%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET199+4 : 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 : n020.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 02:46:54 PM UTC 2026
% Result : Theorem 4.31s 1.29s
% Output : CNFRefutation 4.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 67 ( 3 unt; 0 def)
% Number of atoms : 195 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 215 ( 87 ~; 101 |; 20 &)
% ( 5 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 91 !; 11 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
<=> subset(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI46) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
<=> subset(X0,intersection(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
<~> subset(X0,intersection(X1,X2)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ( ( subset(X0,X2)
& subset(X0,X1) )
| subset(X0,intersection(X1,X2)) )
& ( ~ subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ( ( subset(X0,X2)
& subset(X0,X1) )
| subset(X0,intersection(X1,X2)) )
& ( ~ subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( ( ( subset(sK0,sK2)
& subset(sK0,sK1) )
| subset(sK0,intersection(sK1,sK2)) )
& ( ~ subset(sK0,sK2)
| ~ subset(sK0,sK1)
| ~ subset(sK0,intersection(sK1,sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f17]) ).
fof(f19,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,[],[f15]) ).
fof(f20,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,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK3(X0,X1),X0)
& ~ member(sK3(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( ~ member(X0,intersection(X1,X2))
| ( member(X0,X2)
& member(X0,X1) ) )
& ( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ~ member(X0,intersection(X1,X2))
| ( member(X0,X2)
& member(X0,X1) ) )
& ( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
( subset(sK0,sK2)
| subset(sK0,intersection(sK1,sK2)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f25,plain,
( subset(sK0,sK1)
| subset(sK0,intersection(sK1,sK2)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
( ~ subset(sK0,sK2)
| ~ subset(sK0,sK1)
| ~ subset(sK0,intersection(sK1,sK2)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f28,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f29,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_49,negated_conjecture,
( ~ subset(sK0,sK2)
| ~ subset(sK0,sK1)
| ~ subset(sK0,intersection(sK1,sK2)) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_50,negated_conjecture,
( subset(sK0,sK1)
| subset(sK0,intersection(sK1,sK2)) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,negated_conjecture,
( subset(sK0,sK2)
| subset(sK0,intersection(sK1,sK2)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_104,plain,
( subset(sK0,sK1)
| ~ member(sK3(sK0,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_105,plain,
( subset(sK0,sK1)
| member(sK3(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_106,plain,
( subset(sK0,sK2)
| member(sK3(sK0,sK2),sK0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_107,plain,
( subset(sK0,sK2)
| ~ member(sK3(sK0,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_108,plain,
! [X0: $i] :
( member(sK3(sK0,sK2),X0)
| ~ subset(sK0,X0)
| ~ member(sK3(sK0,sK2),sK0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_111,plain,
( subset(sK0,intersection(sK1,sK2))
| member(sK3(sK0,intersection(sK1,sK2)),sK0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_112,plain,
( subset(sK0,intersection(sK1,sK2))
| ~ member(sK3(sK0,intersection(sK1,sK2)),intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_113,plain,
! [X0: $i] :
( member(sK3(sK0,intersection(sK1,sK2)),X0)
| ~ subset(sK0,X0)
| ~ member(sK3(sK0,intersection(sK1,sK2)),sK0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_118,plain,
! [X0: $i] :
( member(sK3(sK0,sK1),X0)
| ~ subset(sK0,X0)
| ~ member(sK3(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK0,sK2),intersection(X0,X1))
| ~ member(sK3(sK0,sK2),sK0)
| ~ subset(sK0,intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK0,sK2),X1)
| ~ member(sK3(sK0,sK2),intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_139,plain,
! [X0: $i] :
( member(sK3(sK0,sK2),sK2)
| ~ member(sK3(sK0,sK2),intersection(X0,sK2)) ),
inference(instantiation,[status(thm)],[c_124]) ).
tcf(c_173,plain,
! [X0: $i] :
( member(sK3(sK0,sK2),intersection(X0,sK2))
| ~ member(sK3(sK0,sK2),sK0)
| ~ subset(sK0,intersection(X0,sK2)) ),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_198,plain,
( member(sK3(sK0,sK2),intersection(sK1,sK2))
| ~ member(sK3(sK0,sK2),sK0)
| ~ subset(sK0,intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_173]) ).
tcf(c_321,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| member(sK3(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_53,c_54]) ).
tcf(c_442,plain,
( member(sK3(sK0,sK2),sK2)
| ~ member(sK3(sK0,sK2),intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_139]) ).
tcf(c_487,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK0,sK1),intersection(X0,X1))
| ~ member(sK3(sK0,sK1),sK0)
| ~ subset(sK0,intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_118]) ).
tcf(c_489,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK0,sK1),X0)
| ~ member(sK3(sK0,sK1),intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_541,plain,
! [X0: $i] :
( member(sK3(sK0,sK1),sK1)
| ~ member(sK3(sK0,sK1),intersection(sK1,X0)) ),
inference(instantiation,[status(thm)],[c_489]) ).
tcf(c_575,plain,
! [X0: $i] :
( member(sK3(sK0,sK1),intersection(sK1,X0))
| ~ member(sK3(sK0,sK1),sK0)
| ~ subset(sK0,intersection(sK1,X0)) ),
inference(instantiation,[status(thm)],[c_487]) ).
tcf(c_595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X3)
| member(sK3(X0,X3),X2)
| ~ subset(X0,intersection(X1,X2)) ),
inference(superposition,[status(thm)],[c_321,c_57]) ).
tcf(c_650,plain,
( member(sK3(sK0,sK1),intersection(sK1,sK2))
| ~ member(sK3(sK0,sK1),sK0)
| ~ subset(sK0,intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_575]) ).
tcf(c_681,plain,
! [X0: $i] :
( subset(sK0,sK2)
| subset(sK0,X0)
| member(sK3(sK0,X0),sK2) ),
inference(superposition,[status(thm)],[c_51,c_595]) ).
tcf(c_682,plain,
! [X0: $i] :
( subset(sK0,sK1)
| subset(sK0,X0)
| member(sK3(sK0,X0),sK2) ),
inference(superposition,[status(thm)],[c_50,c_595]) ).
tcf(c_721,plain,
subset(sK0,sK2),
inference(global_subsumption_just,[status(thm)],[c_681,c_51,c_107,c_106,c_198,c_442]) ).
tcf(c_723,plain,
( ~ subset(sK0,sK1)
| ~ subset(sK0,intersection(sK1,sK2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_721]) ).
tcf(c_758,plain,
! [X0: $i,X1: $i] :
( subset(sK0,sK1)
| subset(sK0,X1)
| member(sK3(sK0,X1),X0)
| ~ subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_682,c_54]) ).
tcf(c_783,plain,
! [X0: $i] :
( subset(sK0,sK1)
| subset(sK0,X0)
| ~ subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_758,c_52]) ).
tcf(c_860,plain,
( member(sK3(sK0,sK1),sK1)
| ~ member(sK3(sK0,sK1),intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_541]) ).
tcf(c_896,plain,
subset(sK0,sK1),
inference(global_subsumption_just,[status(thm)],[c_783,c_50,c_104,c_105,c_650,c_860]) ).
tcf(c_1040,plain,
! [X0: $i,X1: $i] :
( member(sK3(sK0,intersection(sK1,sK2)),intersection(X0,X1))
| ~ member(sK3(sK0,intersection(sK1,sK2)),X1)
| ~ member(sK3(sK0,intersection(sK1,sK2)),X0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_1127,plain,
( member(sK3(sK0,intersection(sK1,sK2)),intersection(sK1,sK2))
| ~ member(sK3(sK0,intersection(sK1,sK2)),sK2)
| ~ member(sK3(sK0,intersection(sK1,sK2)),sK1) ),
inference(instantiation,[status(thm)],[c_1040]) ).
tcf(c_1164,plain,
( member(sK3(sK0,intersection(sK1,sK2)),sK1)
| ~ subset(sK0,sK1)
| ~ member(sK3(sK0,intersection(sK1,sK2)),sK0) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_1334,plain,
( member(sK3(sK0,intersection(sK1,sK2)),sK2)
| ~ subset(sK0,sK2)
| ~ member(sK3(sK0,intersection(sK1,sK2)),sK0) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_1335,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1334,c_1164,c_1127,c_896,c_723,c_721,c_111,c_112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET199+4 : 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 : n020.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 10:14:04 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 4.31/1.29 % SZS status Started for theBenchmark.p
% 4.31/1.29 % SZS status Theorem for theBenchmark.p
% 4.31/1.29
% 4.31/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.31/1.29
% 4.31/1.29 % ------ iProver source info
% 4.31/1.29
% 4.31/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 4.31/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.31/1.29 % git: non_committed_changes: false
% 4.31/1.29
% 4.31/1.29 % ------ Parsing...
% 4.31/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.31/1.29
% 4.31/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.31/1.29
% 4.31/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.31/1.29 % ------ Proving...
% 4.31/1.29 % ------ Problem Properties
% 4.31/1.29
% 4.31/1.29 %
% 4.31/1.29 % clauses 9
% 4.31/1.29 % conjectures 3
% 4.31/1.29 % EPR 1
% 4.31/1.29 % Horn 6
% 4.31/1.29 % unary 0
% 4.31/1.29 % binary 6
% 4.31/1.29 % lits 21
% 4.31/1.29 % lits eq 0
% 4.31/1.29 % fd_pure 0
% 4.31/1.29 % fd_pseudo 0
% 4.31/1.29 % fd_cond 0
% 4.31/1.29 % fd_pseudo_cond 0
% 4.31/1.29 % AC symbols 0
% 4.31/1.29
% 4.31/1.29 % ------ Schedule dynamic 5 is on
% 4.31/1.29
% 4.31/1.29 % ------ no equalities: superposition off
% 4.31/1.29
% 4.31/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.31/1.29
% 4.31/1.29
% 4.31/1.29 % ------
% 4.31/1.29 % Current options:
% 4.31/1.29 % ------
% 4.31/1.29
% 4.31/1.29
% 4.31/1.29 %
% 4.31/1.29
% 4.31/1.29 % ------ Proving...
% 4.31/1.29 %
% 4.31/1.29
% 4.31/1.29 % SZS status Theorem for theBenchmark.p
% 4.31/1.29
% 4.31/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.31/1.29
% 4.31/1.29
%------------------------------------------------------------------------------