%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU160+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 02:55:40 PM UTC 2026
% Result : Theorem 4.32s 1.27s
% Output : CNFRefutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 93 ( 56 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 34 ~; 41 |; 10 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 1 sgn 26 !; 6 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f44,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f49,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f62,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f70,conjecture,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f71,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f70]) ).
fof(f82,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f95,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f49]) ).
fof(f124,plain,
? [X0,X1] :
( subset(X0,singleton(X1))
<~> ( X0 = singleton(X1)
| X0 = empty_set ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f179,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f180,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f179]) ).
fof(f191,plain,
? [X0,X1] :
( ( subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ~ subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) ) ),
inference(nnf_transformation,[],[f124]) ).
fof(f192,plain,
? [X0,X1] :
( ( subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ~ subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) ) ),
inference(flattening,[],[f191]) ).
fof(f193,plain,
( ( subset(sK19,singleton(sK20))
| sK19 = singleton(sK20)
| empty_set = sK19 )
& ( ~ subset(sK19,singleton(sK20))
| ( sK19 != singleton(sK20)
& empty_set != sK19 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20]),skolemize(X0,sK19),skolemize(X1,sK20)],[f192]) ).
fof(f276,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f180]) ).
fof(f285,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f95]) ).
fof(f299,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f62]) ).
fof(f312,plain,
( subset(sK19,singleton(sK20))
| sK19 = singleton(sK20)
| empty_set = sK19 ),
inference(cnf_transformation,[],[f193]) ).
fof(f313,plain,
( ~ subset(sK19,singleton(sK20))
| sK19 != singleton(sK20) ),
inference(cnf_transformation,[],[f193]) ).
fof(f314,plain,
( ~ subset(sK19,singleton(sK20))
| empty_set != sK19 ),
inference(cnf_transformation,[],[f193]) ).
fof(f328,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f82]) ).
fof(f368,plain,
! [X0,X1] :
( ~ subset(X0,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = X0
| empty_set = X0 ),
inference(definition_unfolding,[],[f276,f328,f328]) ).
fof(f382,plain,
( ~ subset(sK19,unordered_pair(sK20,sK20))
| empty_set != sK19 ),
inference(definition_unfolding,[],[f314,f328]) ).
fof(f383,plain,
( ~ subset(sK19,unordered_pair(sK20,sK20))
| sK19 != unordered_pair(sK20,sK20) ),
inference(definition_unfolding,[],[f313,f328,f328]) ).
fof(f384,plain,
( subset(sK19,unordered_pair(sK20,sK20))
| sK19 = unordered_pair(sK20,sK20)
| empty_set = sK19 ),
inference(definition_unfolding,[],[f312,f328,f328]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( unordered_pair(X1,X1) = X0 )
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f368]) ).
tcf(c_136,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f285]) ).
tcf(c_150,plain,
! [X0: $i] : subset(empty_set,X0),
inference(cnf_transformation,[],[f299]) ).
tcf(c_163,negated_conjecture,
( ~ subset(sK19,unordered_pair(sK20,sK20))
| ( empty_set != sK19 ) ),
inference(cnf_transformation,[],[f382]) ).
tcf(c_164,negated_conjecture,
( ~ subset(sK19,unordered_pair(sK20,sK20))
| ( unordered_pair(sK20,sK20) != sK19 ) ),
inference(cnf_transformation,[],[f383]) ).
tcf(c_165,negated_conjecture,
( subset(sK19,unordered_pair(sK20,sK20))
| ( empty_set = sK19 )
| ( unordered_pair(sK20,sK20) = sK19 ) ),
inference(cnf_transformation,[],[f384]) ).
tcf(c_390,plain,
( ( empty_set = sK19 )
| ( unordered_pair(sK20,sK20) = sK19 ) ),
inference(superposition,[status(thm)],[c_165,c_129]) ).
tcf(c_581,negated_conjecture,
~ subset(sK19,unordered_pair(sK20,sK20)),
inference(global_subsumption_just,[status(thm)],[c_163,c_163,c_164,c_390]) ).
tcf(c_752,plain,
( ( unordered_pair(sK20,sK20) = sK19 )
| ( empty_set = sK19 ) ),
inference(global_subsumption_just,[status(thm)],[c_165,c_165,c_581]) ).
tcf(c_753,negated_conjecture,
( ( empty_set = sK19 )
| ( unordered_pair(sK20,sK20) = sK19 ) ),
inference(renaming,[status(thm)],[c_752]) ).
tcf(c_774,plain,
( ( empty_set = sK19 )
| ~ subset(sK19,sK19) ),
inference(superposition,[status(thm)],[c_753,c_581]) ).
tcf(c_1456,plain,
empty_set = sK19,
inference(forward_subsumption_resolution,[status(thm)],[c_774,c_136]) ).
tcf(c_1457,plain,
~ subset(empty_set,unordered_pair(sK20,sK20)),
inference(superposition,[status(thm)],[c_1456,c_581]) ).
tcf(c_2815,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1457,c_150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU160+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 13:00:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 4.32/1.27 % SZS status Started for theBenchmark.p
% 4.32/1.27 % SZS status Theorem for theBenchmark.p
% 4.32/1.27
% 4.32/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.32/1.27
% 4.32/1.27 % ------ iProver source info
% 4.32/1.27
% 4.32/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 4.32/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.32/1.27 % git: non_committed_changes: false
% 4.32/1.27
% 4.32/1.27 % ------ Parsing...
% 4.32/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.32/1.27 % ------ Proving...
% 4.32/1.27 % ------ Problem Properties
% 4.32/1.27
% 4.32/1.27 %
% 4.32/1.27 % clauses 139
% 4.32/1.27 % conjectures 3
% 4.32/1.27 % EPR 23
% 4.32/1.27 % Horn 110
% 4.32/1.27 % unary 31
% 4.32/1.27 % binary 62
% 4.32/1.27 % lits 300
% 4.32/1.27 % lits eq 86
% 4.32/1.27 % fd_pure 0
% 4.32/1.27 % fd_pseudo 0
% 4.32/1.27 % fd_cond 3
% 4.32/1.27 % fd_pseudo_cond 35
% 4.32/1.27 % AC symbols 0
% 4.32/1.27
% 4.32/1.27 % ------ Input Options Time Limit: Unbounded
% 4.32/1.27
% 4.32/1.27
% 4.32/1.27 % ------
% 4.32/1.27 % Current options:
% 4.32/1.27 % ------
% 4.32/1.27
% 4.32/1.27
% 4.32/1.27 %
% 4.32/1.27
% 4.32/1.27 % ------ Proving...
% 4.32/1.27 %
% 4.32/1.27
% 4.32/1.27 % SZS status Theorem for theBenchmark.p
% 4.32/1.27
% 4.32/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.32/1.27
% 4.32/1.27
%------------------------------------------------------------------------------