%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET201+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 : 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 02:46:55 PM UTC 2026
% Result : Theorem 3.73s 1.30s
% Output : CNFRefutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 14 unt; 2 def)
% Number of atoms : 163 ( 2 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 129 ( 51 ~; 53 |; 19 &)
% ( 3 <=>; 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 80 !; 10 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f6,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(intersection(X0,X2),intersection(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th41) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(intersection(X0,X2),intersection(X1,X3)) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
? [X0,X1,X2,X3] :
( subset(X2,X3)
& subset(X0,X1)
& ~ subset(intersection(X0,X2),intersection(X1,X3)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
? [X0,X1,X2,X3] :
( subset(X2,X3)
& subset(X0,X1)
& ~ subset(intersection(X0,X2),intersection(X1,X3)) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f11]) ).
fof(f13,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,[],[f8]) ).
fof(f14,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,[],[f13]) ).
fof(f15,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))],[f14]) ).
fof(f19,plain,
( subset(sK4,sK5)
& subset(sK2,sK3)
& ~ subset(intersection(sK2,sK4),intersection(sK3,sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f10]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f32,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
~ subset(intersection(sK2,sK4),intersection(sK3,sK5)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_59,negated_conjecture,
~ subset(intersection(sK2,sK4),intersection(sK3,sK5)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_60,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f33]) ).
tcf(c_61,negated_conjecture,
subset(sK4,sK5),
inference(cnf_transformation,[],[f32]) ).
tcf(c_250,definition,
iPr_def_10 = intersection(sK2,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_251,definition,
iPr_def_11 = intersection(sK3,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_252,negated_conjecture,
subset(sK4,sK5),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_253,negated_conjecture,
subset(sK2,sK3),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_254,negated_conjecture,
~ subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_59,c_251,c_250]) ).
tcf(c_444,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,sK5)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_251,c_49]) ).
tcf(c_464,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_250,c_50]) ).
tcf(c_483,plain,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_250,c_51]) ).
tcf(c_510,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| member(sK0(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_522,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),sK2) ),
inference(superposition,[status(thm)],[c_53,c_464]) ).
tcf(c_538,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),sK4) ),
inference(superposition,[status(thm)],[c_53,c_483]) ).
tcf(c_554,plain,
! [X0: $i,X1: $i] :
( subset(iPr_def_10,X1)
| member(sK0(iPr_def_10,X1),X0)
| ~ subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_522,c_54]) ).
tcf(c_575,plain,
! [X0: $i,X1: $i] :
( subset(iPr_def_10,X1)
| member(sK0(iPr_def_10,X1),X0)
| ~ subset(sK4,X0) ),
inference(superposition,[status(thm)],[c_538,c_54]) ).
tcf(c_1024,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),iPr_def_11)
| ~ subset(sK2,sK3)
| ~ member(sK0(iPr_def_10,X0),sK5) ),
inference(superposition,[status(thm)],[c_554,c_444]) ).
tcf(c_1047,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),iPr_def_11)
| ~ member(sK0(iPr_def_10,X0),sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1024,c_253]) ).
tcf(c_1092,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),iPr_def_11)
| ~ subset(iPr_def_10,sK5) ),
inference(superposition,[status(thm)],[c_510,c_1047]) ).
tcf(c_1117,plain,
( subset(iPr_def_10,iPr_def_11)
| ~ subset(iPr_def_10,sK5) ),
inference(superposition,[status(thm)],[c_1092,c_52]) ).
tcf(c_1120,plain,
~ subset(iPr_def_10,sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_1117,c_254]) ).
tcf(c_1327,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ~ subset(sK4,X0) ),
inference(superposition,[status(thm)],[c_575,c_52]) ).
tcf(c_1390,plain,
subset(iPr_def_10,sK5),
inference(superposition,[status(thm)],[c_252,c_1327]) ).
tcf(c_1391,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1390,c_1120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET201+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.39 % Computer : n013.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Thu Sep 24 10:13:51 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 3.73/1.30 % SZS status Started for theBenchmark.p
% 3.73/1.30 % SZS status Theorem for theBenchmark.p
% 3.73/1.30
% 3.73/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.73/1.30
% 3.73/1.30 % ------ iProver source info
% 3.73/1.30
% 3.73/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.73/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.73/1.30 % git: non_committed_changes: false
% 3.73/1.30
% 3.73/1.30 % ------ Parsing...
% 3.73/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.73/1.30
% 3.73/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.73/1.30
% 3.73/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.73/1.30
% 3.73/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.73/1.30 % ------ Proving...
% 3.73/1.30 % ------ Problem Properties
% 3.73/1.30
% 3.73/1.30 %
% 3.73/1.30 % clauses 15
% 3.73/1.30 % conjectures 3
% 3.73/1.30 % EPR 5
% 3.73/1.30 % Horn 13
% 3.73/1.30 % unary 7
% 3.73/1.30 % binary 4
% 3.73/1.30 % lits 27
% 3.73/1.30 % lits eq 5
% 3.73/1.30 % fd_pure 0
% 3.73/1.30 % fd_pseudo 0
% 3.73/1.30 % fd_cond 0
% 3.73/1.30 % fd_pseudo_cond 2
% 3.73/1.30 % AC symbols 0
% 3.73/1.30
% 3.73/1.30 % ------ Schedule dynamic 5 is on
% 3.73/1.30
% 3.73/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.73/1.30
% 3.73/1.30
% 3.73/1.30 % ------
% 3.73/1.30 % Current options:
% 3.73/1.30 % ------
% 3.73/1.30
% 3.73/1.30
% 3.73/1.30 %
% 3.73/1.30
% 3.73/1.30 % ------ Proving...
% 3.73/1.30 %
% 3.73/1.30
% 3.73/1.30 % SZS status Theorem for theBenchmark.p
% 3.73/1.30
% 3.73/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.73/1.31
% 3.73/1.31
%------------------------------------------------------------------------------