%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET591+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:47:28 PM UTC 2026
% Result : Theorem 2.52s 1.28s
% Output : CNFRefutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 14 unt; 1 def)
% Number of atoms : 113 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 117 ( 51 ~; 41 |; 18 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 67 !; 4 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f7,conjecture,
! [X0,X1] :
( subset(X0,difference(X1,X0))
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th50) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,difference(X1,X0))
=> X0 = empty_set ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f10,plain,
? [X0,X1] :
( subset(X0,difference(X1,X0))
& empty_set != X0 ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( subset(sK1,difference(sK2,sK1))
& empty_set != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f10]) ).
fof(f19,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f28,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
subset(sK1,difference(sK2,sK1)),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f18]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_55,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f25]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_60,negated_conjecture,
empty_set != sK1,
inference(cnf_transformation,[],[f31]) ).
tcf(c_61,negated_conjecture,
subset(sK1,difference(sK2,sK1)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_227,definition,
iPr_def_10 = difference(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_228,negated_conjecture,
subset(sK1,iPr_def_10),
inference(demodulation,[status(thm)],[c_61,c_227]) ).
tcf(c_229,negated_conjecture,
empty_set != sK1,
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_391,plain,
! [X0: $i] : subset(empty_set,X0),
inference(superposition,[status(thm)],[c_50,c_55]) ).
tcf(c_406,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_391,c_56]) ).
tcf(c_429,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_10)
| ~ member(X0,sK1) ),
inference(superposition,[status(thm)],[c_227,c_54]) ).
tcf(c_442,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| member(sK0(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ subset(X0,iPr_def_10)
| ~ member(sK0(X0,X1),sK1) ),
inference(superposition,[status(thm)],[c_442,c_429]) ).
tcf(c_1245,plain,
! [X0: $i] :
( subset(sK1,X0)
| ~ subset(sK1,iPr_def_10) ),
inference(superposition,[status(thm)],[c_50,c_600]) ).
tcf(c_1251,plain,
! [X0: $i] : subset(sK1,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_1245,c_228]) ).
tcf(c_1264,plain,
empty_set = sK1,
inference(superposition,[status(thm)],[c_1251,c_406]) ).
tcf(c_1269,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1264,c_229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET591+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n001.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 11:28:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.52/1.28 % SZS status Started for theBenchmark.p
% 2.52/1.28 % SZS status Theorem for theBenchmark.p
% 2.52/1.28
% 2.52/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.52/1.28
% 2.52/1.28 % ------ iProver source info
% 2.52/1.28
% 2.52/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.52/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.52/1.28 % git: non_committed_changes: false
% 2.52/1.28
% 2.52/1.28 % ------ Parsing...
% 2.52/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.52/1.28
% 2.52/1.28 % ------ Preprocessing... sup_sim: 0 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 %
% 2.52/1.28
% 2.52/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.52/1.28
% 2.52/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.52/1.28 % ------ Proving...
% 2.52/1.28 % ------ Problem Properties
% 2.52/1.28
% 2.52/1.28 %
% 2.52/1.28 % clauses 12
% 2.52/1.28 % conjectures 2
% 2.52/1.28 % EPR 6
% 2.52/1.28 % Horn 10
% 2.52/1.28 % unary 5
% 2.52/1.28 % binary 4
% 2.52/1.28 % lits 22
% 2.52/1.28 % lits eq 3
% 2.52/1.28 % fd_pure 0
% 2.52/1.28 % fd_pseudo 0
% 2.52/1.28 % fd_cond 0
% 2.52/1.28 % fd_pseudo_cond 1
% 2.52/1.28 % AC symbols 0
% 2.52/1.28
% 2.52/1.28 % ------ Schedule dynamic 5 is on
% 2.52/1.28
% 2.52/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.52/1.28
% 2.52/1.28
% 2.52/1.28 % ------
% 2.52/1.28 % Current options:
% 2.52/1.28 % ------
% 2.52/1.28
% 2.52/1.28
% 2.52/1.28 %
% 2.52/1.28
% 2.52/1.28 % ------ Proving...
% 2.52/1.28 %
% 2.52/1.28
% 2.52/1.28 % SZS status Theorem for theBenchmark.p
% 2.52/1.28
% 2.52/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.52/1.28
% 2.52/1.28
%------------------------------------------------------------------------------