%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU153+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 : n001.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 02:55:38 PM UTC 2026
% Result : Theorem 3.73s 1.47s
% Output : CNFRefutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 20 unt; 1 def)
% Number of atoms : 71 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 22 ~; 14 |; 7 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 37 !; 2 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f32,conjecture,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f56,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f68,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f73,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f93,plain,
? [X0,X1] :
( in(X0,X1)
& disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f153,plain,
( in(sK8,sK9)
& disjoint(singleton(sK8),sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f93]) ).
fof(f154,plain,
! [X0,X1] :
( ( ~ subset(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f162,plain,
! [X0,X1] :
( ( empty_set != set_difference(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f165,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 )
& ( set_difference(X0,X1) != X0
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f220,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f30]) ).
fof(f222,plain,
in(sK8,sK9),
inference(cnf_transformation,[],[f153]) ).
fof(f223,plain,
disjoint(singleton(sK8),sK9),
inference(cnf_transformation,[],[f153]) ).
fof(f225,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f154]) ).
fof(f252,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f162]) ).
fof(f267,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f68]) ).
fof(f272,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 ),
inference(cnf_transformation,[],[f165]) ).
fof(f292,plain,
! [X0] : empty_set != unordered_pair(X0,X0),
inference(definition_unfolding,[],[f220,f267]) ).
fof(f294,plain,
disjoint(unordered_pair(sK8,sK8),sK9),
inference(definition_unfolding,[],[f223,f267]) ).
fof(f295,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f225,f267]) ).
tcf(c_103,plain,
! [X0: $i] : unordered_pair(X0,X0) != empty_set,
inference(cnf_transformation,[],[f292]) ).
tcf(c_105,negated_conjecture,
disjoint(unordered_pair(sK8,sK8),sK9),
inference(cnf_transformation,[],[f294]) ).
tcf(c_106,negated_conjecture,
in(sK8,sK9),
inference(cnf_transformation,[],[f222]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f295]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = X0 )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_2416,definition,
iPr_def_10 = unordered_pair(sK8,sK8),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2417,negated_conjecture,
in(sK8,sK9),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_2418,negated_conjecture,
disjoint(iPr_def_10,sK9),
inference(demodulation,[status(thm)],[c_105,c_2416]) ).
tcf(c_4040,plain,
empty_set != iPr_def_10,
inference(superposition,[status(thm)],[c_2416,c_103]) ).
tcf(c_4390,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ~ in(sK8,X0) ),
inference(superposition,[status(thm)],[c_2416,c_107]) ).
tcf(c_4503,plain,
subset(iPr_def_10,sK9),
inference(superposition,[status(thm)],[c_2417,c_4390]) ).
tcf(c_4650,plain,
set_difference(iPr_def_10,sK9) = empty_set,
inference(superposition,[status(thm)],[c_4503,c_134]) ).
tcf(c_4879,plain,
set_difference(iPr_def_10,sK9) = iPr_def_10,
inference(superposition,[status(thm)],[c_2418,c_154]) ).
tcf(c_4885,plain,
empty_set = iPr_def_10,
inference(demodulation,[status(thm)],[c_4650,c_4879]) ).
tcf(c_4886,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4885,c_4040]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU153+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.55 % Computer : n001.cluster.edu
% 0.12/0.55 % Model : x86_64 x86_64
% 0.12/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.55 % Memory : 8046.5625MB
% 0.12/0.55 % OS : Linux 6.8.0-71-generic
% 0.12/0.56 % CPULimit : 300
% 0.12/0.56 % WCLimit : 300
% 0.12/0.56 % DateTime : Thu Sep 24 13:04:08 UTC 2026
% 0.12/0.56 % CPUTime :
% 0.12/0.56 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.59 Running first-order theorem proving
% 0.16/0.59 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
% 0.16/0.60
% 0.16/0.60 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.60
% 0.16/0.60 % Detected problem language: tptp
% 0.16/0.62 % Proving...
% 3.73/1.47 % SZS status Started for theBenchmark.p
% 3.73/1.47 % SZS status Theorem for theBenchmark.p
% 3.73/1.47
% 3.73/1.47 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.73/1.47
% 3.73/1.47 % ------ iProver source info
% 3.73/1.47
% 3.73/1.47 % git: date: 2026-07-19 20:42:38 +0200
% 3.73/1.47 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.73/1.47 % git: non_committed_changes: false
% 3.73/1.47
% 3.73/1.47 % ------ Parsing...
% 3.73/1.47 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.73/1.47
% 3.73/1.47 % ------ 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 %
% 3.73/1.47
% 3.73/1.47 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.73/1.47
% 3.73/1.47 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.73/1.47 % ------ Proving...
% 3.73/1.47 % ------ Problem Properties
% 3.73/1.47
% 3.73/1.47 %
% 3.73/1.47 % clauses 100
% 3.73/1.47 % conjectures 2
% 3.73/1.47 % EPR 23
% 3.73/1.47 % Horn 78
% 3.73/1.47 % unary 26
% 3.73/1.47 % binary 40
% 3.73/1.47 % lits 212
% 3.73/1.47 % lits eq 65
% 3.73/1.47 % fd_pure 0
% 3.73/1.47 % fd_pseudo 0
% 3.73/1.47 % fd_cond 3
% 3.73/1.47 % fd_pseudo_cond 26
% 3.73/1.47 % AC symbols 0
% 3.73/1.47
% 3.73/1.47 % ------ Schedule dynamic 5 is on
% 3.73/1.47
% 3.73/1.47 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.73/1.47
% 3.73/1.47
% 3.73/1.47 % ------
% 3.73/1.47 % Current options:
% 3.73/1.47 % ------
% 3.73/1.47
% 3.73/1.47
% 3.73/1.47 %
% 3.73/1.47
% 3.73/1.47 % ------ Proving...
% 3.73/1.47 %
% 3.73/1.47
% 3.73/1.47 % SZS status Theorem for theBenchmark.p
% 3.73/1.47
% 3.73/1.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.73/1.47
% 3.73/1.47
%------------------------------------------------------------------------------