%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET587+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 02:47:27 PM UTC 2026
% Result : Theorem 2.64s 1.18s
% Output : CNFRefutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 10 unt; 1 def)
% Number of atoms : 171 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 160 ( 67 ~; 67 |; 18 &)
% ( 6 <=>; 1 =>; 0 <=; 1 <~>)
% 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 : 93 ( 0 sgn 87 !; 6 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f9,conjecture,
! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_empty_set) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f13,plain,
? [X0,X1] :
( difference(X0,X1) = empty_set
<~> subset(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f16,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(f17,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,[],[f16]) ).
fof(f18,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,[],[f12]) ).
fof(f19,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,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK1(X0,X1),X0)
& ~ member(sK1(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f21]) ).
fof(f26,plain,
? [X0,X1] :
( ( difference(X0,X1) = empty_set
| subset(X0,X1) )
& ( difference(X0,X1) != empty_set
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f27,plain,
( ( empty_set = difference(sK3,sK4)
| subset(sK3,sK4) )
& ( empty_set != difference(sK3,sK4)
| ~ subset(sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f26]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
( empty_set = difference(sK3,sK4)
| subset(sK3,sK4) ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
( empty_set != difference(sK3,sK4)
| ~ subset(sK3,sK4) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f33]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_64,negated_conjecture,
( ~ subset(sK3,sK4)
| ( difference(sK3,sK4) != empty_set ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_65,negated_conjecture,
( subset(sK3,sK4)
| ( difference(sK3,sK4) = empty_set ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_453,definition,
iPr_def_10 = difference(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_454,negated_conjecture,
( subset(sK3,sK4)
| ( iPr_def_10 = empty_set ) ),
inference(demodulation,[status(thm)],[c_65,c_453]) ).
tcf(c_455,negated_conjecture,
( ~ subset(sK3,sK4)
| ( iPr_def_10 != empty_set ) ),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_800,plain,
! [X0: $i] : subset(empty_set,X0),
inference(superposition,[status(thm)],[c_56,c_54]) ).
tcf(c_807,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_453,c_52]) ).
tcf(c_820,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| member(X0,sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_453,c_51]) ).
tcf(c_841,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_10)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_453,c_53]) ).
tcf(c_871,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_800,c_58]) ).
tcf(c_882,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK1(iPr_def_10,X0),sK3) ),
inference(superposition,[status(thm)],[c_56,c_807]) ).
tcf(c_890,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ~ member(sK1(iPr_def_10,X0),sK4) ),
inference(superposition,[status(thm)],[c_56,c_841]) ).
tcf(c_904,plain,
! [X0: $i,X1: $i] :
( subset(iPr_def_10,X1)
| member(sK1(iPr_def_10,X1),X0)
| ~ subset(sK3,X0) ),
inference(superposition,[status(thm)],[c_882,c_57]) ).
tcf(c_932,plain,
! [X0: $i] :
( subset(sK3,X0)
| member(sK1(sK3,X0),iPr_def_10)
| member(sK1(sK3,X0),sK4) ),
inference(superposition,[status(thm)],[c_56,c_820]) ).
tcf(c_1600,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ~ subset(sK3,sK4) ),
inference(superposition,[status(thm)],[c_904,c_890]) ).
tcf(c_1675,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ( empty_set = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_454,c_1600]) ).
tcf(c_1710,plain,
empty_set = iPr_def_10,
inference(superposition,[status(thm)],[c_1675,c_871]) ).
tcf(c_1721,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_54,c_1710]) ).
tcf(c_1722,plain,
( ~ subset(sK3,sK4)
| ( iPr_def_10 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_455,c_1710]) ).
tcf(c_1724,plain,
~ subset(sK3,sK4),
inference(equality_resolution_simp,[status(thm)],[c_1722]) ).
tcf(c_1793,plain,
! [X0: $i] :
( subset(sK3,X0)
| member(sK1(sK3,X0),sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_932,c_1721]) ).
tcf(c_1801,plain,
subset(sK3,sK4),
inference(superposition,[status(thm)],[c_1793,c_55]) ).
tcf(c_1802,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1801,c_1724]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET587+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n009.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 11:21:59 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 2.64/1.18 % SZS status Started for theBenchmark.p
% 2.64/1.18 % SZS status Theorem for theBenchmark.p
% 2.64/1.18
% 2.64/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.64/1.18
% 2.64/1.18 % ------ iProver source info
% 2.64/1.18
% 2.64/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.64/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.64/1.18 % git: non_committed_changes: false
% 2.64/1.18
% 2.64/1.18 % ------ Parsing...
% 2.64/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.64/1.18
% 2.64/1.18 % ------ 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 %
% 2.64/1.18
% 2.64/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.64/1.18
% 2.64/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.64/1.18 % ------ Proving...
% 2.64/1.18 % ------ Problem Properties
% 2.64/1.18
% 2.64/1.18 %
% 2.64/1.18 % clauses 16
% 2.64/1.18 % conjectures 2
% 2.64/1.18 % EPR 6
% 2.64/1.18 % Horn 11
% 2.64/1.18 % unary 3
% 2.64/1.18 % binary 6
% 2.64/1.18 % lits 36
% 2.64/1.18 % lits eq 8
% 2.64/1.18 % fd_pure 0
% 2.64/1.18 % fd_pseudo 0
% 2.64/1.18 % fd_cond 0
% 2.64/1.18 % fd_pseudo_cond 5
% 2.64/1.18 % AC symbols 0
% 2.64/1.18
% 2.64/1.18 % ------ Schedule dynamic 5 is on
% 2.64/1.18
% 2.64/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.64/1.18
% 2.64/1.18
% 2.64/1.18 % ------
% 2.64/1.18 % Current options:
% 2.64/1.18 % ------
% 2.64/1.18
% 2.64/1.18
% 2.64/1.18 %
% 2.64/1.18
% 2.64/1.18 % ------ Proving...
% 2.64/1.18 %
% 2.64/1.18
% 2.64/1.18 % SZS status Theorem for theBenchmark.p
% 2.64/1.18
% 2.64/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.64/1.19
%------------------------------------------------------------------------------