%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN063+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 03:39:03 PM UTC 2026
% Result : Theorem 1.16s 1.28s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 7 unt; 2 def)
% Number of atoms : 197 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 241 ( 88 ~; 102 |; 40 &)
% ( 4 <=>; 4 =>; 0 <=; 3 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 26 ( 0 sgn 22 !; 4 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( ( ( big_p(X0)
=> big_p(b) )
& big_p(a) )
=> big_p(c) )
<=> ! [X1] :
( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel33) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( ( ( big_p(X0)
=> big_p(b) )
& big_p(a) )
=> big_p(c) )
<=> ! [X1] :
( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X0] :
( ( big_p(X0)
& ~ big_p(b) )
| ~ big_p(a)
| big_p(c) )
<~> ! [X1] :
( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( ( big_p(X0)
& ~ big_p(b) )
| ~ big_p(a)
| big_p(c) )
<~> ! [X1] :
( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(flattening,[],[f3]) ).
fof(f8,plain,
( ( ~ sP1
| ! [X0] :
( ( big_p(X0)
& ~ big_p(b) )
| ~ big_p(a)
| big_p(c) ) )
& ( ? [X0] :
( ( ~ big_p(X0)
| big_p(b) )
& big_p(a)
& ~ big_p(c) )
| sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f9,plain,
( ( ~ sP1
| ! [X1] :
( ( big_p(X1)
& ~ big_p(b) )
| ~ big_p(a)
| big_p(c) ) )
& ( ? [X0] :
( ( ~ big_p(X0)
| big_p(b) )
& big_p(a)
& ~ big_p(c) )
| sP1 ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
( ( ~ sP1
| ! [X1] :
( ( big_p(X1)
& ~ big_p(b) )
| ~ big_p(a)
| big_p(c) ) )
& ( ( ( ~ big_p(sK2)
| big_p(b) )
& big_p(a)
& ~ big_p(c) )
| sP1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f9]) ).
fof(f13,plain,
( ( sP1
| ! [X1] :
( sP0
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) )
& ( ~ sP1
| ? [X1] :
( ~ sP0
| ( ~ big_p(c)
& ~ big_p(X1)
& big_p(a) ) ) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f14,plain,
( ( sP1
| ! [X1] :
( sP0
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) )
& ( ~ sP1
| ? [X0] :
( ~ sP0
| ( ~ big_p(c)
& ~ big_p(X0)
& big_p(a) ) ) ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
( ( sP1
| ! [X1] :
( sP0
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) )
& ( ~ sP1
| ~ sP0
| ( ~ big_p(c)
& ~ big_p(sK3)
& big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f14]) ).
fof(f16,plain,
! [X1] :
( ~ sP1
| big_p(X1)
| ~ big_p(a)
| big_p(c) ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
( ~ sP1
| ~ big_p(b)
| ~ big_p(a)
| big_p(c) ),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
( big_p(a)
| sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
( ~ big_p(c)
| sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f25,plain,
( sP1
| sP0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X1] :
( sP1
| big_p(c)
| big_p(X1)
| ~ big_p(a) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
( ~ sP1
| ~ sP0
| ~ big_p(c) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
( ~ sP1
| ~ sP0
| big_p(a) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_49,plain,
( sP1
| ~ big_p(c) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_50,plain,
( sP1
| big_p(a) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_52,plain,
( big_p(c)
| ~ sP1
| ~ big_p(b)
| ~ big_p(a) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_53,plain,
! [X0: $i] :
( big_p(c)
| big_p(X0)
| ~ sP1
| ~ big_p(a) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_58,negated_conjecture,
( big_p(a)
| ~ sP0
| ~ sP1 ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_60,negated_conjecture,
( ~ sP0
| ~ sP1
| ~ big_p(c) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_61,negated_conjecture,
! [X0: $i] :
( sP1
| big_p(c)
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_62,negated_conjecture,
( sP0
| sP1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f5,definition,
( sP0
<=> ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f6,definition,
( sP1
<=> ! [X0] :
( ( big_p(X0)
& ~ big_p(b) )
| ~ big_p(a)
| big_p(c) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f7,plain,
( sP1
<~> ! [X1] :
( sP0
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(definition_folding,[],[f4,f6,f5]) ).
fof(f11,plain,
( ( ~ sP0
| big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ( ( ~ big_p(c)
& big_p(b)
& big_p(a) )
| sP0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f12,plain,
( ( ~ sP0
| big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ( ( ~ big_p(c)
& big_p(b)
& big_p(a) )
| sP0 ) ),
inference(flattening,[],[f11]) ).
fof(f22,plain,
( ~ big_p(c)
| sP0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
( big_p(b)
| sP0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
( big_p(a)
| sP0 ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_54,plain,
( sP0
| big_p(a) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_55,plain,
( sP0
| big_p(b) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_56,plain,
( sP0
| ~ big_p(c) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_63,negated_conjecture,
sP0,
inference(global_subsumption_just,[status(thm)],[c_62,c_62,c_55,c_54,c_56,c_52]) ).
tcf(c_69,plain,
big_p(a),
inference(global_subsumption_just,[status(thm)],[c_50,c_62,c_55,c_54,c_50,c_56,c_58,c_52]) ).
tcf(c_73,plain,
~ big_p(c),
inference(global_subsumption_just,[status(thm)],[c_49,c_49,c_60,c_63]) ).
tcf(c_79,negated_conjecture,
~ big_p(c),
inference(global_subsumption_just,[status(thm)],[c_60,c_73]) ).
tcf(c_83,negated_conjecture,
! [X0: $i] : big_p(X0),
inference(global_subsumption_just,[status(thm)],[c_61,c_62,c_55,c_54,c_56,c_49,c_60,c_61,c_53,c_52,c_69]) ).
tcf(c_85,plain,
! [X0: $i] : big_p(X0),
inference(global_subsumption_just,[status(thm)],[c_53,c_83]) ).
tcf(c_95,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_79,c_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN063+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n005.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 : Fri Sep 25 00:01:02 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
% 0.10/0.42
% 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...
% 1.16/1.28 % SZS status Started for theBenchmark.p
% 1.16/1.28 % SZS status Theorem for theBenchmark.p
% 1.16/1.28
% 1.16/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.16/1.28
% 1.16/1.28 % ------ iProver source info
% 1.16/1.28
% 1.16/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.16/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.16/1.28 % git: non_committed_changes: false
% 1.16/1.28
% 1.16/1.28 % ------ Parsing...
% 1.16/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.16/1.28 %
% 1.16/1.28
% 1.16/1.28 % ------ Preprocessing...%
% 1.16/1.28
% 1.16/1.28 % SZS status Theorem for theBenchmark.p
% 1.16/1.28
% 1.16/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.16/1.28
% 1.16/1.28
%------------------------------------------------------------------------------