%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU199+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 : n014.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 02:55:52 PM UTC 2026
% Result : Theorem 17.31s 3.25s
% Output : CNFRefutation 17.31s
% 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(f10,axiom,
! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
fof(f21,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(f30,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(f61,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f114,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng_restriction(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
fof(f115,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_rng_restriction(X0,X1),X1) ),
inference(negated_conjecture,[status(cth)],[f114]) ).
fof(f174,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f210,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f215,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,[],[f21]) ).
fof(f236,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f61]) ).
fof(f275,plain,
? [X0,X1] :
( relation(X1)
& ~ subset(relation_rng_restriction(X0,X1),X1) ),
inference(ennf_transformation,[],[f115]) ).
fof(f362,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f210]) ).
fof(f363,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(flattening,[],[f362]) ).
fof(f364,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X1)
& in(X6,X0) ) )
& ( ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(rectify,[],[f363]) ).
fof(f365,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X1)
& in(X6,X0) ) )
& ( ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ( ( in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X2)
| ( in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X1)
& in(sK5(X0,X1,X2),X0) ) )
& ( ~ in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X1)
| ~ in(sK5(X0,X1,X2),X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X4,sK5(X0,X1,X2))],[f364]) ).
fof(f396,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,[],[f215]) ).
fof(f397,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,[],[f396]) ).
fof(f398,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(sK24(X0,X1),sK25(X0,X1)),X0)
& ~ in(ordered_pair(sK24(X0,X1),sK25(X0,X1)),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24,sK25]),skolemize(X2,sK24(X0,X1)),skolemize(X3,sK25(X0,X1))],[f397]) ).
fof(f448,plain,
( relation(sK54)
& ~ subset(relation_rng_restriction(sK53,sK54),sK54) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54]),skolemize(X0,sK53),skolemize(X1,sK54)],[f275]) ).
fof(f492,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(ordered_pair(X5,X6),X1) ),
inference(cnf_transformation,[],[f365]) ).
fof(f548,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK24(X0,X1),sK25(X0,X1)),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f398]) ).
fof(f549,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK24(X0,X1),sK25(X0,X1)),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f398]) ).
fof(f581,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f30]) ).
fof(f611,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f236]) ).
fof(f683,plain,
relation(sK54),
inference(cnf_transformation,[],[f448]) ).
fof(f684,plain,
~ subset(relation_rng_restriction(sK53,sK54),sK54),
inference(cnf_transformation,[],[f448]) ).
fof(f767,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f174]) ).
fof(f796,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f581,f767]) ).
fof(f815,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_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)),X1) ),
inference(definition_unfolding,[],[f492,f796,f796]) ).
fof(f830,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK24(X0,X1),sK25(X0,X1)),unordered_pair(sK24(X0,X1),sK24(X0,X1))),X1)
| subset(X0,X1) ),
inference(definition_unfolding,[],[f549,f796]) ).
fof(f831,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK24(X0,X1),sK25(X0,X1)),unordered_pair(sK24(X0,X1),sK24(X0,X1))),X0)
| subset(X0,X1) ),
inference(definition_unfolding,[],[f548,f796]) ).
fof(f920,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_rng_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1) ),
inference(equality_resolution,[],[f815]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ relation(X3)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f920]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK24(X0,X1),sK25(X0,X1)),unordered_pair(sK24(X0,X1),sK24(X0,X1))),X1) ),
inference(cnf_transformation,[],[f830]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| in(unordered_pair(unordered_pair(sK24(X1,X0),sK25(X1,X0)),unordered_pair(sK24(X1,X0),sK24(X1,X0))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f831]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f611]) ).
tcf(c_260,negated_conjecture,
~ subset(relation_rng_restriction(sK53,sK54),sK54),
inference(cnf_transformation,[],[f684]) ).
tcf(c_261,negated_conjecture,
relation(sK54),
inference(cnf_transformation,[],[f683]) ).
tcf(c_2390,plain,
( subset(relation_rng_restriction(sK53,sK54),sK54)
| ~ relation(sK54)
| ~ relation(relation_rng_restriction(sK53,sK54))
| ~ in(unordered_pair(unordered_pair(sK24(relation_rng_restriction(sK53,sK54),sK54),sK25(relation_rng_restriction(sK53,sK54),sK54)),unordered_pair(sK24(relation_rng_restriction(sK53,sK54),sK54),sK24(relation_rng_restriction(sK53,sK54),sK54))),sK54) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_2398,plain,
( subset(relation_rng_restriction(sK53,sK54),sK54)
| in(unordered_pair(unordered_pair(sK24(relation_rng_restriction(sK53,sK54),sK54),sK25(relation_rng_restriction(sK53,sK54),sK54)),unordered_pair(sK24(relation_rng_restriction(sK53,sK54),sK54),sK24(relation_rng_restriction(sK53,sK54),sK54))),relation_rng_restriction(sK53,sK54))
| ~ relation(sK54)
| ~ relation(relation_rng_restriction(sK53,sK54)) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_3446,plain,
( relation(relation_rng_restriction(sK53,sK54))
| ~ relation(sK54) ),
inference(instantiation,[status(thm)],[c_188]) ).
tcf(c_12209,plain,
( in(unordered_pair(unordered_pair(sK24(relation_rng_restriction(sK53,sK54),sK54),sK25(relation_rng_restriction(sK53,sK54),sK54)),unordered_pair(sK24(relation_rng_restriction(sK53,sK54),sK54),sK24(relation_rng_restriction(sK53,sK54),sK54))),sK54)
| ~ relation(sK54)
| ~ relation(relation_rng_restriction(sK53,sK54))
| ~ in(unordered_pair(unordered_pair(sK24(relation_rng_restriction(sK53,sK54),sK54),sK25(relation_rng_restriction(sK53,sK54),sK54)),unordered_pair(sK24(relation_rng_restriction(sK53,sK54),sK54),sK24(relation_rng_restriction(sK53,sK54),sK54))),relation_rng_restriction(sK53,sK54)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_12211,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_12209,c_3446,c_2398,c_2390,c_260,c_261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU199+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 13:09:02 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 17.31/3.25 % SZS status Started for theBenchmark.p
% 17.31/3.25 % SZS status Theorem for theBenchmark.p
% 17.31/3.25
% 17.31/3.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.31/3.25
% 17.31/3.25 % ------ iProver source info
% 17.31/3.25
% 17.31/3.25 % git: date: 2026-07-19 20:42:38 +0200
% 17.31/3.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.31/3.25 % git: non_committed_changes: false
% 17.31/3.25
% 17.31/3.25 % ------ Parsing...
% 17.31/3.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.31/3.25
% 17.31/3.25 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e %
% 17.31/3.25
% 17.31/3.25 % ------ Preprocessing...%
% 17.31/3.25
% 17.31/3.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.31/3.25 % ------ Proving...
% 17.31/3.25 % ------ Problem Properties
% 17.31/3.25
% 17.31/3.25 %
% 17.31/3.25 % clauses 300
% 17.31/3.25 % conjectures 22
% 17.31/3.25 % EPR 32
% 17.31/3.25 % Horn 241
% 17.31/3.25 % unary 53
% 17.31/3.25 % binary 98
% 17.31/3.25 % lits 789
% 17.31/3.25 % lits eq 156
% 17.31/3.25 % fd_pure 0
% 17.31/3.25 % fd_pseudo 0
% 17.31/3.25 % fd_cond 13
% 17.31/3.25 % fd_pseudo_cond 62
% 17.31/3.25 % AC symbols 0
% 17.31/3.25
% 17.31/3.25 % ------ Input Options Time Limit: Unbounded
% 17.31/3.25
% 17.31/3.25
% 17.31/3.25 % ------
% 17.31/3.25 % Current options:
% 17.31/3.25 % ------
% 17.31/3.25
% 17.31/3.25
% 17.31/3.25 %
% 17.31/3.25
% 17.31/3.25 % ------ Proving...
% 17.31/3.25 %
% 17.31/3.25
% 17.31/3.25 % SZS status Theorem for theBenchmark.p
% 17.31/3.25
% 17.31/3.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.31/3.25
% 17.31/3.25
%------------------------------------------------------------------------------