%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU204+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 : n010.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 02:55:53 PM UTC 2026
% Result : Theorem 6.98s 3.70s
% Output : CNFRefutation 6.98s
% 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(f23,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f31,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(f124,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f125,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f126,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(negated_conjecture,[status(cth)],[f125]) ).
fof(f133,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(f181,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f224,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f293,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) ) ),
inference(ennf_transformation,[],[f124]) ).
fof(f294,plain,
? [X0,X1] :
( relation(X1)
& ~ subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(ennf_transformation,[],[f126]) ).
fof(f300,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,[],[f133]) ).
fof(f301,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ),
inference(flattening,[],[f300]) ).
fof(f415,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,[],[f224]) ).
fof(f416,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,[],[f415]) ).
fof(f417,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK29(X0,X1),X0)
& ~ in(sK29(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X2,sK29(X0,X1))],[f416]) ).
fof(f465,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_image(X2,X1))
| ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) )
| in(X0,relation_image(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f293]) ).
fof(f466,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_image(X2,X1))
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) )
| in(X0,relation_image(X2,X1)) ) ) ),
inference(rectify,[],[f465]) ).
fof(f467,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_image(X2,X1))
| ( in(sK57(X0,X1,X2),X1)
& in(ordered_pair(sK57(X0,X1,X2),X0),X2)
& in(sK57(X0,X1,X2),relation_dom(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) )
| in(X0,relation_image(X2,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(X4,sK57(X0,X1,X2))],[f466]) ).
fof(f468,plain,
( relation(sK59)
& ~ subset(relation_image(sK59,sK58),relation_rng(sK59)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58,sK59]),skolemize(X0,sK58),skolemize(X1,sK59)],[f294]) ).
fof(f576,plain,
! [X0,X1] :
( in(sK29(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f417]) ).
fof(f577,plain,
! [X0,X1] :
( ~ in(sK29(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f417]) ).
fof(f606,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f31]) ).
fof(f720,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(ordered_pair(sK57(X0,X1,X2),X0),X2) ),
inference(cnf_transformation,[],[f467]) ).
fof(f723,plain,
relation(sK59),
inference(cnf_transformation,[],[f468]) ).
fof(f724,plain,
~ subset(relation_image(sK59,sK58),relation_rng(sK59)),
inference(cnf_transformation,[],[f468]) ).
fof(f731,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_rng(X2)) ),
inference(cnf_transformation,[],[f301]) ).
fof(f800,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f181]) ).
fof(f829,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f606,f800]) ).
fof(f918,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(unordered_pair(unordered_pair(sK57(X0,X1,X2),X0),unordered_pair(sK57(X0,X1,X2),sK57(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f720,f829]) ).
fof(f923,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X1,relation_rng(X2)) ),
inference(definition_unfolding,[],[f731,f829]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK29(X0,X1),X1) ),
inference(cnf_transformation,[],[f577]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK29(X0,X1),X0) ),
inference(cnf_transformation,[],[f576]) ).
tcf(c_279,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK57(X0,X2,X1),X0),unordered_pair(sK57(X0,X2,X1),sK57(X0,X2,X1))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f918]) ).
tcf(c_281,negated_conjecture,
~ subset(relation_image(sK59,sK58),relation_rng(sK59)),
inference(cnf_transformation,[],[f724]) ).
tcf(c_282,negated_conjecture,
relation(sK59),
inference(cnf_transformation,[],[f723]) ).
tcf(c_290,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f923]) ).
tcf(c_1103,plain,
( subset(relation_image(sK59,sK58),relation_rng(sK59))
| in(sK29(relation_image(sK59,sK58),relation_rng(sK59)),relation_image(sK59,sK58)) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_1182,plain,
( subset(relation_image(sK59,sK58),relation_rng(sK59))
| ~ in(sK29(relation_image(sK59,sK58),relation_rng(sK59)),relation_rng(sK59)) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_2685,plain,
( in(unordered_pair(unordered_pair(sK57(sK29(relation_image(sK59,sK58),relation_rng(sK59)),sK58,sK59),sK29(relation_image(sK59,sK58),relation_rng(sK59))),unordered_pair(sK57(sK29(relation_image(sK59,sK58),relation_rng(sK59)),sK58,sK59),sK57(sK29(relation_image(sK59,sK58),relation_rng(sK59)),sK58,sK59))),sK59)
| ~ relation(sK59)
| ~ in(sK29(relation_image(sK59,sK58),relation_rng(sK59)),relation_image(sK59,sK58)) ),
inference(instantiation,[status(thm)],[c_279]) ).
tcf(c_11854,plain,
( in(sK29(relation_image(sK59,sK58),relation_rng(sK59)),relation_rng(sK59))
| ~ relation(sK59)
| ~ in(unordered_pair(unordered_pair(sK57(sK29(relation_image(sK59,sK58),relation_rng(sK59)),sK58,sK59),sK29(relation_image(sK59,sK58),relation_rng(sK59))),unordered_pair(sK57(sK29(relation_image(sK59,sK58),relation_rng(sK59)),sK58,sK59),sK57(sK29(relation_image(sK59,sK58),relation_rng(sK59)),sK58,sK59))),sK59) ),
inference(instantiation,[status(thm)],[c_290]) ).
tcf(c_11856,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11854,c_2685,c_1182,c_1103,c_281,c_282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU204+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 13:10:31 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 6.98/3.70 % SZS status Started for theBenchmark.p
% 6.98/3.70 % SZS status Theorem for theBenchmark.p
% 6.98/3.70
% 6.98/3.70 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.98/3.70
% 6.98/3.70 % ------ iProver source info
% 6.98/3.70
% 6.98/3.70 % git: date: 2026-07-19 20:42:38 +0200
% 6.98/3.70 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.98/3.70 % git: non_committed_changes: false
% 6.98/3.70
% 6.98/3.70 % ------ Parsing...
% 6.98/3.70 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.98/3.70
% 6.98/3.70 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e %
% 6.98/3.70
% 6.98/3.70 % ------ Preprocessing...%
% 6.98/3.70
% 6.98/3.70 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.98/3.70 % ------ Proving...
% 6.98/3.70 % ------ Problem Properties
% 6.98/3.70
% 6.98/3.70 %
% 6.98/3.70 % clauses 313
% 6.98/3.70 % conjectures 22
% 6.98/3.70 % EPR 32
% 6.98/3.70 % Horn 252
% 6.98/3.70 % unary 53
% 6.98/3.70 % binary 102
% 6.98/3.70 % lits 829
% 6.98/3.70 % lits eq 161
% 6.98/3.70 % fd_pure 0
% 6.98/3.71 % fd_pseudo 0
% 6.98/3.71 % fd_cond 13
% 6.98/3.71 % fd_pseudo_cond 65
% 6.98/3.71 % AC symbols 0
% 6.98/3.71
% 6.98/3.71 % ------ Input Options Time Limit: Unbounded
% 6.98/3.71
% 6.98/3.71
% 6.98/3.71 % ------
% 6.98/3.71 % Current options:
% 6.98/3.71 % ------
% 6.98/3.71
% 6.98/3.71
% 6.98/3.71 %
% 6.98/3.71
% 6.98/3.71 % ------ Proving...
% 6.98/3.71 %
% 6.98/3.71
% 6.98/3.71 % SZS status Theorem for theBenchmark.p
% 6.98/3.71
% 6.98/3.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.98/3.71
% 6.98/3.71
%------------------------------------------------------------------------------