%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU142+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 : n026.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 02:55:34 PM UTC 2026
% Result : Theorem 5.80s 2.21s
% Output : CNFRefutation 5.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 15 unt; 0 def)
% Number of atoms : 186 ( 109 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 226 ( 88 ~; 99 |; 34 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 90 ( 1 sgn 84 !; 6 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f9,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(f31,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f57,conjecture,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f58,negated_conjecture,
~ ! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(negated_conjecture,[status(cth)],[f57]) ).
fof(f68,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f31]) ).
fof(f96,plain,
? [X0] : singleton(X0) != unordered_pair(X0,X0),
inference(ennf_transformation,[],[f58]) ).
fof(f102,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f103,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f105,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f105]) ).
fof(f110,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,[],[f9]) ).
fof(f111,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,[],[f110]) ).
fof(f112,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,[],[f111]) ).
fof(f113,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(sK2(X0,X1,X2),X2)
| sK2(X0,X1,X2) = X1
| sK2(X0,X1,X2) = X0 )
& ( ~ in(sK2(X0,X1,X2),X2)
| ( sK2(X0,X1,X2) != X1
& sK2(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f112]) ).
fof(f138,plain,
singleton(sK12) != unordered_pair(sK12,sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f96]) ).
fof(f147,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f103]) ).
fof(f148,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f106]) ).
fof(f149,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f157,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X2)
| sK2(X0,X1,X2) = X1
| sK2(X0,X1,X2) = X0
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f113]) ).
fof(f158,plain,
! [X2,X0,X1] :
( ~ in(sK2(X0,X1,X2),X2)
| sK2(X0,X1,X2) != X1
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f113]) ).
fof(f194,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f68]) ).
fof(f225,plain,
singleton(sK12) != unordered_pair(sK12,sK12),
inference(cnf_transformation,[],[f138]) ).
fof(f252,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f149]) ).
fof(f253,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f252]) ).
fof(f254,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f148]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_59,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f253]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f254]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X0,X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ( sK2(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| ( unordered_pair(X0,X1) = X2 )
| ( sK2(X0,X1,X2) = X1 )
| ( sK2(X0,X1,X2) = X0 ) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_103,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f194]) ).
tcf(c_133,negated_conjecture,
unordered_pair(sK12,sK12) != singleton(sK12),
inference(cnf_transformation,[],[f225]) ).
tcf(c_1417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2772,plain,
( ( unordered_pair(sK12,sK12) = singleton(sK12) )
| ~ in(sK2(sK12,sK12,singleton(sK12)),singleton(sK12))
| ( sK2(sK12,sK12,singleton(sK12)) != sK12 ) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_2778,plain,
! [X0: $i] :
( ( singleton(sK12) = X0 )
| ~ subset(X0,singleton(sK12))
| ~ subset(singleton(sK12),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_2841,plain,
! [X0: $i,X1: $i] :
( in(sK2(sK12,sK12,singleton(sK12)),singleton(sK12))
| ~ in(X0,X1)
| ( singleton(sK12) != X1 )
| ( sK2(sK12,sK12,singleton(sK12)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1417]) ).
tcf(c_3026,plain,
( ( singleton(sK12) = singleton(sK12) )
| ~ subset(singleton(sK12),singleton(sK12)) ),
inference(instantiation,[status(thm)],[c_2778]) ).
tcf(c_3407,plain,
! [X0: $i] :
( in(sK2(sK12,sK12,singleton(sK12)),singleton(sK12))
| ~ in(X0,singleton(sK12))
| ( singleton(sK12) != singleton(sK12) )
| ( sK2(sK12,sK12,singleton(sK12)) != X0 ) ),
inference(instantiation,[status(thm)],[c_2841]) ).
tcf(c_3725,plain,
subset(singleton(sK12),singleton(sK12)),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_5183,plain,
! [X0: $i] :
( ( sK2(sK12,sK12,singleton(sK12)) = X0 )
| ~ in(sK2(sK12,sK12,singleton(sK12)),singleton(X0)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_5192,plain,
( in(sK2(sK12,sK12,singleton(sK12)),singleton(sK12))
| ~ in(sK12,singleton(sK12))
| ( singleton(sK12) != singleton(sK12) )
| ( sK2(sK12,sK12,singleton(sK12)) != sK12 ) ),
inference(instantiation,[status(thm)],[c_3407]) ).
tcf(c_9167,plain,
in(sK12,singleton(sK12)),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_13071,plain,
( ( sK2(sK12,sK12,singleton(sK12)) = sK12 )
| ~ in(sK2(sK12,sK12,singleton(sK12)),singleton(sK12)) ),
inference(instantiation,[status(thm)],[c_5183]) ).
tcf(c_13096,plain,
( in(sK2(sK12,sK12,singleton(sK12)),singleton(sK12))
| ( unordered_pair(sK12,sK12) = singleton(sK12) )
| ( sK2(sK12,sK12,singleton(sK12)) = sK12 ) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_13304,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13096,c_13071,c_9167,c_5192,c_3725,c_3026,c_2772,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU142+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:58:25 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...
% 5.80/2.21 % SZS status Started for theBenchmark.p
% 5.80/2.21 % SZS status Theorem for theBenchmark.p
% 5.80/2.21
% 5.80/2.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.80/2.21
% 5.80/2.21 % ------ iProver source info
% 5.80/2.21
% 5.80/2.21 % git: date: 2026-07-19 20:42:38 +0200
% 5.80/2.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.80/2.21 % git: non_committed_changes: false
% 5.80/2.21
% 5.80/2.21 % ------ Parsing...
% 5.80/2.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.80/2.21
% 5.80/2.21 % ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 5.80/2.21
% 5.80/2.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.80/2.21
% 5.80/2.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.80/2.21 % ------ Proving...
% 5.80/2.21 % ------ Problem Properties
% 5.80/2.21
% 5.80/2.21 %
% 5.80/2.21 % clauses 84
% 5.80/2.21 % conjectures 1
% 5.80/2.21 % EPR 21
% 5.80/2.21 % Horn 66
% 5.80/2.21 % unary 23
% 5.80/2.21 % binary 32
% 5.80/2.21 % lits 178
% 5.80/2.21 % lits eq 50
% 5.80/2.21 % fd_pure 0
% 5.80/2.21 % fd_pseudo 0
% 5.80/2.21 % fd_cond 3
% 5.80/2.21 % fd_pseudo_cond 19
% 5.80/2.21 % AC symbols 0
% 5.80/2.21
% 5.80/2.21 % ------ Input Options Time Limit: Unbounded
% 5.80/2.21
% 5.80/2.21
% 5.80/2.21 % ------
% 5.80/2.21 % Current options:
% 5.80/2.21 % ------
% 5.80/2.21
% 5.80/2.21
% 5.80/2.21 %
% 5.80/2.21
% 5.80/2.21 % ------ Proving...
% 5.80/2.21 %
% 5.80/2.21
% 5.80/2.21 % SZS status Theorem for theBenchmark.p
% 5.80/2.21
% 5.80/2.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.80/2.21
% 5.80/2.21
%------------------------------------------------------------------------------