%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU187+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 : n018.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 02:55:48 PM UTC 2026
% Result : Theorem 3.61s 1.08s
% Output : CNFRefutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 14 unt; 0 def)
% Number of atoms : 160 ( 47 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 195 ( 82 ~; 78 |; 24 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 88 !; 18 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f19,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f23,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f25,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f64,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f151,conjecture,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f152,negated_conjecture,
~ ( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(negated_conjecture,[status(cth)],[f151]) ).
fof(f156,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f187,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f188,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f286,plain,
( empty_set != relation_rng(empty_set)
| empty_set != relation_dom(empty_set) ),
inference(ennf_transformation,[],[f152]) ).
fof(f312,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f313,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f312]) ).
fof(f314,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK7(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f313]) ).
fof(f337,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(nnf_transformation,[],[f187]) ).
fof(f338,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X5,X7),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X2,X4),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(rectify,[],[f337]) ).
fof(f339,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK20(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK18(X0,X1),X1)
| in(ordered_pair(sK18(X0,X1),sK19(X0,X1)),X0) )
& ( ~ in(sK18(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK18(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20]),skolemize(X2,sK18(X0,X1)),skolemize(X4,sK19(X0,X1)),skolemize(X7,sK20(X0,X5))],[f338]) ).
fof(f347,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f188]) ).
fof(f348,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X7,X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X4,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f347]) ).
fof(f349,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK27(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK25(X0,X1),X1)
| in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0) )
& ( ~ in(sK25(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK25(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27]),skolemize(X2,sK25(X0,X1)),skolemize(X4,sK26(X0,X1)),skolemize(X7,sK27(X0,X5))],[f348]) ).
fof(f418,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f419,plain,
! [X0] :
( in(sK7(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f314]) ).
fof(f457,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK20(X0,X5)),X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f474,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK27(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f479,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f25]) ).
fof(f516,plain,
relation(empty_set),
inference(cnf_transformation,[],[f64]) ).
fof(f637,plain,
( empty_set != relation_rng(empty_set)
| empty_set != relation_dom(empty_set) ),
inference(cnf_transformation,[],[f286]) ).
fof(f642,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f156]) ).
fof(f659,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f479,f642]) ).
fof(f680,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,sK20(X0,X5)),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f457,f659]) ).
fof(f684,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(sK27(X0,X5),X5),unordered_pair(sK27(X0,X5),sK27(X0,X5))),X0) ),
inference(definition_unfolding,[],[f474,f659]) ).
fof(f754,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f418]) ).
fof(f774,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK20(X0,X5)),unordered_pair(X5,X5)),X0) ),
inference(equality_resolution,[],[f680]) ).
fof(f782,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK27(X0,X5),X5),unordered_pair(sK27(X0,X5),sK27(X0,X5))),X0) ),
inference(equality_resolution,[],[f684]) ).
tcf(c_73,plain,
! [X0: $i] :
( in(sK7(X0),X0)
| ( X0 = empty_set ) ),
inference(cnf_transformation,[],[f419]) ).
tcf(c_74,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f754]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK20(X1,X0)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f774]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK27(X1,X0),X0),unordered_pair(sK27(X1,X0),sK27(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f782]) ).
tcf(c_171,plain,
relation(empty_set),
inference(cnf_transformation,[],[f516]) ).
tcf(c_290,negated_conjecture,
( ( relation_rng(empty_set) != empty_set )
| ( relation_dom(empty_set) != empty_set ) ),
inference(cnf_transformation,[],[f637]) ).
tcf(c_460,plain,
! [X0: $i] :
( ~ relation(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_115,c_74]) ).
tcf(c_481,plain,
! [X0: $i] :
( ~ relation(empty_set)
| ~ in(X0,relation_rng(empty_set)) ),
inference(superposition,[status(thm)],[c_132,c_74]) ).
tcf(c_609,plain,
! [X0: $i] : ~ in(X0,relation_dom(empty_set)),
inference(global_subsumption_just,[status(thm)],[c_460,c_171,c_460]) ).
tcf(c_612,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_73,c_609]) ).
tcf(c_658,plain,
! [X0: $i] : ~ in(X0,relation_rng(empty_set)),
inference(global_subsumption_just,[status(thm)],[c_481,c_171,c_481]) ).
tcf(c_661,plain,
relation_rng(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_73,c_658]) ).
tcf(c_669,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_661,c_612,c_290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU187+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n018.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 13:08:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.42
% 0.15/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42
% 0.15/0.42 % Detected problem language: tptp
% 0.15/0.43 % Proving...
% 3.61/1.08 % SZS status Started for theBenchmark.p
% 3.61/1.08 % SZS status Theorem for theBenchmark.p
% 3.61/1.08
% 3.61/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.61/1.08
% 3.61/1.08 % ------ iProver source info
% 3.61/1.08
% 3.61/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 3.61/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.61/1.08 % git: non_committed_changes: false
% 3.61/1.08
% 3.61/1.08 % ------ Parsing...
% 3.61/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.61/1.08 % ------ Proving...
% 3.61/1.08 % ------ Problem Properties
% 3.61/1.08
% 3.61/1.08 %
% 3.61/1.08 % clauses 262
% 3.61/1.08 % conjectures 1
% 3.61/1.08 % EPR 36
% 3.61/1.08 % Horn 208
% 3.61/1.08 % unary 52
% 3.61/1.08 % binary 96
% 3.61/1.08 % lits 642
% 3.61/1.08 % lits eq 136
% 3.61/1.08 % fd_pure 0
% 3.61/1.08 % fd_pseudo 0
% 3.61/1.08 % fd_cond 11
% 3.61/1.08 % fd_pseudo_cond 51
% 3.61/1.08 % AC symbols 0
% 3.61/1.08
% 3.61/1.08 % ------ Input Options Time Limit: Unbounded
% 3.61/1.08
% 3.61/1.08
% 3.61/1.08 % ------
% 3.61/1.08 % Current options:
% 3.61/1.08 % ------
% 3.61/1.08
% 3.61/1.08
% 3.61/1.08 %
% 3.61/1.08
% 3.61/1.08 % ------ Proving...
% 3.61/1.08 %
% 3.61/1.08
% 3.61/1.08 % SZS status Theorem for theBenchmark.p
% 3.61/1.08
% 3.61/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.61/1.08
% 3.61/1.08
%------------------------------------------------------------------------------