%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU186+2 : 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 : n003.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 02:55:48 PM UTC 2026
% Result : Theorem 0.97s 1.08s
% Output : CNFRefutation 0.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 66 ( 26 unt; 0 def)
% Number of atoms : 184 ( 61 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 205 ( 87 ~; 81 |; 25 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 141 ( 0 sgn 121 !; 20 ?; 29 :)
% 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(f8,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : X1 != ordered_pair(X2,X3)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f11,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f23,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f25,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(f147,conjecture,
! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f148,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f147]) ).
fof(f153,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f180,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f185,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f276,plain,
? [X0] :
( relation(X0)
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& empty_set != X0 ),
inference(ennf_transformation,[],[f148]) ).
fof(f277,plain,
? [X0] :
( relation(X0)
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& empty_set != X0 ),
inference(flattening,[],[f276]) ).
fof(f295,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) )
& ( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
| relation(X0) ) ),
inference(nnf_transformation,[],[f180]) ).
fof(f296,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) ) )
& ( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
| relation(X0) ) ),
inference(rectify,[],[f295]) ).
fof(f297,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X4] :
( ordered_pair(sK1(X4),sK2(X4)) = X4
| ~ in(X4,X0) ) )
& ( ( ! [X2,X3] : ordered_pair(X2,X3) != sK0(X0)
& in(sK0(X0),X0) )
| relation(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0(X0)),skolemize(X5,sK1(X4)),skolemize(X6,sK2(X4))],[f296]) ).
fof(f304,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f305,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f304]) ).
fof(f306,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK7(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f305]) ).
fof(f339,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f185]) ).
fof(f340,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X7,X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X4,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f339]) ).
fof(f341,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK27(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK25(X0,X1),X1)
| in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0) )
& ( ~ in(sK25(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK25(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27]),skolemize(X2,sK25(X0,X1)),skolemize(X4,sK26(X0,X1)),skolemize(X7,sK27(X0,X5))],[f340]) ).
fof(f382,plain,
( relation(sK47)
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),sK47)
& empty_set != sK47 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(X0,sK47)],[f277]) ).
fof(f389,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f395,plain,
! [X0,X4] :
( ~ relation(X0)
| ordered_pair(sK1(X4),sK2(X4)) = X4
| ~ in(X4,X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f411,plain,
! [X0] :
( in(sK7(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f306]) ).
fof(f466,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK27(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f468,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK25(X0,X1),X1)
| in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f341]) ).
fof(f471,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f25]) ).
fof(f625,plain,
relation(sK47),
inference(cnf_transformation,[],[f382]) ).
fof(f626,plain,
! [X2,X1] : ~ in(ordered_pair(X1,X2),sK47),
inference(cnf_transformation,[],[f382]) ).
fof(f627,plain,
empty_set != sK47,
inference(cnf_transformation,[],[f382]) ).
fof(f633,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f153]) ).
fof(f650,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f471,f633]) ).
fof(f653,plain,
! [X0,X4] :
( ~ relation(X0)
| unordered_pair(unordered_pair(sK1(X4),sK2(X4)),unordered_pair(sK1(X4),sK1(X4))) = X4
| ~ in(X4,X0) ),
inference(definition_unfolding,[],[f395,f650]) ).
fof(f673,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK25(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK26(X0,X1),sK26(X0,X1))),X0)
| relation_rng(X0) = X1 ),
inference(definition_unfolding,[],[f468,f650]) ).
fof(f675,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(sK27(X0,X5),X5),unordered_pair(sK27(X0,X5),sK27(X0,X5))),X0) ),
inference(definition_unfolding,[],[f466,f650]) ).
fof(f727,plain,
! [X2,X1] : ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),sK47),
inference(definition_unfolding,[],[f626,f650]) ).
fof(f773,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK27(X0,X5),X5),unordered_pair(sK27(X0,X5),sK27(X0,X5))),X0) ),
inference(equality_resolution,[],[f675]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f389]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK1(X0),sK2(X0)),unordered_pair(sK1(X0),sK1(X0))) = X0 )
| ~ relation(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f653]) ).
tcf(c_73,plain,
! [X0: $i] :
( in(sK7(X0),X0)
| ( X0 = empty_set ) ),
inference(cnf_transformation,[],[f411]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i] :
( in(sK25(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK26(X0,X1),sK26(X0,X1))),X0)
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f673]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK27(X1,X0),X0),unordered_pair(sK27(X1,X0),sK27(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f773]) ).
tcf(c_286,negated_conjecture,
empty_set != sK47,
inference(cnf_transformation,[],[f627]) ).
tcf(c_287,negated_conjecture,
! [X0: $i,X1: $i] : ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK47),
inference(cnf_transformation,[],[f727]) ).
tcf(c_288,negated_conjecture,
relation(sK47),
inference(cnf_transformation,[],[f625]) ).
tcf(c_3095,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK1(X0),sK1(X0)),unordered_pair(sK1(X0),sK2(X0))) = X0 )
| ~ relation(X1)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_60,c_52]) ).
tcf(c_3133,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK27(X1,X0)),unordered_pair(sK27(X1,X0),sK27(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(demodulation,[status(thm)],[c_132,c_52]) ).
tcf(c_3236,plain,
! [X0: $i,X1: $i] :
( in(sK25(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK26(X0,X1),sK26(X0,X1))),X0)
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_130,c_52]) ).
tcf(c_6354,negated_conjecture,
relation(sK47),
inference(demodulation,[status(thm)],[c_288]) ).
tcf(c_6355,negated_conjecture,
! [X0: $i,X1: $i] : ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK47),
inference(demodulation,[status(thm)],[c_287]) ).
tcf(c_6356,negated_conjecture,
empty_set != sK47,
inference(demodulation,[status(thm)],[c_286]) ).
tcf(c_10611,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),sK47),
inference(superposition,[status(thm)],[c_52,c_6355]) ).
tcf(c_10615,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),sK47),
inference(superposition,[status(thm)],[c_52,c_6355]) ).
tcf(c_11057,plain,
! [X0: $i] :
( ~ relation(sK47)
| ~ in(X0,relation_rng(sK47)) ),
inference(superposition,[status(thm)],[c_3133,c_10611]) ).
tcf(c_11058,plain,
! [X0: $i] : ~ in(X0,relation_rng(sK47)),
inference(forward_subsumption_resolution,[status(thm)],[c_11057,c_6354]) ).
tcf(c_11198,plain,
relation_rng(sK47) = empty_set,
inference(superposition,[status(thm)],[c_73,c_11058]) ).
tcf(c_11398,plain,
! [X0: $i] :
( in(sK25(sK47,X0),X0)
| ( relation_rng(sK47) = X0 )
| ~ relation(sK47) ),
inference(superposition,[status(thm)],[c_3236,c_10611]) ).
tcf(c_11399,plain,
! [X0: $i] :
( in(sK25(sK47,X0),X0)
| ( X0 = empty_set )
| ~ relation(sK47) ),
inference(light_normalisation,[status(thm)],[c_11398,c_11198]) ).
tcf(c_11400,plain,
! [X0: $i] :
( in(sK25(sK47,X0),X0)
| ( X0 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11399,c_6354]) ).
tcf(c_11558,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(sK1(sK25(sK47,X0)),sK1(sK25(sK47,X0))),unordered_pair(sK1(sK25(sK47,X0)),sK2(sK25(sK47,X0)))) = sK25(sK47,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_11400,c_3095]) ).
tcf(c_11633,plain,
( ( empty_set = sK47 )
| ( unordered_pair(unordered_pair(sK1(sK25(sK47,sK47)),sK1(sK25(sK47,sK47))),unordered_pair(sK1(sK25(sK47,sK47)),sK2(sK25(sK47,sK47)))) = sK25(sK47,sK47) ) ),
inference(superposition,[status(thm)],[c_6354,c_11558]) ).
tcf(c_11635,plain,
unordered_pair(unordered_pair(sK1(sK25(sK47,sK47)),sK1(sK25(sK47,sK47))),unordered_pair(sK1(sK25(sK47,sK47)),sK2(sK25(sK47,sK47)))) = sK25(sK47,sK47),
inference(forward_subsumption_resolution,[status(thm)],[c_11633,c_6356]) ).
tcf(c_11670,plain,
~ in(sK25(sK47,sK47),sK47),
inference(superposition,[status(thm)],[c_11635,c_10615]) ).
tcf(c_11979,plain,
empty_set = sK47,
inference(superposition,[status(thm)],[c_11400,c_11670]) ).
tcf(c_11980,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11979,c_6356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU186+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 13:07:52 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 0.97/1.08 % SZS status Started for theBenchmark.p
% 0.97/1.08 % SZS status Theorem for theBenchmark.p
% 0.97/1.08
% 0.97/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.97/1.08
% 0.97/1.08 % ------ iProver source info
% 0.97/1.08
% 0.97/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 0.97/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.97/1.08 % git: non_committed_changes: false
% 0.97/1.08
% 0.97/1.08 % ------ Parsing...
% 0.97/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.97/1.08
% 0.97/1.08 % ------ Preprocessing... sup_sim: 20 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.97/1.08
% 0.97/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.97/1.08
% 0.97/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.97/1.08 % ------ Proving...
% 0.97/1.08 % ------ Problem Properties
% 0.97/1.08
% 0.97/1.08 %
% 0.97/1.08 % clauses 229
% 0.97/1.08 % conjectures 3
% 0.97/1.08 % EPR 35
% 0.97/1.08 % Horn 179
% 0.97/1.08 % unary 42
% 0.97/1.08 % binary 84
% 0.97/1.08 % lits 568
% 0.97/1.08 % lits eq 126
% 0.97/1.08 % fd_pure 0
% 0.97/1.08 % fd_pseudo 0
% 0.97/1.08 % fd_cond 10
% 0.97/1.08 % fd_pseudo_cond 50
% 0.97/1.08 % AC symbols 0
% 0.97/1.08
% 0.97/1.08 % ------ Schedule dynamic 5 is on
% 0.97/1.08
% 0.97/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.97/1.08
% 0.97/1.08
% 0.97/1.08 % ------
% 0.97/1.08 % Current options:
% 0.97/1.08 % ------
% 0.97/1.08
% 0.97/1.08
% 0.97/1.08 %
% 0.97/1.08
% 0.97/1.08 % ------ Proving...
% 0.97/1.08 %
% 0.97/1.08
% 0.97/1.08 % SZS status Theorem for theBenchmark.p
% 0.97/1.08
% 0.97/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.97/1.08
% 0.97/1.08
%------------------------------------------------------------------------------