%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET013-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 6.10s 1.77s
% Output : CNFRefutation 6.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 17 unt; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 125 ( 57 ~; 68 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 88 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',membership_in_subsets) ).
fof(f3,axiom,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set2) ).
fof(f14,axiom,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_sets(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',set_equal_sets_are_subsets2) ).
fof(f15,axiom,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_are_set_equal_sets) ).
fof(f17,axiom,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ equal_sets(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',symmetry_for_set_equal) ).
fof(f22,axiom,
equal_sets(intersection(as,bs),cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_a_and_b_is_c) ).
fof(f23,axiom,
equal_sets(intersection(bs,as),ds),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_b_and_a_is_d) ).
fof(f24,negated_conjecture,
~ equal_sets(cs,ds),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(member_of_1_not_of_2(X0,X1),X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( equal_sets(X1,X0)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_94,plain,
equal_sets(intersection(as,bs),cs),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,plain,
equal_sets(intersection(bs,as),ds),
inference(cnf_transformation,[],[f23]) ).
tcf(c_96,negated_conjecture,
~ equal_sets(cs,ds),
inference(cnf_transformation,[],[f24]) ).
tcf(c_437,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)
| ~ equal_sets(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1) ),
inference(subtyping,[status(esa)],[c_89]) ).
tcf(c_439,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_87]) ).
tcf(c_440,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1,X1_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(X1_iProver_equal_sets_1,X0_iProver_equal_sets_1)
| ~ equal_sets(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1) ),
inference(subtyping,[status(esa)],[c_86]) ).
tcf(c_442,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_84]) ).
tcf(c_443,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_83]) ).
tcf(c_444,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_82]) ).
tcf(c_450,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_76]) ).
tcf(c_451,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_75]) ).
tcf(c_452,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)
| ~ subset(X0_iProver_equal_sets_1,X1_iProver_equal_sets_1)
| ~ member(X0_iProver_member_1,X0_iProver_equal_sets_1) ),
inference(subtyping,[status(esa)],[c_74]) ).
tcf(c_455,plain,
equal_sets(intersection(bs,as),ds),
inference(subtyping,[status(esa)],[c_95]) ).
tcf(c_456,plain,
equal_sets(intersection(as,bs),cs),
inference(subtyping,[status(esa)],[c_94]) ).
tcf(c_466,plain,
( equal_sets(cs,ds)
| ~ subset(ds,cs)
| ~ subset(cs,ds) ),
inference(instantiation,[status(thm)],[c_439]) ).
tcf(c_696,plain,
equal_sets(cs,intersection(as,bs)),
inference(superposition,[status(thm)],[c_456,c_437]) ).
tcf(c_697,plain,
equal_sets(ds,intersection(bs,as)),
inference(superposition,[status(thm)],[c_455,c_437]) ).
tcf(c_721,plain,
subset(cs,intersection(as,bs)),
inference(superposition,[status(thm)],[c_456,c_440]) ).
tcf(c_722,plain,
subset(ds,intersection(bs,as)),
inference(superposition,[status(thm)],[c_455,c_440]) ).
tcf(c_724,plain,
subset(intersection(as,bs),cs),
inference(superposition,[status(thm)],[c_696,c_440]) ).
tcf(c_725,plain,
subset(intersection(bs,as),ds),
inference(superposition,[status(thm)],[c_697,c_440]) ).
tcf(c_990,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,intersection(as,bs))
| ~ member(X0_iProver_member_1,cs) ),
inference(superposition,[status(thm)],[c_721,c_452]) ).
tcf(c_991,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,intersection(bs,as))
| ~ member(X0_iProver_member_1,ds) ),
inference(superposition,[status(thm)],[c_722,c_452]) ).
tcf(c_993,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,cs)
| ~ member(X0_iProver_member_1,intersection(as,bs)) ),
inference(superposition,[status(thm)],[c_724,c_452]) ).
tcf(c_994,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,ds)
| ~ member(X0_iProver_member_1,intersection(bs,as)) ),
inference(superposition,[status(thm)],[c_725,c_452]) ).
tcf(c_1294,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,as)
| ~ member(X0_iProver_member_1,cs) ),
inference(superposition,[status(thm)],[c_990,c_443]) ).
tcf(c_1295,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,bs)
| ~ member(X0_iProver_member_1,cs) ),
inference(superposition,[status(thm)],[c_990,c_442]) ).
tcf(c_1348,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,bs)
| ~ member(X0_iProver_member_1,ds) ),
inference(superposition,[status(thm)],[c_991,c_443]) ).
tcf(c_1349,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,as)
| ~ member(X0_iProver_member_1,ds) ),
inference(superposition,[status(thm)],[c_991,c_442]) ).
tcf(c_1416,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(cs,X0_iProver_equal_sets_1)
| member(member_of_1_not_of_2(cs,X0_iProver_equal_sets_1),as) ),
inference(superposition,[status(thm)],[c_451,c_1294]) ).
tcf(c_1418,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(cs,X0_iProver_equal_sets_1)
| member(member_of_1_not_of_2(cs,X0_iProver_equal_sets_1),bs) ),
inference(superposition,[status(thm)],[c_451,c_1295]) ).
tcf(c_1444,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(ds,X0_iProver_equal_sets_1)
| member(member_of_1_not_of_2(ds,X0_iProver_equal_sets_1),bs) ),
inference(superposition,[status(thm)],[c_451,c_1348]) ).
tcf(c_1453,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(ds,X0_iProver_equal_sets_1)
| member(member_of_1_not_of_2(ds,X0_iProver_equal_sets_1),as) ),
inference(superposition,[status(thm)],[c_451,c_1349]) ).
tcf(c_4139,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,cs)
| ~ member(X0_iProver_member_1,bs)
| ~ member(X0_iProver_member_1,as) ),
inference(superposition,[status(thm)],[c_444,c_993]) ).
tcf(c_4146,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,ds)
| ~ member(X0_iProver_member_1,bs)
| ~ member(X0_iProver_member_1,as) ),
inference(superposition,[status(thm)],[c_444,c_994]) ).
tcf(c_4186,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(ds,X0_iProver_equal_sets_1)
| member(member_of_1_not_of_2(ds,X0_iProver_equal_sets_1),cs)
| ~ member(member_of_1_not_of_2(ds,X0_iProver_equal_sets_1),as) ),
inference(superposition,[status(thm)],[c_1444,c_4139]) ).
tcf(c_4195,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(cs,X0_iProver_equal_sets_1)
| member(member_of_1_not_of_2(cs,X0_iProver_equal_sets_1),ds)
| ~ member(member_of_1_not_of_2(cs,X0_iProver_equal_sets_1),as) ),
inference(superposition,[status(thm)],[c_1418,c_4146]) ).
tcf(c_7806,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,cs)
| ~ member(X0_iProver_member_1,bs)
| ~ member(X0_iProver_member_1,as) ),
inference(superposition,[status(thm)],[c_444,c_993]) ).
tcf(c_7809,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,ds)
| ~ member(X0_iProver_member_1,bs)
| ~ member(X0_iProver_member_1,as) ),
inference(superposition,[status(thm)],[c_444,c_994]) ).
tcf(c_8195,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(ds,X0_iProver_equal_sets_1)
| member(member_of_1_not_of_2(ds,X0_iProver_equal_sets_1),cs)
| ~ member(member_of_1_not_of_2(ds,X0_iProver_equal_sets_1),as) ),
inference(superposition,[status(thm)],[c_1444,c_7806]) ).
tcf(c_9484,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(cs,X0_iProver_equal_sets_1)
| member(member_of_1_not_of_2(cs,X0_iProver_equal_sets_1),ds)
| ~ member(member_of_1_not_of_2(cs,X0_iProver_equal_sets_1),as) ),
inference(superposition,[status(thm)],[c_1418,c_7809]) ).
tcf(c_9628,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(ds,X0_iProver_equal_sets_1)
| member(member_of_1_not_of_2(ds,X0_iProver_equal_sets_1),cs) ),
inference(global_subsumption_just,[status(thm)],[c_8195,c_1453,c_4186]) ).
tcf(c_9631,plain,
subset(ds,cs),
inference(superposition,[status(thm)],[c_9628,c_450]) ).
tcf(c_10010,plain,
! [X0_iProver_equal_sets_1: iProver_equal_sets_1] :
( subset(cs,X0_iProver_equal_sets_1)
| member(member_of_1_not_of_2(cs,X0_iProver_equal_sets_1),ds) ),
inference(global_subsumption_just,[status(thm)],[c_9484,c_1416,c_4195]) ).
tcf(c_10013,plain,
subset(cs,ds),
inference(superposition,[status(thm)],[c_10010,c_450]) ).
tcf(c_10018,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10013,c_9631,c_466,c_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET013-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 09:07:04 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 6.10/1.77 % SZS status Started for theBenchmark.p
% 6.10/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 6.10/1.77
% 6.10/1.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.10/1.77
% 6.10/1.77 % ------ iProver source info
% 6.10/1.77
% 6.10/1.77 % git: date: 2026-07-19 20:42:38 +0200
% 6.10/1.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.10/1.77 % git: non_committed_changes: false
% 6.10/1.77
% 6.10/1.77 % ------ Parsing...% successful
% 6.10/1.77
% 6.10/1.77
% 6.10/1.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.10/1.77
% 6.10/1.77 % ------ Preprocessing... sf_s rm: 3 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 6.10/1.77
% 6.10/1.77 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 6.10/1.77 % ------ Proving...
% 6.10/1.77 % ------ Problem Properties
% 6.10/1.77
% 6.10/1.77 %
% 6.10/1.77 % clauses 21
% 6.10/1.77 % conjectures 1
% 6.10/1.77 % EPR 9
% 6.10/1.77 % Horn 18
% 6.10/1.77 % unary 5
% 6.10/1.77 % binary 11
% 6.10/1.77 % lits 42
% 6.10/1.77 % lits eq 0
% 6.10/1.77 % fd_pure 0
% 6.10/1.77 % fd_pseudo 0
% 6.10/1.77 % fd_cond 0
% 6.10/1.77 % fd_pseudo_cond 0
% 6.10/1.77 % AC symbols 0
% 6.10/1.77
% 6.10/1.77 % ------ Input Options Time Limit: Unbounded
% 6.10/1.77
% 6.10/1.77
% 6.10/1.77 % ------
% 6.10/1.77 % Current options:
% 6.10/1.77 % ------
% 6.10/1.77
% 6.10/1.77
% 6.10/1.77 %
% 6.10/1.77
% 6.10/1.77 % ------ Proving...
% 6.10/1.77 %
% 6.10/1.77
% 6.10/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 6.10/1.77
% 6.10/1.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.10/1.77
% 6.10/1.77
%------------------------------------------------------------------------------