%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET014-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 02:46:02 PM UTC 2026
% Result : Unsatisfiable 39.92s 9.98s
% Output : CNFRefutation 39.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 11 unt; 0 def)
% Number of atoms : 88 ( 5 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 98 ( 53 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f8,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ little_set(X0)
| member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f10,axiom,
! [X0,X1] : union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f13,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset1) ).
fof(f14,axiom,
! [X0,X1] :
( member(f17(X0,X1),X0)
| subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2) ).
fof(f15,axiom,
! [X0,X1] :
( ~ member(f17(X0,X1),X1)
| subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset3) ).
fof(f16,axiom,
subset(as,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_subset_of_c) ).
fof(f17,axiom,
subset(bs,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_subset_of_c) ).
fof(f18,negated_conjecture,
~ subset(union(as,bs),cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_union_b_subset_of_c) ).
fof(f19,plain,
~ subset(complement(intersection(complement(as),complement(bs))),cs),
inference(definition_unfolding,[],[f18,f10]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( little_set(X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(f17(X0,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(f17(X0,X1),X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_81,plain,
subset(as,cs),
inference(cnf_transformation,[],[f16]) ).
tcf(c_82,plain,
subset(bs,cs),
inference(cnf_transformation,[],[f17]) ).
tcf(c_83,negated_conjecture,
~ subset(complement(intersection(complement(as),complement(bs))),cs),
inference(cnf_transformation,[],[f19]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] :
( ~ member(f17(X0,X1),X1)
| ( X1 != cs )
| ( complement(intersection(complement(as),complement(bs))) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_80,c_83]) ).
tcf(c_177,plain,
~ member(f17(complement(intersection(complement(as),complement(bs))),cs),cs),
inference(unflattening,[status(thm)],[c_176]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i] :
( member(f17(X0,X1),X0)
| ( X1 != cs )
| ( complement(intersection(complement(as),complement(bs))) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_79,c_83]) ).
tcf(c_182,plain,
member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(intersection(complement(as),complement(bs)))),
inference(unflattening,[status(thm)],[c_181]) ).
tcf(c_27055,plain,
! [X0: $i] :
( member(f17(complement(intersection(complement(as),complement(bs))),cs),cs)
| ~ subset(X0,cs)
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),X0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_28083,plain,
! [X0: $i] :
( little_set(f17(complement(intersection(complement(as),complement(bs))),cs))
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),X0) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_28173,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(f17(X0,X1),X2)
| ~ member(f17(X0,X1),complement(X2)) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_28538,plain,
( little_set(f17(complement(intersection(complement(as),complement(bs))),cs))
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(intersection(complement(as),complement(bs)))) ),
inference(instantiation,[status(thm)],[c_28083]) ).
tcf(c_28596,plain,
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),intersection(complement(as),complement(bs)))
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(intersection(complement(as),complement(bs)))) ),
inference(instantiation,[status(thm)],[c_28173]) ).
tcf(c_31270,plain,
! [X0: $i] :
( member(f17(complement(intersection(complement(as),complement(bs))),cs),cs)
| ~ subset(X0,cs)
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),X0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_31274,plain,
! [X0: $i] :
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),X0)
| ~ subset(X0,cs) ),
inference(global_subsumption_just,[status(thm)],[c_31270,c_177,c_27055]) ).
tcf(c_31275,plain,
! [X0: $i] :
( ~ subset(X0,cs)
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),X0) ),
inference(renaming,[status(thm)],[c_31274]) ).
tcf(c_31311,plain,
( member(f17(complement(intersection(complement(as),complement(bs))),cs),intersection(complement(as),complement(bs)))
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs))
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(as)) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_31312,plain,
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(as))
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs)) ),
inference(global_subsumption_just,[status(thm)],[c_31311,c_182,c_28596,c_31311]) ).
tcf(c_31313,plain,
( ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs))
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(as)) ),
inference(renaming,[status(thm)],[c_31312]) ).
tcf(c_31441,plain,
( member(f17(complement(intersection(complement(as),complement(bs))),cs),bs)
| member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs))
| ~ little_set(f17(complement(intersection(complement(as),complement(bs))),cs)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_31442,plain,
( member(f17(complement(intersection(complement(as),complement(bs))),cs),bs)
| member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(bs)) ),
inference(global_subsumption_just,[status(thm)],[c_31441,c_182,c_28538,c_31441]) ).
tcf(c_31716,plain,
( member(f17(complement(intersection(complement(as),complement(bs))),cs),as)
| member(f17(complement(intersection(complement(as),complement(bs))),cs),complement(as))
| ~ little_set(f17(complement(intersection(complement(as),complement(bs))),cs)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_32413,plain,
( ~ subset(bs,cs)
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),bs) ),
inference(instantiation,[status(thm)],[c_31275]) ).
tcf(c_32809,plain,
( ~ subset(as,cs)
| ~ member(f17(complement(intersection(complement(as),complement(bs))),cs),as) ),
inference(instantiation,[status(thm)],[c_31275]) ).
tcf(c_32810,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_32809,c_32413,c_31716,c_31442,c_31313,c_28538,c_182,c_81,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 09:10:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 39.92/9.98 % SZS status Started for theBenchmark.p
% 39.92/9.98 % SZS status Unsatisfiable for theBenchmark.p
% 39.92/9.98
% 39.92/9.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 39.92/9.98
% 39.92/9.98 % ------ iProver source info
% 39.92/9.98
% 39.92/9.98 % git: date: 2026-07-19 20:42:38 +0200
% 39.92/9.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 39.92/9.98 % git: non_committed_changes: false
% 39.92/9.98
% 39.92/9.98 % ------ Parsing...% successful
% 39.92/9.98
% 39.92/9.98
% 39.92/9.98 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 39.92/9.98
% 39.92/9.98 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe_e %
% 39.92/9.98
% 39.92/9.98 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 0 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 39.92/9.98
% 39.92/9.98 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 % ------ Problem Properties
% 39.92/9.98
% 39.92/9.98 %
% 39.92/9.98 % clauses 17
% 39.92/9.98 % conjectures 1
% 39.92/9.98 % EPR 6
% 39.92/9.98 % Horn 13
% 39.92/9.98 % unary 4
% 39.92/9.98 % binary 8
% 39.92/9.98 % lits 35
% 39.92/9.98 % lits eq 3
% 39.92/9.98 % fd_pure 0
% 39.92/9.98 % fd_pseudo 0
% 39.92/9.98 % fd_cond 0
% 39.92/9.98 % fd_pseudo_cond 3
% 39.92/9.98 % AC symbols 0
% 39.92/9.98
% 39.92/9.98 % ------ Input Options Time Limit: Unbounded
% 39.92/9.98
% 39.92/9.98
% 39.92/9.98 % ------
% 39.92/9.98 % Current options:
% 39.92/9.98 % ------
% 39.92/9.98
% 39.92/9.98
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % ------ Proving...
% 39.92/9.98 %
% 39.92/9.98
% 39.92/9.98 % SZS status Unsatisfiable for theBenchmark.p
% 39.92/9.98
% 39.92/9.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 39.92/9.98
% 39.92/9.98
%------------------------------------------------------------------------------