%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET143+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 : n005.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 02:46:44 PM UTC 2026
% Result : Theorem 0.55s 1.20s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 51 ( 7 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 132 ( 59 ~; 57 |; 9 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 68 !; 4 ?; 20 :)
% 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(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
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] : equal_set(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI08) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] : equal_set(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X1,X2))),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f16,plain,
? [X0,X1,X2] : ~ equal_set(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X1,X2))),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f20,plain,
~ equal_set(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
fof(f21,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(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(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,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))],[f19]) ).
fof(f24,plain,
~ equal_set(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),
inference(cnf_transformation,[],[f20]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f28,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f30,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_49,negated_conjecture,
~ equal_set(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),
inference(cnf_transformation,[],[f24]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_91,plain,
( ~ subset(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2))
| ~ subset(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))) ),
inference(resolution,[status(thm)],[c_49,c_53]) ).
tcf(c_126,plain,
( subset(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2)))
| ~ member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),intersection(sK0,intersection(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_127,plain,
( subset(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2)))
| member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),intersection(intersection(sK0,sK1),sK2)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_128,plain,
( subset(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2))
| member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),intersection(sK0,intersection(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_129,plain,
( subset(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2))
| ~ member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),intersection(intersection(sK0,sK1),sK2)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_132,plain,
( member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),intersection(sK1,sK2))
| ~ member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),intersection(sK0,intersection(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_133,plain,
( member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),sK0)
| ~ member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),intersection(sK0,intersection(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_138,plain,
( member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),sK2)
| ~ member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),intersection(intersection(sK0,sK1),sK2)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_139,plain,
( member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),intersection(sK0,sK1))
| ~ member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),intersection(intersection(sK0,sK1),sK2)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_142,plain,
( member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),sK2)
| ~ member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_143,plain,
( member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),sK1)
| ~ member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_144,plain,
! [X0: $i] :
( member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),intersection(sK0,X0))
| ~ member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),sK0)
| ~ member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),X0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i] :
( member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),intersection(X0,X1))
| ~ member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),X1)
| ~ member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),X0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_225,plain,
( member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),intersection(intersection(sK0,sK1),sK2))
| ~ member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),sK2)
| ~ member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),intersection(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_158]) ).
tcf(c_239,plain,
( member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),sK1)
| ~ member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),intersection(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_240,plain,
( member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),sK0)
| ~ member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),intersection(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_269,plain,
! [X0: $i] :
( member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),intersection(sK1,X0))
| ~ member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),sK1)
| ~ member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),X0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_335,plain,
( member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),intersection(sK0,sK1))
| ~ member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),sK1)
| ~ member(sK3(intersection(sK0,intersection(sK1,sK2)),intersection(intersection(sK0,sK1),sK2)),sK0) ),
inference(instantiation,[status(thm)],[c_144]) ).
tcf(c_456,plain,
! [X0: $i] :
( member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),intersection(sK0,X0))
| ~ member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),sK0)
| ~ member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),X0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_679,plain,
( member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),intersection(sK0,intersection(sK1,sK2)))
| ~ member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),sK0)
| ~ member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_456]) ).
tcf(c_729,plain,
( member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),intersection(sK1,sK2))
| ~ member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),sK2)
| ~ member(sK3(intersection(intersection(sK0,sK1),sK2),intersection(sK0,intersection(sK1,sK2))),sK1) ),
inference(instantiation,[status(thm)],[c_269]) ).
tcf(c_730,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_729,c_679,c_335,c_239,c_240,c_225,c_142,c_143,c_138,c_139,c_132,c_133,c_128,c_129,c_127,c_126,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET143+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 10:00:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 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...
% 0.55/1.20 % SZS status Started for theBenchmark.p
% 0.55/1.20 % SZS status Theorem for theBenchmark.p
% 0.55/1.20
% 0.55/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.55/1.20
% 0.55/1.20 % ------ iProver source info
% 0.55/1.20
% 0.55/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 0.55/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.55/1.20 % git: non_committed_changes: false
% 0.55/1.20
% 0.55/1.20 % ------ Parsing...
% 0.55/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.55/1.20
% 0.55/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.55/1.20
% 0.55/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.55/1.20 % ------ Proving...
% 0.55/1.20 % ------ Problem Properties
% 0.55/1.20
% 0.55/1.20 %
% 0.55/1.20 % clauses 6
% 0.55/1.20 % conjectures 0
% 0.55/1.20 % EPR 0
% 0.55/1.20 % Horn 5
% 0.55/1.20 % unary 0
% 0.55/1.20 % binary 5
% 0.55/1.20 % lits 13
% 0.55/1.20 % lits eq 0
% 0.55/1.20 % fd_pure 0
% 0.55/1.20 % fd_pseudo 0
% 0.55/1.20 % fd_cond 0
% 0.55/1.20 % fd_pseudo_cond 0
% 0.55/1.20 % AC symbols 0
% 0.55/1.20
% 0.55/1.20 % ------ Schedule dynamic 5 is on
% 0.55/1.20
% 0.55/1.20 % ------ no conjectures: strip conj schedule
% 0.55/1.20
% 0.55/1.20 % ------ no equalities: superposition off
% 0.55/1.20
% 0.55/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.55/1.20
% 0.55/1.20
% 0.55/1.20 % ------
% 0.55/1.20 % Current options:
% 0.55/1.20 % ------
% 0.55/1.20
% 0.55/1.20
% 0.55/1.20 %
% 0.55/1.20
% 0.55/1.20 % ------ Proving...
% 0.55/1.20 %
% 0.55/1.20
% 0.55/1.20 % SZS status Theorem for theBenchmark.p
% 0.55/1.20
% 0.55/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.55/1.21
% 0.55/1.21
%------------------------------------------------------------------------------