%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU160+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.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 02:55:40 PM UTC 2026
% Result : Theorem 1.84s 1.25s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 14 unt; 1 def)
% Number of atoms : 111 ( 74 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 43 ~; 50 |; 10 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 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 : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 37 ( 1 sgn 31 !; 6 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f5,conjecture,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f8,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f1]) ).
fof(f9,plain,
? [X0,X1] :
( subset(X0,singleton(X1))
<~> ( X0 = singleton(X1)
| X0 = empty_set ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
? [X0,X1] :
( ( subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ~ subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f13,plain,
? [X0,X1] :
( ( subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ~ subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
( ( subset(sK2,singleton(sK3))
| sK2 = singleton(sK3)
| empty_set = sK2 )
& ( ~ subset(sK2,singleton(sK3))
| ( sK2 != singleton(sK3)
& empty_set != sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f16,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f21,plain,
( subset(sK2,singleton(sK3))
| sK2 = singleton(sK3)
| empty_set = sK2 ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
( ~ subset(sK2,singleton(sK3))
| sK2 != singleton(sK3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
( ~ subset(sK2,singleton(sK3))
| empty_set != sK2 ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X0,X1] :
( empty_set != X0
| subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X1] : subset(empty_set,singleton(X1)),
inference(equality_resolution,[],[f26]) ).
tcf(c_49,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f17]) ).
tcf(c_53,negated_conjecture,
( ~ subset(sK2,singleton(sK3))
| ( empty_set != sK2 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_54,negated_conjecture,
( ~ subset(sK2,singleton(sK3))
| ( singleton(sK3) != sK2 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_55,negated_conjecture,
( subset(sK2,singleton(sK3))
| ( empty_set = sK2 )
| ( singleton(sK3) = sK2 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_56,plain,
! [X0: $i] : subset(empty_set,singleton(X0)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( singleton(X1) = X0 )
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_129,plain,
! [X0: $i] :
( ( X0 != sK2 )
| ( singleton(sK3) != sK2 )
| ( singleton(sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_54]) ).
tcf(c_130,plain,
singleton(sK3) != sK2,
inference(unflattening,[status(thm)],[c_129]) ).
tcf(c_139,plain,
! [X0: $i] :
( ( empty_set != sK2 )
| ( singleton(X0) != singleton(sK3) ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_56]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( ( empty_set = sK2 )
| ( X1 = empty_set )
| ( singleton(sK3) = sK2 )
| ( singleton(X0) = X1 )
| ( X1 != sK2 )
| ( singleton(X0) != singleton(sK3) ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_58]) ).
tcf(c_148,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( empty_set = sK2 )
| ( singleton(sK3) = sK2 )
| ( singleton(X0) = sK2 )
| ( singleton(X0) != singleton(sK3) ) ),
inference(unflattening,[status(thm)],[c_147]) ).
tcf(c_150,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( singleton(X0) = sK2 )
| ( singleton(X0) != singleton(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_148,c_130,c_139,c_148]) ).
tcf(c_211,definition,
iPr_def_10 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_212,plain,
! [X0: $i] :
( ( sK2 = empty_set )
| ( singleton(X0) = sK2 )
| ( singleton(X0) != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_150,c_211]) ).
tcf(c_213,plain,
! [X0: $i] :
( ( empty_set != sK2 )
| ( singleton(X0) != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_139]) ).
tcf(c_214,plain,
iPr_def_10 != sK2,
inference(demodulation,[status(thm)],[c_130]) ).
tcf(c_311,plain,
( ( empty_set = sK2 )
| ( singleton(sK3) = sK2 ) ),
inference(superposition,[status(thm)],[c_211,c_212]) ).
tcf(c_312,plain,
empty_set != sK2,
inference(superposition,[status(thm)],[c_211,c_213]) ).
tcf(c_313,plain,
singleton(sK3) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_311,c_312]) ).
tcf(c_314,plain,
sK2 = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_313,c_211]) ).
tcf(c_316,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_214,c_314]) ).
tcf(c_317,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_316]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU160+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:59:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 0.12/0.39
% 0.12/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.39
% 0.12/0.39 % Detected problem language: tptp
% 0.12/0.40 % Proving...
% 1.84/1.25 % SZS status Started for theBenchmark.p
% 1.84/1.25 % SZS status Theorem for theBenchmark.p
% 1.84/1.25
% 1.84/1.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.84/1.25
% 1.84/1.25 % ------ iProver source info
% 1.84/1.25
% 1.84/1.25 % git: date: 2026-07-19 20:42:38 +0200
% 1.84/1.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.84/1.25 % git: non_committed_changes: false
% 1.84/1.25
% 1.84/1.25 % ------ Parsing...
% 1.84/1.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.84/1.25
% 1.84/1.25 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.84/1.25
% 1.84/1.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.84/1.25
% 1.84/1.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.84/1.25 % ------ Proving...
% 1.84/1.25 % ------ Problem Properties
% 1.84/1.25
% 1.84/1.25 %
% 1.84/1.25 % clauses 7
% 1.84/1.25 % conjectures 0
% 1.84/1.25 % EPR 4
% 1.84/1.25 % Horn 6
% 1.84/1.25 % unary 5
% 1.84/1.25 % binary 1
% 1.84/1.25 % lits 10
% 1.84/1.25 % lits eq 7
% 1.84/1.25 % fd_pure 0
% 1.84/1.25 % fd_pseudo 0
% 1.84/1.25 % fd_cond 0
% 1.84/1.25 % fd_pseudo_cond 0
% 1.84/1.25 % AC symbols 0
% 1.84/1.25
% 1.84/1.25 % ------ Schedule dynamic 5 is on
% 1.84/1.25
% 1.84/1.25 % ------ no conjectures: strip conj schedule
% 1.84/1.25
% 1.84/1.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.84/1.25
% 1.84/1.25
% 1.84/1.25 % ------
% 1.84/1.25 % Current options:
% 1.84/1.25 % ------
% 1.84/1.25
% 1.84/1.25
% 1.84/1.25 %
% 1.84/1.25
% 1.84/1.25 % ------ Proving...
% 1.84/1.25 %
% 1.84/1.25
% 1.84/1.25 % SZS status Theorem for theBenchmark.p
% 1.84/1.25
% 1.84/1.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.84/1.26
% 1.84/1.26
%------------------------------------------------------------------------------