%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU209+1 : 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 : n011.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 3.70s 1.39s
% Output : CNFRefutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 7 unt; 0 def)
% Number of atoms : 183 ( 22 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 226 ( 87 ~; 90 |; 34 &)
% ( 10 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 126 ( 0 sgn 106 !; 20 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f32,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(f33,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f43,plain,
? [X0,X1] :
( relation(X1)
& ~ subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f44,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f49,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f50,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f61,plain,
( relation(sK1)
& ~ subset(relation_inverse_image(sK1,sK0),relation_dom(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f43]) ).
fof(f62,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f63,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK4(X0,X1,X6),X1)
& in(ordered_pair(X6,sK4(X0,X1,X6)),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK2(X0,X1,X2),X2)
| ( in(sK3(X0,X1,X2),X1)
& in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X0) ) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK2(X0,X1,X2),X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X5,sK3(X0,X1,X2)),skolemize(X8,sK4(X0,X1,X6))],[f63]) ).
fof(f67,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,[],[f49]) ).
fof(f68,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,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK9(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK7(X0,X1),X1)
| in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0) )
& ( ~ in(sK7(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f68]) ).
fof(f71,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,[],[f50]) ).
fof(f72,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,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK10(X0,X1),X0)
& ~ in(sK10(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f72]) ).
fof(f79,plain,
relation(sK1),
inference(cnf_transformation,[],[f61]) ).
fof(f80,plain,
~ subset(relation_inverse_image(sK1,sK0),relation_dom(sK1)),
inference(cnf_transformation,[],[f61]) ).
fof(f82,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(ordered_pair(X6,sK4(X0,X1,X6)),X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f96,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f103,plain,
! [X0,X1] :
( in(sK10(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f104,plain,
! [X0,X1] :
( ~ in(sK10(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f122,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(ordered_pair(X6,sK4(X0,X1,X6)),X0) ),
inference(equality_resolution,[],[f82]) ).
fof(f124,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f96]) ).
tcf(c_49,negated_conjecture,
~ subset(relation_inverse_image(sK1,sK0),relation_dom(sK1)),
inference(cnf_transformation,[],[f80]) ).
tcf(c_50,negated_conjecture,
relation(sK1),
inference(cnf_transformation,[],[f79]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X0,sK4(X1,X2,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK10(X0,X1),X1) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i] :
( ~ in(sK10(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_72]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK10(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_134]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] :
( in(sK10(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_73]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK10(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_136]) ).
tcf(c_815,plain,
! [X0: $i,X1: $i] :
( in(sK10(X0,X1),X0)
| ( relation_dom(sK1) != X1 )
| ( relation_inverse_image(sK1,sK0) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_137]) ).
tcf(c_816,plain,
in(sK10(relation_inverse_image(sK1,sK0),relation_dom(sK1)),relation_inverse_image(sK1,sK0)),
inference(unflattening,[status(thm)],[c_815]) ).
tcf(c_820,plain,
! [X0: $i,X1: $i] :
( ~ in(sK10(X0,X1),X1)
| ( relation_dom(sK1) != X1 )
| ( relation_inverse_image(sK1,sK0) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_135]) ).
tcf(c_821,plain,
~ in(sK10(relation_inverse_image(sK1,sK0),relation_dom(sK1)),relation_dom(sK1)),
inference(unflattening,[status(thm)],[c_820]) ).
tcf(c_3073,plain,
( in(ordered_pair(sK10(relation_inverse_image(sK1,sK0),relation_dom(sK1)),sK4(sK1,sK0,sK10(relation_inverse_image(sK1,sK0),relation_dom(sK1)))),sK1)
| ~ relation(sK1)
| ~ in(sK10(relation_inverse_image(sK1,sK0),relation_dom(sK1)),relation_inverse_image(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_4769,plain,
( in(sK10(relation_inverse_image(sK1,sK0),relation_dom(sK1)),relation_dom(sK1))
| ~ relation(sK1)
| ~ in(ordered_pair(sK10(relation_inverse_image(sK1,sK0),relation_dom(sK1)),sK4(sK1,sK0,sK10(relation_inverse_image(sK1,sK0),relation_dom(sK1)))),sK1) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_4770,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4769,c_3073,c_821,c_816,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU209+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.41 % Computer : n011.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Thu Sep 24 13:10:59 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.46 Running first-order theorem proving
% 0.17/0.46 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
% 0.17/0.47
% 0.17/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.17/0.47
% 0.17/0.48 % Detected problem language: tptp
% 0.17/0.49 % Proving...
% 3.70/1.39 % SZS status Started for theBenchmark.p
% 3.70/1.39 % SZS status Theorem for theBenchmark.p
% 3.70/1.39
% 3.70/1.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.70/1.39
% 3.70/1.39 % ------ iProver source info
% 3.70/1.39
% 3.70/1.39 % git: date: 2026-07-19 20:42:38 +0200
% 3.70/1.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.70/1.39 % git: non_committed_changes: false
% 3.70/1.39
% 3.70/1.39 % ------ Parsing...
% 3.70/1.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.70/1.39
% 3.70/1.39 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.70/1.39
% 3.70/1.39 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.70/1.39
% 3.70/1.39 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.70/1.39 % ------ Proving...
% 3.70/1.39 % ------ Problem Properties
% 3.70/1.39
% 3.70/1.39 %
% 3.70/1.39 % clauses 42
% 3.70/1.39 % conjectures 2
% 3.70/1.39 % EPR 17
% 3.70/1.39 % Horn 36
% 3.70/1.39 % unary 14
% 3.70/1.39 % binary 12
% 3.70/1.39 % lits 93
% 3.70/1.39 % lits eq 6
% 3.70/1.39 % fd_pure 0
% 3.70/1.39 % fd_pseudo 0
% 3.70/1.39 % fd_cond 0
% 3.70/1.39 % fd_pseudo_cond 6
% 3.70/1.39 % AC symbols 0
% 3.70/1.39
% 3.70/1.39 % ------ Schedule dynamic 5 is on
% 3.70/1.39
% 3.70/1.39 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.70/1.39
% 3.70/1.39
% 3.70/1.39 % ------
% 3.70/1.39 % Current options:
% 3.70/1.39 % ------
% 3.70/1.39
% 3.70/1.39
% 3.70/1.39 %
% 3.70/1.39
% 3.70/1.39 % ------ Proving...
% 3.70/1.39 %
% 3.70/1.39
% 3.70/1.39 % SZS status Theorem for theBenchmark.p
% 3.70/1.39
% 3.70/1.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.70/1.39
% 3.70/1.39
%------------------------------------------------------------------------------