%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU143+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 : 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 02:55:34 PM UTC 2026
% Result : Theorem 3.50s 1.28s
% Output : CNFRefutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 18 unt; 1 def)
% Number of atoms : 103 ( 65 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 115 ( 46 ~; 43 |; 23 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 48 !; 6 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f9,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f28,conjecture,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f29,negated_conjecture,
~ ! [X0] : singleton(X0) != empty_set,
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f59,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f80,plain,
? [X0] : singleton(X0) = empty_set,
inference(ennf_transformation,[],[f29]) ).
fof(f108,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f109,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f108]) ).
fof(f110,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK1(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f109]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f111]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(rectify,[],[f112]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ( ( in(sK2(X0,X1,X2),X2)
| sK2(X0,X1,X2) = X1
| sK2(X0,X1,X2) = X0 )
& ( ~ in(sK2(X0,X1,X2),X2)
| ( sK2(X0,X1,X2) != X1
& sK2(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f113]) ).
fof(f131,plain,
empty_set = singleton(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f80]) ).
fof(f153,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f156,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X1 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f191,plain,
empty_set = singleton(sK7),
inference(cnf_transformation,[],[f131]) ).
fof(f227,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f59]) ).
fof(f249,plain,
empty_set = unordered_pair(sK7,sK7),
inference(definition_unfolding,[],[f191,f227]) ).
fof(f262,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f153]) ).
fof(f265,plain,
! [X2,X0,X4] :
( unordered_pair(X0,X4) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f156]) ).
fof(f266,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f265]) ).
tcf(c_62,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f262]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f266]) ).
tcf(c_99,negated_conjecture,
unordered_pair(sK7,sK7) = empty_set,
inference(cnf_transformation,[],[f249]) ).
tcf(c_2021,definition,
iPr_def_10 = unordered_pair(sK7,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2022,negated_conjecture,
iPr_def_10 = empty_set,
inference(demodulation,[status(thm)],[c_99,c_2021]) ).
tcf(c_3354,plain,
! [X0: $i] : ~ in(X0,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_62,c_2022]) ).
tcf(c_3364,plain,
in(sK7,iPr_def_10),
inference(superposition,[status(thm)],[c_2021,c_67]) ).
tcf(c_3366,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3364,c_3354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU143+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:57:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 3.50/1.28 % SZS status Started for theBenchmark.p
% 3.50/1.28 % SZS status Theorem for theBenchmark.p
% 3.50/1.28
% 3.50/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.50/1.28
% 3.50/1.28 % ------ iProver source info
% 3.50/1.28
% 3.50/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.50/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.50/1.28 % git: non_committed_changes: false
% 3.50/1.28
% 3.50/1.28 % ------ Parsing...
% 3.50/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.50/1.28
% 3.50/1.28 % ------ Preprocessing... sup_sim: 3 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 %
% 3.50/1.28
% 3.50/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.50/1.28
% 3.50/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.50/1.28 % ------ Proving...
% 3.50/1.28 % ------ Problem Properties
% 3.50/1.28
% 3.50/1.28 %
% 3.50/1.28 % clauses 84
% 3.50/1.28 % conjectures 1
% 3.50/1.28 % EPR 22
% 3.50/1.28 % Horn 66
% 3.50/1.28 % unary 23
% 3.50/1.28 % binary 32
% 3.50/1.28 % lits 178
% 3.50/1.28 % lits eq 51
% 3.50/1.28 % fd_pure 0
% 3.50/1.28 % fd_pseudo 0
% 3.50/1.28 % fd_cond 3
% 3.50/1.28 % fd_pseudo_cond 19
% 3.50/1.28 % AC symbols 0
% 3.50/1.28
% 3.50/1.28 % ------ Schedule dynamic 5 is on
% 3.50/1.28
% 3.50/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.50/1.28
% 3.50/1.28
% 3.50/1.28 % ------
% 3.50/1.28 % Current options:
% 3.50/1.28 % ------
% 3.50/1.28
% 3.50/1.28
% 3.50/1.28 %
% 3.50/1.28
% 3.50/1.28 % ------ Proving...
% 3.50/1.28 %
% 3.50/1.28
% 3.50/1.28 % SZS status Theorem for theBenchmark.p
% 3.50/1.28
% 3.50/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.50/1.28
% 3.50/1.28
%------------------------------------------------------------------------------