%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU268+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 : n026.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 02:56:26 PM UTC 2026
% Result : Theorem 50.63s 7.90s
% Output : CNFRefutation 50.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 19 unt; 0 def)
% Number of atoms : 218 ( 40 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 271 ( 107 ~; 112 |; 39 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 95 !; 9 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f34,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = inclusion_relation(X0)
<=> ( ! [X2,X3] :
( ( in(X3,X0)
& in(X2,X0) )
=> ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) )
& relation_field(X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord2) ).
fof(f61,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(f86,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f157,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).
fof(f259,conjecture,
! [X0] : reflexive(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_wellord2) ).
fof(f260,negated_conjecture,
~ ! [X0] : reflexive(inclusion_relation(X0)),
inference(negated_conjecture,[status(cth)],[f259]) ).
fof(f321,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f361,plain,
! [X0] :
( ~ relation(X0)
| ( reflexive(X0)
<=> ! [X1] :
( ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0) ) ) ),
inference(ennf_transformation,[],[f157]) ).
fof(f453,plain,
? [X0] : ~ reflexive(inclusion_relation(X0)),
inference(ennf_transformation,[],[f260]) ).
fof(f632,plain,
! [X0,X1] :
( ~ relation(X1)
| ( X1 = inclusion_relation(X0)
<=> ( ! [X2,X3] :
( ~ in(X3,X0)
| ~ in(X2,X0)
| ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) )
& relation_field(X1) = X0 ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f633,plain,
! [X0,X1] :
( ~ relation(X1)
| ( X1 = inclusion_relation(X0)
<=> ( ! [X2,X3] :
( ~ in(X3,X0)
| ~ in(X2,X0)
| ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) )
& relation_field(X1) = X0 ) ) ),
inference(flattening,[],[f632]) ).
fof(f690,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| ! [X1] :
( ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0) ) )
& ( ? [X1] :
( in(X1,relation_field(X0))
& ~ in(ordered_pair(X1,X1),X0) )
| reflexive(X0) ) ) ),
inference(nnf_transformation,[],[f361]) ).
fof(f691,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| ! [X2] :
( ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ) )
& ( ? [X1] :
( in(X1,relation_field(X0))
& ~ in(ordered_pair(X1,X1),X0) )
| reflexive(X0) ) ) ),
inference(rectify,[],[f690]) ).
fof(f692,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| ! [X2] :
( ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ) )
& ( ( in(sK3(X0),relation_field(X0))
& ~ in(ordered_pair(sK3(X0),sK3(X0)),X0) )
| reflexive(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f691]) ).
fof(f732,plain,
~ reflexive(inclusion_relation(sK19)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X0,sK19)],[f453]) ).
fof(f814,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f815,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f814]) ).
fof(f892,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( inclusion_relation(X0) != X1
| ( ! [X2,X3] :
( ~ in(X3,X0)
| ~ in(X2,X0)
| ( ( ~ in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ subset(X2,X3)
| in(ordered_pair(X2,X3),X1) ) ) )
& relation_field(X1) = X0 ) )
& ( ? [X2,X3] :
( in(X3,X0)
& in(X2,X0)
& ( in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) ) )
| relation_field(X1) != X0
| X1 = inclusion_relation(X0) ) ) ),
inference(nnf_transformation,[],[f633]) ).
fof(f893,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( inclusion_relation(X0) != X1
| ( ! [X2,X3] :
( ~ in(X3,X0)
| ~ in(X2,X0)
| ( ( ~ in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ subset(X2,X3)
| in(ordered_pair(X2,X3),X1) ) ) )
& relation_field(X1) = X0 ) )
& ( ? [X2,X3] :
( in(X3,X0)
& in(X2,X0)
& ( in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) ) )
| relation_field(X1) != X0
| X1 = inclusion_relation(X0) ) ) ),
inference(flattening,[],[f892]) ).
fof(f894,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( inclusion_relation(X0) != X1
| ( ! [X4,X5] :
( ~ in(X5,X0)
| ~ in(X4,X0)
| ( ( ~ in(ordered_pair(X4,X5),X1)
| subset(X4,X5) )
& ( ~ subset(X4,X5)
| in(ordered_pair(X4,X5),X1) ) ) )
& relation_field(X1) = X0 ) )
& ( ? [X2,X3] :
( in(X3,X0)
& in(X2,X0)
& ( in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) ) )
| relation_field(X1) != X0
| X1 = inclusion_relation(X0) ) ) ),
inference(rectify,[],[f893]) ).
fof(f895,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( inclusion_relation(X0) != X1
| ( ! [X4,X5] :
( ~ in(X5,X0)
| ~ in(X4,X0)
| ( ( ~ in(ordered_pair(X4,X5),X1)
| subset(X4,X5) )
& ( ~ subset(X4,X5)
| in(ordered_pair(X4,X5),X1) ) ) )
& relation_field(X1) = X0 ) )
& ( ( in(sK104(X0,X1),X0)
& in(sK103(X0,X1),X0)
& ( in(ordered_pair(sK103(X0,X1),sK104(X0,X1)),X1)
| subset(sK103(X0,X1),sK104(X0,X1)) )
& ( ~ in(ordered_pair(sK103(X0,X1),sK104(X0,X1)),X1)
| ~ subset(sK103(X0,X1),sK104(X0,X1)) ) )
| relation_field(X1) != X0
| X1 = inclusion_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103,sK104]),skolemize(X2,sK103(X0,X1)),skolemize(X3,sK104(X0,X1))],[f894]) ).
fof(f950,plain,
! [X0] :
( ~ relation(X0)
| in(sK3(X0),relation_field(X0))
| reflexive(X0) ),
inference(cnf_transformation,[],[f692]) ).
fof(f951,plain,
! [X0] :
( ~ relation(X0)
| ~ in(ordered_pair(sK3(X0),sK3(X0)),X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f692]) ).
fof(f1070,plain,
~ reflexive(inclusion_relation(sK19)),
inference(cnf_transformation,[],[f732]) ).
fof(f1176,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f321]) ).
fof(f1280,plain,
! [X0,X1] :
( X0 != X1
| subset(X1,X0) ),
inference(cnf_transformation,[],[f815]) ).
fof(f1355,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f61]) ).
fof(f1487,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f1489,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ subset(X4,X5)
| in(ordered_pair(X4,X5),X1) ),
inference(cnf_transformation,[],[f895]) ).
fof(f1490,plain,
! [X0,X1] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| relation_field(X1) = X0 ),
inference(cnf_transformation,[],[f895]) ).
fof(f1621,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1355,f1176]) ).
fof(f1622,plain,
! [X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK3(X0),sK3(X0)),unordered_pair(sK3(X0),sK3(X0))),X0)
| reflexive(X0) ),
inference(definition_unfolding,[],[f951,f1621]) ).
fof(f1783,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ subset(X4,X5)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1) ),
inference(definition_unfolding,[],[f1489,f1621]) ).
fof(f1859,plain,
! [X1] : subset(X1,X1),
inference(equality_resolution,[],[f1280]) ).
fof(f1916,plain,
! [X0] :
( ~ relation(inclusion_relation(X0))
| relation_field(inclusion_relation(X0)) = X0 ),
inference(equality_resolution,[],[f1490]) ).
fof(f1917,plain,
! [X0,X4,X5] :
( ~ relation(inclusion_relation(X0))
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ subset(X4,X5)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),inclusion_relation(X0)) ),
inference(equality_resolution,[],[f1783]) ).
tcf(c_49,plain,
! [X0: $i] :
( reflexive(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK3(X0),sK3(X0)),unordered_pair(sK3(X0),sK3(X0))),X0) ),
inference(cnf_transformation,[],[f1622]) ).
tcf(c_50,plain,
! [X0: $i] :
( reflexive(X0)
| in(sK3(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f950]) ).
tcf(c_170,negated_conjecture,
~ reflexive(inclusion_relation(sK19)),
inference(cnf_transformation,[],[f1070]) ).
tcf(c_380,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f1859]) ).
tcf(c_583,plain,
! [X0: $i] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f1487]) ).
tcf(c_588,plain,
! [X0: $i] :
( ( relation_field(inclusion_relation(X0)) = X0 )
| ~ relation(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f1916]) ).
tcf(c_589,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),inclusion_relation(X1))
| ~ relation(inclusion_relation(X1))
| ~ subset(X0,X2)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1917]) ).
tcf(c_1157,plain,
! [X0: $i] : relation_field(inclusion_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_588,c_583,c_588]) ).
tcf(c_2792,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),inclusion_relation(X1))
| ~ subset(X0,X2)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_589,c_583]) ).
tcf(c_43644,plain,
! [X0: $i] :
( reflexive(inclusion_relation(X0))
| in(sK3(inclusion_relation(X0)),X0)
| ~ relation(inclusion_relation(X0)) ),
inference(superposition,[status(thm)],[c_1157,c_50]) ).
tcf(c_43666,plain,
! [X0: $i] :
( reflexive(inclusion_relation(X0))
| in(sK3(inclusion_relation(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43644,c_583]) ).
tcf(c_67842,plain,
! [X0: $i] :
( reflexive(inclusion_relation(X0))
| in(sK3(inclusion_relation(X0)),X0)
| ~ relation(inclusion_relation(X0)) ),
inference(superposition,[status(thm)],[c_1157,c_50]) ).
tcf(c_67864,plain,
! [X0: $i] :
( reflexive(inclusion_relation(X0))
| in(sK3(inclusion_relation(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67842,c_583]) ).
tcf(c_126100,plain,
! [X0: $i] :
( reflexive(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ in(sK3(inclusion_relation(X0)),X0)
| ~ subset(sK3(inclusion_relation(X0)),sK3(inclusion_relation(X0))) ),
inference(superposition,[status(thm)],[c_2792,c_49]) ).
tcf(c_126169,plain,
! [X0: $i] :
( reflexive(inclusion_relation(X0))
| ~ in(sK3(inclusion_relation(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_126100,c_583,c_380]) ).
tcf(c_179036,plain,
! [X0: $i] : reflexive(inclusion_relation(X0)),
inference(global_subsumption_just,[status(thm)],[c_67864,c_43666,c_126169]) ).
tcf(c_179039,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_170,c_179036]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU268+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 13:31:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 50.63/7.90 % SZS status Started for theBenchmark.p
% 50.63/7.90 % SZS status Theorem for theBenchmark.p
% 50.63/7.90
% 50.63/7.90 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 50.63/7.90
% 50.63/7.90 % ------ iProver source info
% 50.63/7.90
% 50.63/7.90 % git: date: 2026-07-19 20:42:38 +0200
% 50.63/7.90 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 50.63/7.90 % git: non_committed_changes: false
% 50.63/7.90
% 50.63/7.90 % ------ Parsing...
% 50.63/7.90 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 50.63/7.90
% 50.63/7.90 % ------ Preprocessing... sup_sim: 70 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 50.63/7.90
% 50.63/7.90 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 50.63/7.90
% 50.63/7.90 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 50.63/7.90 % ------ Proving...
% 50.63/7.90 % ------ Problem Properties
% 50.63/7.90
% 50.63/7.90 %
% 50.63/7.90 % clauses 604
% 50.63/7.90 % conjectures 1
% 50.63/7.90 % EPR 93
% 50.63/7.90 % Horn 474
% 50.63/7.90 % unary 75
% 50.63/7.90 % binary 166
% 50.63/7.90 % lits 1808
% 50.63/7.90 % lits eq 273
% 50.63/7.90 % fd_pure 0
% 50.63/7.90 % fd_pseudo 0
% 50.63/7.90 % fd_cond 18
% 50.63/7.90 % fd_pseudo_cond 96
% 50.63/7.90 % AC symbols 0
% 50.63/7.90
% 50.63/7.90 % ------ Schedule dynamic 5 is on
% 50.63/7.90
% 50.63/7.90 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 50.63/7.90
% 50.63/7.90
% 50.63/7.90 % ------
% 50.63/7.90 % Current options:
% 50.63/7.90 % ------
% 50.63/7.90
% 50.63/7.90
% 50.63/7.90 %
% 50.63/7.90
% 50.63/7.90 % ------ Proving...
% 50.63/7.90 %
% 50.63/7.90
% 50.63/7.90 % SZS status Theorem for theBenchmark.p
% 50.63/7.90
% 50.63/7.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 50.63/7.90
% 50.63/7.90
%------------------------------------------------------------------------------