%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL499+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 : n018.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 02:06:47 PM UTC 2026
% Result : Theorem 2.64s 1.18s
% Output : CNFRefutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 32 unt; 0 def)
% Number of atoms : 112 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 85 ( 38 ~; 33 |; 2 &)
% ( 4 <=>; 8 =>; 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 : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 67 !; 1 ?; 31 :)
% 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(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(f22,axiom,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
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(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_and) ).
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(f33,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(f36,axiom,
r1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(f45,conjecture,
kn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f46,negated_conjecture,
~ kn1,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ kn1,
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(f52,plain,
( r1
=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f53,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
=> kn1 ),
inference(unused_predicate_definition_removal,[],[f16]) ).
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] : ~ is_a_theorem(implies(X0,and(X0,X0)))
| kn1 ),
inference(ennf_transformation,[],[f53]) ).
fof(f60,plain,
( ~ r1
| ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(ennf_transformation,[],[f52]) ).
fof(f62,plain,
( ~ r3
| ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(ennf_transformation,[],[f50]) ).
fof(f66,plain,
( ~ op_and
| ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f28]) ).
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,and(sK0,sK0)))
| kn1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[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,and(sK0,sK0)))
| kn1 ),
inference(cnf_transformation,[],[f70]) ).
fof(f74,plain,
! [X0] :
( ~ r1
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f76,plain,
! [X0,X1] :
( ~ r3
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f80,plain,
! [X0,X1] :
( ~ op_and
| and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f66]) ).
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(f85,plain,
op_and,
inference(cnf_transformation,[],[f33]) ).
fof(f87,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f88,plain,
r1,
inference(cnf_transformation,[],[f36]) ).
fof(f90,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f97,plain,
~ kn1,
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,
( kn1
| ~ is_a_theorem(implies(sK0,and(sK0,sK0))) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_52,plain,
! [X0: $i] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[],[f74]) ).
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_58,plain,
! [X0: $i,X1: $i] :
( ( not(or(not(X0),not(X1))) = and(X0,X1) )
| ~ op_and ),
inference(cnf_transformation,[],[f80]) ).
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_63,plain,
op_and,
inference(cnf_transformation,[],[f85]) ).
tcf(c_65,plain,
modus_ponens,
inference(cnf_transformation,[],[f87]) ).
tcf(c_66,plain,
r1,
inference(cnf_transformation,[],[f88]) ).
tcf(c_68,plain,
r3,
inference(cnf_transformation,[],[f90]) ).
tcf(c_75,negated_conjecture,
~ kn1,
inference(cnf_transformation,[],[f97]) ).
tcf(c_90,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_52,c_66,c_52]) ).
tcf(c_93,plain,
~ is_a_theorem(implies(sK0,and(sK0,sK0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_75,c_51]) ).
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_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_191,plain,
! [X0: $i,X1: $i] : not(implies(X0,not(X1))) = and(X0,X1),
inference(demodulation,[status(thm)],[c_109,c_98]) ).
tcf(c_402,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,not(X0)),not(X0))),
inference(superposition,[status(thm)],[c_98,c_90]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_191,c_98]) ).
tcf(c_436,plain,
! [X0: $i] : is_a_theorem(or(and(X0,X0),not(X0))),
inference(demodulation,[status(thm)],[c_402,c_435]) ).
tcf(c_587,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_95,c_108]) ).
tcf(c_736,plain,
! [X0: $i] : is_a_theorem(or(not(X0),and(X0,X0))),
inference(superposition,[status(thm)],[c_436,c_587]) ).
tcf(c_821,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
inference(demodulation,[status(thm)],[c_736,c_98]) ).
tcf(c_822,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_93,c_821]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL499+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n018.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 23:36:03 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 2.64/1.18 % SZS status Started for theBenchmark.p
% 2.64/1.18 % SZS status Theorem for theBenchmark.p
% 2.64/1.18
% 2.64/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.64/1.18
% 2.64/1.18 % ------ iProver source info
% 2.64/1.18
% 2.64/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.64/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.64/1.18 % git: non_committed_changes: false
% 2.64/1.18
% 2.64/1.18 % ------ Parsing...
% 2.64/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.64/1.18
% 2.64/1.18 % ------ 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 %
% 2.64/1.18
% 2.64/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.64/1.18
% 2.64/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.64/1.18 % ------ Proving...
% 2.64/1.18 % ------ Problem Properties
% 2.64/1.18
% 2.64/1.18 %
% 2.64/1.18 % clauses 13
% 2.64/1.18 % conjectures 0
% 2.64/1.18 % EPR 0
% 2.64/1.18 % Horn 13
% 2.64/1.18 % unary 11
% 2.64/1.18 % binary 1
% 2.64/1.18 % lits 16
% 2.64/1.18 % lits eq 6
% 2.64/1.18 % fd_pure 0
% 2.64/1.18 % fd_pseudo 0
% 2.64/1.18 % fd_cond 0
% 2.64/1.18 % fd_pseudo_cond 1
% 2.64/1.18 % AC symbols 0
% 2.64/1.18
% 2.64/1.18 % ------ Schedule dynamic 5 is on
% 2.64/1.18
% 2.64/1.18 % ------ no conjectures: strip conj schedule
% 2.64/1.18
% 2.64/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.64/1.18
% 2.64/1.18
% 2.64/1.18 % ------
% 2.64/1.18 % Current options:
% 2.64/1.18 % ------
% 2.64/1.18
% 2.64/1.18
% 2.64/1.18 %
% 2.64/1.18
% 2.64/1.18 % ------ Proving...
% 2.64/1.18 %
% 2.64/1.18
% 2.64/1.18 % SZS status Theorem for theBenchmark.p
% 2.64/1.18
% 2.64/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.64/1.19
% 2.64/1.19
%------------------------------------------------------------------------------