%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN056+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 : n009.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 03:39:01 PM UTC 2026
% Result : Theorem 1.06s 1.17s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 49 ( 5 unt; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 190 ( 85 ~; 79 |; 14 &)
% ( 6 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 5 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 : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 74 ( 0 sgn 64 !; 10 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( ? [X0] : big_p(X0)
<=> ? [X1] : big_q(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26_1) ).
fof(f2,axiom,
! [X0,X1] :
( ( big_q(X1)
& big_p(X0) )
=> ( big_r(X0)
<=> big_s(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26_2) ).
fof(f3,conjecture,
( ! [X0] :
( big_p(X0)
=> big_r(X0) )
<=> ! [X1] :
( big_q(X1)
=> big_s(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26) ).
fof(f4,negated_conjecture,
~ ( ! [X0] :
( big_p(X0)
=> big_r(X0) )
<=> ! [X1] :
( big_q(X1)
=> big_s(X1) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( ~ big_q(X1)
| ~ big_p(X0)
| ( big_r(X0)
<=> big_s(X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f6,plain,
! [X0,X1] :
( ~ big_q(X1)
| ~ big_p(X0)
| ( big_r(X0)
<=> big_s(X1) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
( ! [X0] :
( ~ big_p(X0)
| big_r(X0) )
<~> ! [X1] :
( ~ big_q(X1)
| big_s(X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f8,plain,
( ( ! [X0] : ~ big_p(X0)
| ? [X1] : big_q(X1) )
& ( ! [X1] : ~ big_q(X1)
| ? [X0] : big_p(X0) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f9,plain,
( ( ! [X3] : ~ big_p(X3)
| ? [X2] : big_q(X2) )
& ( ! [X1] : ~ big_q(X1)
| ? [X0] : big_p(X0) ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
( ( ! [X3] : ~ big_p(X3)
| big_q(sK1) )
& ( ! [X1] : ~ big_q(X1)
| big_p(sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ~ big_q(X1)
| ~ big_p(X0)
| ( ( ~ big_r(X0)
| big_s(X1) )
& ( ~ big_s(X1)
| big_r(X0) ) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f12,plain,
( ( ! [X0] :
( ~ big_p(X0)
| big_r(X0) )
| ! [X1] :
( ~ big_q(X1)
| big_s(X1) ) )
& ( ? [X0] :
( big_p(X0)
& ~ big_r(X0) )
| ? [X1] :
( big_q(X1)
& ~ big_s(X1) ) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f13,plain,
( ( ! [X3] :
( ~ big_p(X3)
| big_r(X3) )
| ! [X2] :
( ~ big_q(X2)
| big_s(X2) ) )
& ( ? [X1] :
( big_p(X1)
& ~ big_r(X1) )
| ? [X0] :
( big_q(X0)
& ~ big_s(X0) ) ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
( ( ! [X3] :
( ~ big_p(X3)
| big_r(X3) )
| ! [X2] :
( ~ big_q(X2)
| big_s(X2) ) )
& ( ( big_p(sK3)
& ~ big_r(sK3) )
| ( big_q(sK2)
& ~ big_s(sK2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f13]) ).
fof(f15,plain,
! [X3] :
( ~ big_p(X3)
| big_q(sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
! [X1] :
( ~ big_q(X1)
| big_p(sK0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
! [X0,X1] :
( ~ big_q(X1)
| ~ big_p(X0)
| ~ big_r(X0)
| big_s(X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0,X1] :
( ~ big_q(X1)
| ~ big_p(X0)
| ~ big_s(X1)
| big_r(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f19,plain,
! [X2,X3] :
( ~ big_p(X3)
| big_r(X3)
| ~ big_q(X2)
| big_s(X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f20,plain,
( big_p(sK3)
| big_q(sK2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
( ~ big_r(sK3)
| big_q(sK2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
( big_p(sK3)
| ~ big_s(sK2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
( ~ big_r(sK3)
| ~ big_s(sK2) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_49,plain,
! [X0: $i] :
( big_p(sK0)
| ~ big_q(X0) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_50,plain,
! [X0: $i] :
( big_q(sK1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( big_r(X0)
| ~ big_s(X1)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( big_s(X1)
| ~ big_r(X0)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_53,negated_conjecture,
( ~ big_s(sK2)
| ~ big_r(sK3) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_54,negated_conjecture,
( big_p(sK3)
| ~ big_s(sK2) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_55,negated_conjecture,
( big_q(sK2)
| ~ big_r(sK3) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_56,negated_conjecture,
( big_q(sK2)
| big_p(sK3) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_57,negated_conjecture,
! [X0: $i,X1: $i] :
( big_s(X1)
| big_r(X0)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( big_s(X1)
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_57,c_52]) ).
tcf(c_64,negated_conjecture,
! [X0: $i,X1: $i] :
( big_s(X1)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(renaming,[status(thm)],[c_63]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( big_s(X1)
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_64]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( big_s(X1)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(renaming,[status(thm)],[c_66]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( big_r(X0)
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_57,c_52,c_51]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( big_r(X0)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(renaming,[status(thm)],[c_68]) ).
tcf(c_107,plain,
! [X0: $i] :
( big_q(sK2)
| ~ big_p(sK3)
| ~ big_q(X0) ),
inference(resolution,[status(thm)],[c_69,c_55]) ).
tcf(c_108,plain,
! [X0: $i] :
( big_q(sK2)
| ~ big_q(X0) ),
inference(global_subsumption_just,[status(thm)],[c_107,c_56,c_107]) ).
tcf(c_116,plain,
! [X0: $i] :
( ~ big_s(sK2)
| ~ big_p(sK3)
| ~ big_q(X0) ),
inference(resolution,[status(thm)],[c_69,c_53]) ).
tcf(c_118,plain,
! [X0: $i] :
( ~ big_s(sK2)
| ~ big_q(X0) ),
inference(global_subsumption_just,[status(thm)],[c_116,c_54,c_116]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] :
( ~ big_q(sK2)
| ~ big_q(X1)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[c_67,c_118]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( ~ big_q(X1)
| ~ big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_131,c_108]) ).
tcf(c_153,plain,
! [X0: $i] : ~ big_q(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_139]) ).
tcf(c_155,plain,
! [X0: $i] : ~ big_p(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_50,c_139]) ).
tcf(c_156,plain,
~ big_q(sK2),
inference(instantiation,[status(thm)],[c_153]) ).
tcf(c_160,plain,
big_q(sK2),
inference(resolution,[status(thm)],[c_155,c_56]) ).
tcf(c_161,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_160,c_156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN056+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n009.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 : Thu Sep 24 23:58:14 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.06/1.17 % SZS status Started for theBenchmark.p
% 1.06/1.17 % SZS status Theorem for theBenchmark.p
% 1.06/1.17
% 1.06/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.06/1.17
% 1.06/1.17 % ------ iProver source info
% 1.06/1.17
% 1.06/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 1.06/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.06/1.17 % git: non_committed_changes: false
% 1.06/1.17
% 1.06/1.17 % ------ Parsing...
% 1.06/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.06/1.17 %
% 1.06/1.17
% 1.06/1.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s%
% 1.06/1.17
% 1.06/1.17 % SZS status Theorem for theBenchmark.p
% 1.06/1.17
% 1.06/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.06/1.17
% 1.06/1.17
%------------------------------------------------------------------------------