%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL456+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 : n017.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 02:06:42 PM UTC 2026
% Result : Theorem 2.64s 1.07s
% Output : CNFRefutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 61 ( 34 unt; 0 def)
% Number of atoms : 88 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 51 ( 24 ~; 19 |; 0 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 72 !; 2 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
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(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
fof(f50,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f51,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
fof(f53,conjecture,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
fof(f54,negated_conjecture,
~ r3,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ r3,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
=> r3 ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f69,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f75,plain,
( ~ modus_tollens
| ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f69]) ).
fof(f88,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| r3 ),
inference(ennf_transformation,[],[f56]) ).
fof(f89,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f90,plain,
( ~ op_and
| ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f28]) ).
fof(f91,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f92,plain,
( ~ op_implies_or
| ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f94,plain,
( ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))
| r3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f88]) ).
fof(f97,plain,
! [X0,X1] :
( ~ modus_tollens
| is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f75]) ).
fof(f110,plain,
( ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))
| r3 ),
inference(cnf_transformation,[],[f94]) ).
fof(f111,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f89]) ).
fof(f112,plain,
! [X0,X1] :
( ~ op_and
| and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f90]) ).
fof(f113,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f91]) ).
fof(f114,plain,
! [X0,X1] :
( ~ op_implies_or
| implies(X0,X1) = or(not(X0),X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f116,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f117,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f120,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f134,plain,
op_implies_or,
inference(cnf_transformation,[],[f50]) ).
fof(f135,plain,
op_and,
inference(cnf_transformation,[],[f51]) ).
fof(f137,plain,
~ r3,
inference(cnf_transformation,[],[f55]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_64,plain,
( r3
| ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( not(and(not(X0),not(X1))) = or(X0,X1) )
| ~ op_or ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( not(or(not(X0),not(X1))) = and(X0,X1) )
| ~ op_and ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ( or(not(X0),X1) = implies(X0,X1) )
| ~ op_implies_or ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_70,plain,
op_or,
inference(cnf_transformation,[],[f116]) ).
tcf(c_71,plain,
op_implies_and,
inference(cnf_transformation,[],[f117]) ).
tcf(c_74,plain,
modus_tollens,
inference(cnf_transformation,[],[f120]) ).
tcf(c_88,plain,
op_implies_or,
inference(cnf_transformation,[],[f134]) ).
tcf(c_89,plain,
op_and,
inference(cnf_transformation,[],[f135]) ).
tcf(c_91,negated_conjecture,
~ r3,
inference(cnf_transformation,[],[f137]) ).
tcf(c_144,plain,
~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))),
inference(global_subsumption_just,[status(thm)],[c_64,c_91,c_64]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] : or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_68,c_88,c_68]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_67,c_71,c_67]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_74,c_51]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i] : not(or(not(X0),not(X1))) = and(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_66,c_89,c_66]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] : not(implies(X0,not(X1))) = and(X0,X1),
inference(demodulation,[status(thm)],[c_208,c_154]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_211,c_154]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(not(X0),X1),implies(X1,X0))),
inference(demodulation,[status(thm)],[c_176,c_215]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_65,c_70,c_65]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_227,c_165]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i,X2: $i] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_165,c_230]) ).
tcf(c_605,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(not(X0),not(X1)),or(X1,X0))),
inference(superposition,[status(thm)],[c_230,c_219]) ).
tcf(c_3566,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(demodulation,[status(thm)],[c_605,c_230,c_231]) ).
tcf(c_3574,plain,
$false,
inference(superposition,[status(thm)],[c_3566,c_144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL456+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 23:22:15 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 2.64/1.07 % SZS status Started for theBenchmark.p
% 2.64/1.07 % SZS status Theorem for theBenchmark.p
% 2.64/1.07
% 2.64/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.64/1.07
% 2.64/1.07 % ------ iProver source info
% 2.64/1.07
% 2.64/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 2.64/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.64/1.07 % git: non_committed_changes: false
% 2.64/1.07
% 2.64/1.07 % ------ Parsing...
% 2.64/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.64/1.07 % ------ Proving...
% 2.64/1.07 % ------ Problem Properties
% 2.64/1.07
% 2.64/1.07 %
% 2.64/1.07 % clauses 43
% 2.64/1.07 % conjectures 1
% 2.64/1.07 % EPR 22
% 2.64/1.07 % Horn 43
% 2.64/1.07 % unary 22
% 2.64/1.07 % binary 19
% 2.64/1.07 % lits 67
% 2.64/1.07 % lits eq 6
% 2.64/1.07 % fd_pure 0
% 2.64/1.07 % fd_pseudo 0
% 2.64/1.07 % fd_cond 0
% 2.64/1.07 % fd_pseudo_cond 1
% 2.64/1.07 % AC symbols 0
% 2.64/1.07
% 2.64/1.07 % ------ Input Options Time Limit: Unbounded
% 2.64/1.07
% 2.64/1.07
% 2.64/1.07 % ------
% 2.64/1.07 % Current options:
% 2.64/1.07 % ------
% 2.64/1.07
% 2.64/1.07
% 2.64/1.07 %
% 2.64/1.07
% 2.64/1.07 % ------ Proving...
% 2.64/1.07 %
% 2.64/1.07
% 2.64/1.07 % ------ Proving...
% 2.64/1.07 %
% 2.64/1.07
% 2.64/1.07 % ------ Proving...
% 2.64/1.07 %
% 2.64/1.07
% 2.64/1.07 % SZS status Theorem for theBenchmark.p
% 2.64/1.07
% 2.64/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.64/1.07
%------------------------------------------------------------------------------