%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU230+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 02:56:15 PM UTC 2026
% Result : Theorem 2.37s 1.32s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 16 unt; 0 def)
% Number of atoms : 148 ( 61 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 187 ( 70 ~; 73 |; 40 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 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 : 7 ( 7 usr; 1 con; 0-3 aty)
% Number of variables : 75 ( 0 sgn 68 !; 7 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f26,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f27,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f143,conjecture,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f144,negated_conjecture,
~ ! [X0] : in(X0,succ(X0)),
inference(negated_conjecture,[status(cth)],[f143]) ).
fof(f233,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f366,plain,
? [X0] : ~ in(X0,succ(X0)),
inference(ennf_transformation,[],[f144]) ).
fof(f546,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f547,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f546]) ).
fof(f548,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(rectify,[],[f547]) ).
fof(f549,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ( ( in(sK29(X0,X1,X2),X2)
| sK29(X0,X1,X2) = X1
| sK29(X0,X1,X2) = X0 )
& ( ~ in(sK29(X0,X1,X2),X2)
| ( sK29(X0,X1,X2) != X1
& sK29(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X3,sK29(X0,X1,X2))],[f548]) ).
fof(f550,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f551,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f550]) ).
fof(f552,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f551]) ).
fof(f553,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK30(X0,X1,X2),X2)
| in(sK30(X0,X1,X2),X1)
| in(sK30(X0,X1,X2),X0) )
& ( ~ in(sK30(X0,X1,X2),X2)
| ( ~ in(sK30(X0,X1,X2),X1)
& ~ in(sK30(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(X3,sK30(X0,X1,X2))],[f552]) ).
fof(f621,plain,
~ in(sK75,succ(sK75)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(X0,sK75)],[f366]) ).
fof(f737,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f769,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f549]) ).
fof(f774,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f553]) ).
fof(f968,plain,
~ in(sK75,succ(sK75)),
inference(cnf_transformation,[],[f621]) ).
fof(f1110,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f233]) ).
fof(f1147,plain,
! [X0] : succ(X0) = set_union2(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f737,f1110]) ).
fof(f1241,plain,
~ in(sK75,set_union2(sK75,unordered_pair(sK75,sK75))),
inference(definition_unfolding,[],[f968,f1147]) ).
fof(f1332,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f769]) ).
fof(f1333,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f1332]) ).
fof(f1338,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f774]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f1333]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1338]) ).
tcf(c_341,negated_conjecture,
~ in(sK75,set_union2(sK75,unordered_pair(sK75,sK75))),
inference(cnf_transformation,[],[f1241]) ).
tcf(c_617,plain,
~ in(sK75,unordered_pair(sK75,sK75)),
inference(superposition,[status(thm)],[c_151,c_341]) ).
tcf(c_883,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_617,c_144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU230+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n017.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 : Thu Sep 24 13:14:01 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.15/0.43
% 0.15/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.43
% 0.15/0.43 % Detected problem language: tptp
% 0.15/0.44 % Proving...
% 2.37/1.32 % SZS status Started for theBenchmark.p
% 2.37/1.32 % SZS status Theorem for theBenchmark.p
% 2.37/1.32
% 2.37/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.37/1.32
% 2.37/1.32 % ------ iProver source info
% 2.37/1.32
% 2.37/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 2.37/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.37/1.32 % git: non_committed_changes: false
% 2.37/1.32
% 2.37/1.32 % ------ Parsing...
% 2.37/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.37/1.32 % ------ Proving...
% 2.37/1.32 % ------ Problem Properties
% 2.37/1.32
% 2.37/1.32 %
% 2.37/1.32 % clauses 468
% 2.37/1.32 % conjectures 1
% 2.37/1.32 % EPR 55
% 2.37/1.32 % Horn 382
% 2.37/1.32 % unary 80
% 2.37/1.32 % binary 122
% 2.37/1.32 % lits 1372
% 2.37/1.32 % lits eq 247
% 2.37/1.32 % fd_pure 0
% 2.37/1.32 % fd_pseudo 0
% 2.37/1.32 % fd_cond 14
% 2.37/1.32 % fd_pseudo_cond 92
% 2.37/1.32 % AC symbols 0
% 2.37/1.32
% 2.37/1.32 % ------ Input Options Time Limit: Unbounded
% 2.37/1.32
% 2.37/1.32
% 2.37/1.32 % ------
% 2.37/1.32 % Current options:
% 2.37/1.32 % ------
% 2.37/1.32
% 2.37/1.32
% 2.37/1.32 %
% 2.37/1.32
% 2.37/1.32 % ------ Proving...
% 2.37/1.32 %
% 2.37/1.32
% 2.37/1.32 % SZS status Theorem for theBenchmark.p
% 2.37/1.32
% 2.37/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.37/1.32
% 2.37/1.32
%------------------------------------------------------------------------------