%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU209+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 : n007.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 02:55:54 PM UTC 2026
% Result : Theorem 26.53s 4.28s
% Output : CNFRefutation 26.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 127 ( 5 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 140 ( 54 ~; 52 |; 24 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 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 : 88 ( 0 sgn 80 !; 8 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f32,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(f131,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
fof(f132,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
fof(f133,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
inference(negated_conjecture,[status(cth)],[f132]) ).
fof(f140,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f188,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f232,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f306,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) ) ),
inference(ennf_transformation,[],[f131]) ).
fof(f307,plain,
? [X0,X1] :
( relation(X1)
& ~ subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
inference(ennf_transformation,[],[f133]) ).
fof(f313,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ),
inference(ennf_transformation,[],[f140]) ).
fof(f314,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ),
inference(flattening,[],[f313]) ).
fof(f431,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f432,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f431]) ).
fof(f433,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK32(X0,X1),X0)
& ~ in(sK32(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(X2,sK32(X0,X1))],[f432]) ).
fof(f484,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_inverse_image(X2,X1))
| ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) )
| in(X0,relation_inverse_image(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f306]) ).
fof(f485,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_inverse_image(X2,X1))
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) )
| in(X0,relation_inverse_image(X2,X1)) ) ) ),
inference(rectify,[],[f484]) ).
fof(f486,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_inverse_image(X2,X1))
| ( in(sK61(X0,X1,X2),X1)
& in(ordered_pair(X0,sK61(X0,X1,X2)),X2)
& in(sK61(X0,X1,X2),relation_rng(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) )
| in(X0,relation_inverse_image(X2,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(X4,sK61(X0,X1,X2))],[f485]) ).
fof(f487,plain,
( relation(sK63)
& ~ subset(relation_inverse_image(sK63,sK62),relation_dom(sK63)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62,sK63]),skolemize(X0,sK62),skolemize(X1,sK63)],[f307]) ).
fof(f601,plain,
! [X0,X1] :
( in(sK32(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f433]) ).
fof(f602,plain,
! [X0,X1] :
( ~ in(sK32(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f433]) ).
fof(f631,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f32]) ).
fof(f753,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(ordered_pair(X0,sK61(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f486]) ).
fof(f756,plain,
relation(sK63),
inference(cnf_transformation,[],[f487]) ).
fof(f757,plain,
~ subset(relation_inverse_image(sK63,sK62),relation_dom(sK63)),
inference(cnf_transformation,[],[f487]) ).
fof(f765,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f314]) ).
fof(f833,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f188]) ).
fof(f862,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f631,f833]) ).
fof(f958,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(unordered_pair(unordered_pair(X0,sK61(X0,X1,X2)),unordered_pair(X0,X0)),X2) ),
inference(definition_unfolding,[],[f753,f862]) ).
fof(f962,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X0,relation_dom(X2)) ),
inference(definition_unfolding,[],[f765,f862]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK32(X0,X1),X1) ),
inference(cnf_transformation,[],[f602]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK32(X0,X1),X0) ),
inference(cnf_transformation,[],[f601]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK61(X0,X2,X1)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f958]) ).
tcf(c_295,negated_conjecture,
~ subset(relation_inverse_image(sK63,sK62),relation_dom(sK63)),
inference(cnf_transformation,[],[f757]) ).
tcf(c_296,negated_conjecture,
relation(sK63),
inference(cnf_transformation,[],[f756]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f962]) ).
tcf(c_1150,plain,
( subset(relation_inverse_image(sK63,sK62),relation_dom(sK63))
| in(sK32(relation_inverse_image(sK63,sK62),relation_dom(sK63)),relation_inverse_image(sK63,sK62)) ),
inference(instantiation,[status(thm)],[c_141]) ).
tcf(c_1223,plain,
( subset(relation_inverse_image(sK63,sK62),relation_dom(sK63))
| ~ in(sK32(relation_inverse_image(sK63,sK62),relation_dom(sK63)),relation_dom(sK63)) ),
inference(instantiation,[status(thm)],[c_140]) ).
tcf(c_2748,plain,
( in(unordered_pair(unordered_pair(sK32(relation_inverse_image(sK63,sK62),relation_dom(sK63)),sK61(sK32(relation_inverse_image(sK63,sK62),relation_dom(sK63)),sK62,sK63)),unordered_pair(sK32(relation_inverse_image(sK63,sK62),relation_dom(sK63)),sK32(relation_inverse_image(sK63,sK62),relation_dom(sK63)))),sK63)
| ~ relation(sK63)
| ~ in(sK32(relation_inverse_image(sK63,sK62),relation_dom(sK63)),relation_inverse_image(sK63,sK62)) ),
inference(instantiation,[status(thm)],[c_293]) ).
tcf(c_11844,plain,
( in(sK32(relation_inverse_image(sK63,sK62),relation_dom(sK63)),relation_dom(sK63))
| ~ relation(sK63)
| ~ in(unordered_pair(unordered_pair(sK32(relation_inverse_image(sK63,sK62),relation_dom(sK63)),sK61(sK32(relation_inverse_image(sK63,sK62),relation_dom(sK63)),sK62,sK63)),unordered_pair(sK32(relation_inverse_image(sK63,sK62),relation_dom(sK63)),sK32(relation_inverse_image(sK63,sK62),relation_dom(sK63)))),sK63) ),
inference(instantiation,[status(thm)],[c_303]) ).
tcf(c_11845,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11844,c_2748,c_1223,c_1150,c_295,c_296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU209+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 13:09:24 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 26.53/4.28 % SZS status Started for theBenchmark.p
% 26.53/4.28 % SZS status Theorem for theBenchmark.p
% 26.53/4.28
% 26.53/4.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 26.53/4.28
% 26.53/4.28 % ------ iProver source info
% 26.53/4.28
% 26.53/4.28 % git: date: 2026-07-19 20:42:38 +0200
% 26.53/4.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 26.53/4.28 % git: non_committed_changes: false
% 26.53/4.28
% 26.53/4.28 % ------ Parsing...
% 26.53/4.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 26.53/4.28
% 26.53/4.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e %
% 26.53/4.28
% 26.53/4.28 % ------ Preprocessing...%
% 26.53/4.28
% 26.53/4.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 26.53/4.28 % ------ Proving...
% 26.53/4.28 % ------ Problem Properties
% 26.53/4.28
% 26.53/4.28 %
% 26.53/4.28 % clauses 326
% 26.53/4.28 % conjectures 22
% 26.53/4.28 % EPR 32
% 26.53/4.28 % Horn 263
% 26.53/4.28 % unary 53
% 26.53/4.28 % binary 105
% 26.53/4.28 % lits 870
% 26.53/4.28 % lits eq 167
% 26.53/4.28 % fd_pure 0
% 26.53/4.28 % fd_pseudo 0
% 26.53/4.28 % fd_cond 13
% 26.53/4.28 % fd_pseudo_cond 68
% 26.53/4.28 % AC symbols 0
% 26.53/4.28
% 26.53/4.28 % ------ Input Options Time Limit: Unbounded
% 26.53/4.28
% 26.53/4.28
% 26.53/4.28 % ------
% 26.53/4.28 % Current options:
% 26.53/4.28 % ------
% 26.53/4.28
% 26.53/4.28
% 26.53/4.28 %
% 26.53/4.28
% 26.53/4.28 % ------ Proving...
% 26.53/4.28 %
% 26.53/4.28
% 26.53/4.28 % SZS status Theorem for theBenchmark.p
% 26.53/4.28
% 26.53/4.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.53/4.28
% 26.53/4.28
%------------------------------------------------------------------------------