%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU193+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 : 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 02:55:50 PM UTC 2026
% Result : Theorem 7.16s 3.62s
% Output : CNFRefutation 7.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 192 ( 17 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 251 ( 102 ~; 105 |; 30 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 5 ( 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 : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 112 ( 0 sgn 100 !; 12 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation(X2)
=> ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f19,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
fof(f28,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f57,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f166,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f175,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom_restriction(X1,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
fof(f176,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_dom_restriction(X1,X0),X1) ),
inference(negated_conjecture,[status(cth)],[f175]) ).
fof(f199,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f203,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( subset(X0,X1)
<=> ! [X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) ) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f222,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f57]) ).
fof(f322,plain,
? [X0,X1] :
( relation(X1)
& ~ subset(relation_dom_restriction(X1,X0),X1) ),
inference(ennf_transformation,[],[f176]) ).
fof(f337,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f199]) ).
fof(f338,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(flattening,[],[f337]) ).
fof(f339,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) ) )
& ( ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(rectify,[],[f338]) ).
fof(f340,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) ) )
& ( ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ( ( in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X2)
| ( in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X0)
& in(sK2(X0,X1,X2),X1) ) )
& ( ~ in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X0)
| ~ in(sK2(X0,X1,X2),X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X4,sK3(X0,X1,X2))],[f339]) ).
fof(f368,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( ~ subset(X0,X1)
| ! [X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) ) )
& ( ? [X2,X3] :
( in(ordered_pair(X2,X3),X0)
& ~ in(ordered_pair(X2,X3),X1) )
| subset(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f203]) ).
fof(f369,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( ~ subset(X0,X1)
| ! [X4,X5] :
( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) ) )
& ( ? [X2,X3] :
( in(ordered_pair(X2,X3),X0)
& ~ in(ordered_pair(X2,X3),X1) )
| subset(X0,X1) ) ) ) ),
inference(rectify,[],[f368]) ).
fof(f370,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( ~ subset(X0,X1)
| ! [X4,X5] :
( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) ) )
& ( ( in(ordered_pair(sK20(X0,X1),sK21(X0,X1)),X0)
& ~ in(ordered_pair(sK20(X0,X1),sK21(X0,X1)),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21]),skolemize(X2,sK20(X0,X1)),skolemize(X3,sK21(X0,X1))],[f369]) ).
fof(f439,plain,
( relation(sK56)
& ~ subset(relation_dom_restriction(sK56,sK55),sK56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55,sK56]),skolemize(X0,sK55),skolemize(X1,sK56)],[f322]) ).
fof(f456,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(ordered_pair(X5,X6),X0) ),
inference(cnf_transformation,[],[f340]) ).
fof(f508,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK20(X0,X1),sK21(X0,X1)),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f370]) ).
fof(f509,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK20(X0,X1),sK21(X0,X1)),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f370]) ).
fof(f541,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f569,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f222]) ).
fof(f719,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f166]) ).
fof(f734,plain,
relation(sK56),
inference(cnf_transformation,[],[f439]) ).
fof(f735,plain,
~ subset(relation_dom_restriction(sK56,sK55),sK56),
inference(cnf_transformation,[],[f439]) ).
fof(f746,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f541,f719]) ).
fof(f759,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f456,f746,f746]) ).
fof(f770,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK20(X0,X1),sK21(X0,X1)),unordered_pair(sK20(X0,X1),sK20(X0,X1))),X1)
| subset(X0,X1) ),
inference(definition_unfolding,[],[f509,f746]) ).
fof(f771,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK20(X0,X1),sK21(X0,X1)),unordered_pair(sK20(X0,X1),sK20(X0,X1))),X0)
| subset(X0,X1) ),
inference(definition_unfolding,[],[f508,f746]) ).
fof(f855,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_dom_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0) ),
inference(equality_resolution,[],[f759]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f855]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK20(X0,X1),sK21(X0,X1)),unordered_pair(sK20(X0,X1),sK20(X0,X1))),X1) ),
inference(cnf_transformation,[],[f770]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| in(unordered_pair(unordered_pair(sK20(X1,X0),sK21(X1,X0)),unordered_pair(sK20(X1,X0),sK20(X1,X0))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f771]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f569]) ).
tcf(c_339,negated_conjecture,
~ subset(relation_dom_restriction(sK56,sK55),sK56),
inference(cnf_transformation,[],[f735]) ).
tcf(c_340,negated_conjecture,
relation(sK56),
inference(cnf_transformation,[],[f734]) ).
tcf(c_2353,plain,
( subset(relation_dom_restriction(sK56,sK55),sK56)
| ~ relation(sK56)
| ~ relation(relation_dom_restriction(sK56,sK55))
| ~ in(unordered_pair(unordered_pair(sK20(relation_dom_restriction(sK56,sK55),sK56),sK21(relation_dom_restriction(sK56,sK55),sK56)),unordered_pair(sK20(relation_dom_restriction(sK56,sK55),sK56),sK20(relation_dom_restriction(sK56,sK55),sK56))),sK56) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_2372,plain,
( subset(relation_dom_restriction(sK56,sK55),sK56)
| in(unordered_pair(unordered_pair(sK20(relation_dom_restriction(sK56,sK55),sK56),sK21(relation_dom_restriction(sK56,sK55),sK56)),unordered_pair(sK20(relation_dom_restriction(sK56,sK55),sK56),sK20(relation_dom_restriction(sK56,sK55),sK56))),relation_dom_restriction(sK56,sK55))
| ~ relation(sK56)
| ~ relation(relation_dom_restriction(sK56,sK55)) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_3370,plain,
( relation(relation_dom_restriction(sK56,sK55))
| ~ relation(sK56) ),
inference(instantiation,[status(thm)],[c_176]) ).
tcf(c_11963,plain,
( in(unordered_pair(unordered_pair(sK20(relation_dom_restriction(sK56,sK55),sK56),sK21(relation_dom_restriction(sK56,sK55),sK56)),unordered_pair(sK20(relation_dom_restriction(sK56,sK55),sK56),sK20(relation_dom_restriction(sK56,sK55),sK56))),sK56)
| ~ relation(sK56)
| ~ relation(relation_dom_restriction(sK56,sK55))
| ~ in(unordered_pair(unordered_pair(sK20(relation_dom_restriction(sK56,sK55),sK56),sK21(relation_dom_restriction(sK56,sK55),sK56)),unordered_pair(sK20(relation_dom_restriction(sK56,sK55),sK56),sK20(relation_dom_restriction(sK56,sK55),sK56))),relation_dom_restriction(sK56,sK55)) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_11965,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11963,c_3370,c_2372,c_2353,c_339,c_340]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU193+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 : n017.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 13:03:15 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 7.16/3.62 % SZS status Started for theBenchmark.p
% 7.16/3.62 % SZS status Theorem for theBenchmark.p
% 7.16/3.62
% 7.16/3.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.16/3.62
% 7.16/3.62 % ------ iProver source info
% 7.16/3.62
% 7.16/3.62 % git: date: 2026-07-19 20:42:38 +0200
% 7.16/3.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.16/3.62 % git: non_committed_changes: false
% 7.16/3.62
% 7.16/3.62 % ------ Parsing...
% 7.16/3.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.16/3.62
% 7.16/3.62 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e %
% 7.16/3.62
% 7.16/3.62 % ------ Preprocessing...%
% 7.16/3.62
% 7.16/3.62 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.16/3.62 % ------ Proving...
% 7.16/3.62 % ------ Problem Properties
% 7.16/3.62
% 7.16/3.62 %
% 7.16/3.62 % clauses 282
% 7.16/3.62 % conjectures 22
% 7.16/3.62 % EPR 32
% 7.16/3.62 % Horn 226
% 7.16/3.62 % unary 53
% 7.16/3.62 % binary 92
% 7.16/3.62 % lits 725
% 7.16/3.62 % lits eq 149
% 7.16/3.62 % fd_pure 0
% 7.16/3.62 % fd_pseudo 0
% 7.16/3.62 % fd_cond 13
% 7.16/3.62 % fd_pseudo_cond 57
% 7.16/3.62 % AC symbols 0
% 7.16/3.62
% 7.16/3.62 % ------ Input Options Time Limit: Unbounded
% 7.16/3.62
% 7.16/3.62
% 7.16/3.62 % ------
% 7.16/3.62 % Current options:
% 7.16/3.62 % ------
% 7.16/3.62
% 7.16/3.62
% 7.16/3.62 %
% 7.16/3.62
% 7.16/3.62 % ------ Proving...
% 7.16/3.62 %
% 7.16/3.62
% 7.16/3.62 % SZS status Theorem for theBenchmark.p
% 7.16/3.62
% 7.16/3.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.16/3.62
% 7.16/3.62
%------------------------------------------------------------------------------