%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU148+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 : n014.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 02:55:36 PM UTC 2026
% Result : Theorem 0.45s 1.29s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 18 unt; 2 def)
% Number of atoms : 115 ( 69 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 109 ( 45 ~; 44 |; 15 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 49 !; 4 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
? [X0,X1] :
( subset(singleton(X0),singleton(X1))
& X0 != X1 ),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f15]) ).
fof(f17,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,[],[f5]) ).
fof(f18,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,[],[f17]) ).
fof(f21,plain,
( subset(singleton(sK3),singleton(sK4))
& sK3 != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f13]) ).
fof(f23,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f16]) ).
fof(f24,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
subset(singleton(sK3),singleton(sK4)),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f24]) ).
fof(f38,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f37]) ).
fof(f39,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f23]) ).
tcf(c_52,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_55,plain,
! [X0: $i] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f28]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( singleton(X1) = X0 )
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_62,negated_conjecture,
sK3 != sK4,
inference(cnf_transformation,[],[f36]) ).
tcf(c_63,negated_conjecture,
subset(singleton(sK3),singleton(sK4)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ( singleton(X0) = X1 )
| ( singleton(sK3) != X1 )
| ( singleton(X0) != singleton(sK4) ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_63]) ).
tcf(c_164,plain,
! [X0: $i] :
( ( singleton(sK3) = empty_set )
| ( singleton(X0) = singleton(sK3) )
| ( singleton(X0) != singleton(sK4) ) ),
inference(unflattening,[status(thm)],[c_163]) ).
tcf(c_172,plain,
! [X0: $i] :
( ( singleton(X0) = singleton(sK3) )
| ( singleton(X0) != singleton(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_164,c_55]) ).
tcf(c_252,definition,
iPr_def_10 = singleton(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_253,definition,
iPr_def_11 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_254,plain,
! [X0: $i] :
( ( singleton(X0) = iPr_def_11 )
| ( singleton(X0) != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_172,c_253,c_252]) ).
tcf(c_255,negated_conjecture,
sK3 != sK4,
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_402,plain,
in(sK4,iPr_def_10),
inference(superposition,[status(thm)],[c_252,c_52]) ).
tcf(c_403,plain,
singleton(sK4) = iPr_def_11,
inference(superposition,[status(thm)],[c_252,c_254]) ).
tcf(c_404,plain,
iPr_def_10 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_403,c_252]) ).
tcf(c_406,plain,
singleton(sK3) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_253,c_404]) ).
tcf(c_419,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_406,c_53]) ).
tcf(c_450,plain,
sK3 = sK4,
inference(superposition,[status(thm)],[c_402,c_419]) ).
tcf(c_452,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_450,c_255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU148+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 12:57:03 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 0.45/1.29 % SZS status Started for theBenchmark.p
% 0.45/1.29 % SZS status Theorem for theBenchmark.p
% 0.45/1.29
% 0.45/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.45/1.29
% 0.45/1.29 % ------ iProver source info
% 0.45/1.29
% 0.45/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.45/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.45/1.29 % git: non_committed_changes: false
% 0.45/1.29
% 0.45/1.29 % ------ Parsing...
% 0.45/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.45/1.29
% 0.45/1.29 % ------ 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 %
% 0.45/1.29
% 0.45/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.45/1.29
% 0.45/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.45/1.29 % ------ Proving...
% 0.45/1.29 % ------ Problem Properties
% 0.45/1.29
% 0.45/1.29 %
% 0.45/1.29 % clauses 13
% 0.45/1.29 % conjectures 1
% 0.45/1.29 % EPR 5
% 0.45/1.29 % Horn 12
% 0.45/1.29 % unary 8
% 0.45/1.29 % binary 3
% 0.45/1.29 % lits 20
% 0.45/1.29 % lits eq 11
% 0.45/1.29 % fd_pure 0
% 0.45/1.29 % fd_pseudo 0
% 0.45/1.29 % fd_cond 0
% 0.45/1.29 % fd_pseudo_cond 2
% 0.45/1.29 % AC symbols 0
% 0.45/1.29
% 0.45/1.29 % ------ Schedule dynamic 5 is on
% 0.45/1.29
% 0.45/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.45/1.29
% 0.45/1.29
% 0.45/1.29 % ------
% 0.45/1.29 % Current options:
% 0.45/1.29 % ------
% 0.45/1.29
% 0.45/1.29
% 0.45/1.29 %
% 0.45/1.29
% 0.45/1.29 % ------ Proving...
% 0.45/1.29 %
% 0.45/1.29
% 0.45/1.29 % SZS status Theorem for theBenchmark.p
% 0.45/1.29
% 0.45/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.29
% 0.45/1.29
%------------------------------------------------------------------------------