%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU255+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 02:56:22 PM UTC 2026
% Result : Theorem 1.97s 1.28s
% Output : CNFRefutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 64 ( 21 unt; 1 def)
% Number of atoms : 228 ( 24 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 208 ( 86 ~; 87 |; 22 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 82 !; 8 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f11,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f20,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> ! [X1,X2] :
( ( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_wellord1) ).
fof(f26,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f28,conjecture,
! [X0,X1] :
( relation(X1)
=> ( antisymmetric(X1)
=> antisymmetric(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord1) ).
fof(f29,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( antisymmetric(X1)
=> antisymmetric(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f43,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f44,plain,
! [X0] :
( ~ relation(X0)
| ( antisymmetric(X0)
<=> ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f45,plain,
! [X0] :
( ~ relation(X0)
| ( antisymmetric(X0)
<=> ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f48,plain,
? [X0,X1] :
( relation(X1)
& antisymmetric(X1)
& ~ antisymmetric(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f49,plain,
? [X0,X1] :
( relation(X1)
& antisymmetric(X1)
& ~ antisymmetric(relation_restriction(X1,X0)) ),
inference(flattening,[],[f48]) ).
fof(f56,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ antisymmetric(X0)
| ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) )
& ( ? [X1,X2] :
( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0)
& X1 != X2 )
| antisymmetric(X0) ) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f57,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ antisymmetric(X0)
| ! [X3,X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0)
| X3 = X4 ) )
& ( ? [X1,X2] :
( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0)
& X1 != X2 )
| antisymmetric(X0) ) ) ),
inference(rectify,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ antisymmetric(X0)
| ! [X3,X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0)
| X3 = X4 ) )
& ( ( in(ordered_pair(sK2(X0),sK1(X0)),X0)
& in(ordered_pair(sK1(X0),sK2(X0)),X0)
& sK1(X0) != sK2(X0) )
| antisymmetric(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f57]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ) ) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
( relation(sK9)
& antisymmetric(sK9)
& ~ antisymmetric(relation_restriction(sK9,sK8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f49]) ).
fof(f71,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f73,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f75,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f80,plain,
! [X3,X0,X4] :
( ~ relation(X0)
| ~ antisymmetric(X0)
| ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0)
| X3 = X4 ),
inference(cnf_transformation,[],[f58]) ).
fof(f81,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK2(X0),sK1(X0)),X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f82,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK1(X0),sK2(X0)),X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f83,plain,
! [X0] :
( ~ relation(X0)
| sK1(X0) != sK2(X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_restriction(X2,X1))
| in(X0,X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f97,plain,
relation(sK9),
inference(cnf_transformation,[],[f66]) ).
fof(f98,plain,
antisymmetric(sK9),
inference(cnf_transformation,[],[f66]) ).
fof(f99,plain,
~ antisymmetric(relation_restriction(sK9,sK8)),
inference(cnf_transformation,[],[f66]) ).
fof(f106,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK1(X0),sK2(X0)),singleton(sK1(X0))),X0)
| antisymmetric(X0) ),
inference(definition_unfolding,[],[f82,f73]) ).
fof(f107,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK2(X0),sK1(X0)),singleton(sK2(X0))),X0)
| antisymmetric(X0) ),
inference(definition_unfolding,[],[f81,f73]) ).
fof(f108,plain,
! [X3,X0,X4] :
( ~ relation(X0)
| ~ antisymmetric(X0)
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X0)
| X3 = X4 ),
inference(definition_unfolding,[],[f80,f73,f73]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f71]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_59,plain,
! [X0: $i] :
( antisymmetric(X0)
| ~ relation(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_60,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK1(X0),sK2(X0)),singleton(sK1(X0))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_61,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK2(X0),sK1(X0)),singleton(sK2(X0))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ antisymmetric(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ relation(X1)
| ~ in(X0,relation_restriction(X1,X2)) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_76,negated_conjecture,
~ antisymmetric(relation_restriction(sK9,sK8)),
inference(cnf_transformation,[],[f99]) ).
tcf(c_77,negated_conjecture,
antisymmetric(sK9),
inference(cnf_transformation,[],[f98]) ).
tcf(c_78,negated_conjecture,
relation(sK9),
inference(cnf_transformation,[],[f97]) ).
tcf(c_285,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(singleton(sK2(X0)),unordered_pair(sK1(X0),sK2(X0))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_61,c_51]) ).
tcf(c_295,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(singleton(sK1(X0)),unordered_pair(sK1(X0),sK2(X0))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_60,c_51]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ antisymmetric(X2)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_62,c_51]) ).
tcf(c_792,definition,
iPr_def_10 = relation_restriction(sK9,sK8),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_793,negated_conjecture,
relation(sK9),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_794,negated_conjecture,
antisymmetric(sK9),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_795,negated_conjecture,
~ antisymmetric(iPr_def_10),
inference(demodulation,[status(thm)],[c_76,c_792]) ).
tcf(c_1147,plain,
( relation(iPr_def_10)
| ~ relation(sK9) ),
inference(superposition,[status(thm)],[c_792,c_54]) ).
tcf(c_1148,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1147,c_793]) ).
tcf(c_1205,plain,
! [X0: $i] :
( in(X0,sK9)
| ~ relation(sK9)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_792,c_73]) ).
tcf(c_1206,plain,
! [X0: $i] :
( in(X0,sK9)
| ~ in(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1205,c_793]) ).
tcf(c_1330,plain,
( antisymmetric(iPr_def_10)
| in(unordered_pair(singleton(sK2(iPr_def_10)),unordered_pair(sK1(iPr_def_10),sK2(iPr_def_10))),sK9)
| ~ relation(iPr_def_10) ),
inference(superposition,[status(thm)],[c_285,c_1206]) ).
tcf(c_1334,plain,
in(unordered_pair(singleton(sK2(iPr_def_10)),unordered_pair(sK1(iPr_def_10),sK2(iPr_def_10))),sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_1330,c_795,c_1148]) ).
tcf(c_1360,plain,
( antisymmetric(iPr_def_10)
| in(unordered_pair(singleton(sK1(iPr_def_10)),unordered_pair(sK1(iPr_def_10),sK2(iPr_def_10))),sK9)
| ~ relation(iPr_def_10) ),
inference(superposition,[status(thm)],[c_295,c_1206]) ).
tcf(c_1361,plain,
in(unordered_pair(singleton(sK1(iPr_def_10)),unordered_pair(sK1(iPr_def_10),sK2(iPr_def_10))),sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_1360,c_795,c_1148]) ).
tcf(c_1437,plain,
( antisymmetric(iPr_def_10)
| ~ relation(iPr_def_10)
| ( sK1(iPr_def_10) != sK2(iPr_def_10) ) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1497,plain,
( ( sK1(iPr_def_10) = sK2(iPr_def_10) )
| ~ antisymmetric(sK9)
| ~ relation(sK9)
| ~ in(unordered_pair(singleton(sK2(iPr_def_10)),unordered_pair(sK2(iPr_def_10),sK1(iPr_def_10))),sK9) ),
inference(superposition,[status(thm)],[c_1361,c_313]) ).
tcf(c_1498,plain,
( ( sK1(iPr_def_10) = sK2(iPr_def_10) )
| ~ in(unordered_pair(singleton(sK2(iPr_def_10)),unordered_pair(sK2(iPr_def_10),sK1(iPr_def_10))),sK9) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1497,c_794,c_793]) ).
tcf(c_1501,plain,
~ in(unordered_pair(singleton(sK2(iPr_def_10)),unordered_pair(sK2(iPr_def_10),sK1(iPr_def_10))),sK9),
inference(global_subsumption_just,[status(thm)],[c_1498,c_795,c_1148,c_1437,c_1498]) ).
tcf(c_1503,plain,
~ in(unordered_pair(singleton(sK2(iPr_def_10)),unordered_pair(sK1(iPr_def_10),sK2(iPr_def_10))),sK9),
inference(demodulation,[status(thm)],[c_1501,c_51]) ).
tcf(c_1504,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1503,c_1334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU255+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 13:20:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.97/1.28 % SZS status Started for theBenchmark.p
% 1.97/1.28 % SZS status Theorem for theBenchmark.p
% 1.97/1.28
% 1.97/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.97/1.28
% 1.97/1.28 % ------ iProver source info
% 1.97/1.28
% 1.97/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.97/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.97/1.28 % git: non_committed_changes: false
% 1.97/1.28
% 1.97/1.28 % ------ Parsing...
% 1.97/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.97/1.28
% 1.97/1.28 % ------ Preprocessing... sup_sim: 4 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 1.97/1.28
% 1.97/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.97/1.28
% 1.97/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.97/1.28 % ------ Proving...
% 1.97/1.28 % ------ Problem Properties
% 1.97/1.28
% 1.97/1.28 %
% 1.97/1.28 % clauses 30
% 1.97/1.28 % conjectures 3
% 1.97/1.28 % EPR 14
% 1.97/1.28 % Horn 27
% 1.97/1.28 % unary 16
% 1.97/1.28 % binary 6
% 1.97/1.28 % lits 55
% 1.97/1.28 % lits eq 10
% 1.97/1.28 % fd_pure 0
% 1.97/1.28 % fd_pseudo 0
% 1.97/1.28 % fd_cond 1
% 1.97/1.28 % fd_pseudo_cond 2
% 1.97/1.28 % AC symbols 0
% 1.97/1.28
% 1.97/1.28 % ------ Schedule dynamic 5 is on
% 1.97/1.28
% 1.97/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.97/1.28
% 1.97/1.28
% 1.97/1.28 % ------
% 1.97/1.28 % Current options:
% 1.97/1.28 % ------
% 1.97/1.28
% 1.97/1.28
% 1.97/1.28 %
% 1.97/1.28
% 1.97/1.28 % ------ Proving...
% 1.97/1.28 %
% 1.97/1.28
% 1.97/1.28 % SZS status Theorem for theBenchmark.p
% 1.97/1.28
% 1.97/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.97/1.28
% 1.97/1.28
%------------------------------------------------------------------------------