%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET013-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 02:46:01 PM UTC 2026
% Result : Unsatisfiable 2.31s 0.96s
% Output : CNFRefutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 3 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 73 ( 35 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',subsets_axiom1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',subsets_axiom2) ).
fof(f10,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',member_of_both_is_member_of_intersection) ).
fof(f11,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set1) ).
fof(f12,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set2) ).
fof(f15,axiom,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',subsets_are_set_equal_sets) ).
fof(f22,negated_conjecture,
~ equal_sets(intersection(as,bs),intersection(bs,as)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(member_of_1_not_of_2(X0,X1),X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_92,negated_conjecture,
~ equal_sets(intersection(as,bs),intersection(bs,as)),
inference(cnf_transformation,[],[f22]) ).
tcf(c_423,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X1_iProver_equal_sets_1: iProver_equal_sets_1] :
( equal_sets(X1_iProver_equal_sets_1,X0_iProver_equal_sets_1)
| ~ subset(X1_iProver_equal_sets_1,X0_iProver_equal_sets_1)
| ~ subset(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1) ),
inference(subtyping,[status(esa)],[c_85]) ).
tcf(c_426,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X0_iProver_member_1: iProver_member_1,X1_iProver_equal_sets_1: iProver_equal_sets_1] :
( member(X0_iProver_member_1,X1_iProver_equal_sets_1)
| ~ member(X0_iProver_member_1,intersection(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1)) ),
inference(subtyping,[status(esa)],[c_82]) ).
tcf(c_427,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X0_iProver_member_1: iProver_member_1,X1_iProver_equal_sets_1: iProver_equal_sets_1] :
( member(X0_iProver_member_1,X0_iProver_equal_sets_1)
| ~ member(X0_iProver_member_1,intersection(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1)) ),
inference(subtyping,[status(esa)],[c_81]) ).
tcf(c_428,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X0_iProver_member_1: iProver_member_1,X1_iProver_equal_sets_1: iProver_equal_sets_1] :
( member(X0_iProver_member_1,intersection(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1))
| ~ member(X0_iProver_member_1,X1_iProver_equal_sets_1)
| ~ member(X0_iProver_member_1,X0_iProver_equal_sets_1) ),
inference(subtyping,[status(esa)],[c_80]) ).
tcf(c_434,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X1_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1)
| ~ member(member_of_1_not_of_2(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1),X1_iProver_equal_sets_1) ),
inference(subtyping,[status(esa)],[c_74]) ).
tcf(c_435,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X1_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1)
| member(member_of_1_not_of_2(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1),X0_iProver_equal_sets_1) ),
inference(subtyping,[status(esa)],[c_73]) ).
tcf(c_495,plain,
( equal_sets(intersection(as,bs),intersection(bs,as))
| ~ subset(intersection(bs,as),intersection(as,bs))
| ~ subset(intersection(as,bs),intersection(bs,as)) ),
inference(instantiation,[status(thm)],[c_423]) ).
tcf(c_539,plain,
( subset(intersection(bs,as),intersection(as,bs))
| member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),intersection(bs,as)) ),
inference(instantiation,[status(thm)],[c_435]) ).
tcf(c_540,plain,
( subset(intersection(bs,as),intersection(as,bs))
| ~ member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),intersection(as,bs)) ),
inference(instantiation,[status(thm)],[c_434]) ).
tcf(c_758,plain,
( subset(intersection(as,bs),intersection(bs,as))
| member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),intersection(as,bs)) ),
inference(instantiation,[status(thm)],[c_435]) ).
tcf(c_759,plain,
( subset(intersection(as,bs),intersection(bs,as))
| ~ member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),intersection(bs,as)) ),
inference(instantiation,[status(thm)],[c_434]) ).
tcf(c_903,plain,
( member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),intersection(as,bs))
| ~ member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),bs)
| ~ member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),as) ),
inference(instantiation,[status(thm)],[c_428]) ).
tcf(c_1135,plain,
( member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),as)
| ~ member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),intersection(bs,as)) ),
inference(instantiation,[status(thm)],[c_426]) ).
tcf(c_1144,plain,
( member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),bs)
| ~ member(member_of_1_not_of_2(intersection(bs,as),intersection(as,bs)),intersection(bs,as)) ),
inference(instantiation,[status(thm)],[c_427]) ).
tcf(c_1541,plain,
( member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),as)
| ~ member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),intersection(as,bs)) ),
inference(instantiation,[status(thm)],[c_427]) ).
tcf(c_1542,plain,
( member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),bs)
| ~ member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),intersection(as,bs)) ),
inference(instantiation,[status(thm)],[c_426]) ).
tcf(c_2956,plain,
( member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),intersection(bs,as))
| ~ member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),bs)
| ~ member(member_of_1_not_of_2(intersection(as,bs),intersection(bs,as)),as) ),
inference(instantiation,[status(thm)],[c_428]) ).
tcf(c_3484,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2956,c_1541,c_1542,c_1144,c_1135,c_903,c_758,c_759,c_539,c_540,c_495,c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET013-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 09:05:07 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.03/0.32
% 0.03/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.32
% 0.03/0.32 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 2.31/0.96 % SZS status Started for theBenchmark.p
% 2.31/0.96 % SZS status Unsatisfiable for theBenchmark.p
% 2.31/0.96
% 2.31/0.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.31/0.96
% 2.31/0.96 % ------ iProver source info
% 2.31/0.96
% 2.31/0.96 % git: date: 2026-07-19 20:42:38 +0200
% 2.31/0.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.31/0.96 % git: non_committed_changes: false
% 2.31/0.96
% 2.31/0.96 % ------ Parsing...% successful
% 2.31/0.96
% 2.31/0.96
% 2.31/0.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.31/0.96
% 2.31/0.96 % ------ Preprocessing... sf_s rm: 3 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.31/0.96
% 2.31/0.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.31/0.96 % ------ Proving...
% 2.31/0.96 % ------ Problem Properties
% 2.31/0.96
% 2.31/0.96 %
% 2.31/0.96 % clauses 19
% 2.31/0.96 % conjectures 1
% 2.31/0.96 % EPR 8
% 2.31/0.96 % Horn 16
% 2.31/0.96 % unary 3
% 2.31/0.96 % binary 11
% 2.31/0.96 % lits 40
% 2.31/0.96 % lits eq 0
% 2.31/0.96 % fd_pure 0
% 2.31/0.96 % fd_pseudo 0
% 2.31/0.96 % fd_cond 0
% 2.31/0.96 % fd_pseudo_cond 0
% 2.31/0.96 % AC symbols 0
% 2.31/0.96
% 2.31/0.96 % ------ Input Options Time Limit: Unbounded
% 2.31/0.96
% 2.31/0.96
% 2.31/0.96 % ------
% 2.31/0.96 % Current options:
% 2.31/0.96 % ------
% 2.31/0.96
% 2.31/0.96
% 2.31/0.96 %
% 2.31/0.96
% 2.31/0.96 % ------ Proving...
% 2.31/0.96 %
% 2.31/0.96
% 2.31/0.96 % SZS status Unsatisfiable for theBenchmark.p
% 2.31/0.96
% 2.31/0.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.31/0.96
% 2.31/0.96
%------------------------------------------------------------------------------