%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL459+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 : n020.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 2.08s 1.28s
% Output : CNFRefutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 19 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 32 ~; 27 |; 2 &)
% ( 4 <=>; 6 =>; 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 : 6 ( 5 usr; 5 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 45 !; 1 ?; 17 :)
% 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(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(f53,conjecture,
kn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f54,negated_conjecture,
~ kn1,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ kn1,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
=> kn1 ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f63,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f67,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f71,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(f74,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f75,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f74]) ).
fof(f79,plain,
( ~ implies_2
| ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f67]) ).
fof(f83,plain,
( ~ and_3
| ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(ennf_transformation,[],[f63]) ).
fof(f90,plain,
( ? [X0] : ~ is_a_theorem(implies(X0,and(X0,X0)))
| kn1 ),
inference(ennf_transformation,[],[f56]) ).
fof(f94,plain,
( ~ is_a_theorem(implies(sK0,and(sK0,sK0)))
| kn1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f90]) ).
fof(f95,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f99,plain,
! [X0,X1] :
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f79]) ).
fof(f103,plain,
! [X0,X1] :
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f83]) ).
fof(f110,plain,
( ~ is_a_theorem(implies(sK0,and(sK0,sK0)))
| kn1 ),
inference(cnf_transformation,[],[f94]) ).
fof(f117,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f120,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f124,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f135,plain,
~ kn1,
inference(cnf_transformation,[],[f55]) ).
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,[],[f95]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_64,plain,
( kn1
| ~ is_a_theorem(implies(sK0,and(sK0,sK0))) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_71,plain,
modus_ponens,
inference(cnf_transformation,[],[f117]) ).
tcf(c_74,plain,
implies_2,
inference(cnf_transformation,[],[f120]) ).
tcf(c_78,plain,
and_3,
inference(cnf_transformation,[],[f124]) ).
tcf(c_89,negated_conjecture,
~ kn1,
inference(cnf_transformation,[],[f135]) ).
tcf(c_107,plain,
~ is_a_theorem(implies(sK0,and(sK0,sK0))),
inference(global_subsumption_just,[status(thm)],[c_64,c_89,c_64]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(global_subsumption_just,[status(thm)],[c_57,c_78,c_57]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(global_subsumption_just,[status(thm)],[c_53,c_74,c_53]) ).
tcf(c_142,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_71,c_49]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_142]) ).
tcf(c_550,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_136,c_143]) ).
tcf(c_946,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_127,c_550]) ).
tcf(c_955,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_107,c_946]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL459+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n020.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 23:28:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.08/1.28 % SZS status Started for theBenchmark.p
% 2.08/1.28 % SZS status Theorem for theBenchmark.p
% 2.08/1.28
% 2.08/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.08/1.28
% 2.08/1.28 % ------ iProver source info
% 2.08/1.28
% 2.08/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.08/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.08/1.28 % git: non_committed_changes: false
% 2.08/1.28
% 2.08/1.28 % ------ Parsing...
% 2.08/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.08/1.28
% 2.08/1.28 % ------ Preprocessing... sup_sim: 2 sf_s rm: 20 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.08/1.28
% 2.08/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.08/1.28
% 2.08/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.08/1.28 % ------ Proving...
% 2.08/1.28 % ------ Problem Properties
% 2.08/1.28
% 2.08/1.28 %
% 2.08/1.28 % clauses 19
% 2.08/1.28 % conjectures 0
% 2.08/1.28 % EPR 0
% 2.08/1.28 % Horn 19
% 2.08/1.28 % unary 17
% 2.08/1.28 % binary 1
% 2.08/1.28 % lits 22
% 2.08/1.28 % lits eq 4
% 2.08/1.28 % fd_pure 0
% 2.08/1.28 % fd_pseudo 0
% 2.08/1.28 % fd_cond 0
% 2.08/1.28 % fd_pseudo_cond 1
% 2.08/1.28 % AC symbols 0
% 2.08/1.28
% 2.08/1.28 % ------ Schedule dynamic 5 is on
% 2.08/1.28
% 2.08/1.28 % ------ no conjectures: strip conj schedule
% 2.08/1.28
% 2.08/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.08/1.28
% 2.08/1.28
% 2.08/1.28 % ------
% 2.08/1.28 % Current options:
% 2.08/1.28 % ------
% 2.08/1.28
% 2.08/1.28
% 2.08/1.28 %
% 2.08/1.28
% 2.08/1.28 % ------ Proving...
% 2.08/1.28 %
% 2.08/1.28
% 2.08/1.28 % SZS status Theorem for theBenchmark.p
% 2.08/1.28
% 2.08/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.08/1.28
% 2.08/1.28
%------------------------------------------------------------------------------