/1.41 % lits eq 6
% 4.11/1.41 % fd_pure 0
% 4.11/1.41 % fd_pseudo 0
% 4.11/1.41 % fd_cond 0
% 4.11/1.41 % fd_pseudo_cond 1
% 4.11/1.41 % AC symbols 0
% 4.11/1.41
% 4.11/1.41 % ------ Schedule dynamic 5 is on
% 4.11/1.41
% 4.11/1.41 % ------ no conjectures: strip conj schedule
% 4.11/1.41
% 4.11/1.41 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 4.11/1.41
% 4.11/1.41
% 4.11/1.41 % ------
% 4.11/1.41 % Current options:
% 4.11/1.41 % ------
% 4.11/1.41
% 4.11/1.41
% 4.11/1.41 %
% 4.11/1.41
% 4.11/1.41 % ------ Proving...
% 4.11/1.41 %
% 4.11/1.41
% 4.11/1.41 % SZS status Theorem for theBenchmark.p
% 4.11/1.41
% 4.11/1.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.11/1.41
% 4.11/1.41
%------------------------------------------------------------------------------