%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : TOP005-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 03:54:59 PM UTC 2026
% Result : Unsatisfiable 3.51s 1.30s
% Output : CNFRefutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 7 unt; 0 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 149 ( 79 ~; 70 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 8 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 86 ( 0 sgn 86 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( element_of_set(X0,f1(X1,X0))
| ~ element_of_set(X0,union_of_members(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_1) ).
fof(f2,axiom,
! [X0,X1] :
( element_of_collection(f1(X1,X0),X1)
| ~ element_of_set(X0,union_of_members(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_2) ).
fof(f3,axiom,
! [X2,X0,X1] :
( element_of_set(X2,f10(X1,X0,X2))
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_37) ).
fof(f4,axiom,
! [X2,X0,X1] :
( element_of_collection(f10(X1,X0,X2),X1)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_38) ).
fof(f5,axiom,
! [X2,X0,X1] :
( subset_sets(f10(X1,X0,X2),X0)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_39) ).
fof(f6,axiom,
! [X0,X1] :
( element_of_set(f11(X1,X0),X0)
| element_of_collection(X0,top_of_basis(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_40) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ subset_sets(X2,X0)
| ~ element_of_collection(X2,X1)
| ~ element_of_set(f11(X1,X0),X2)
| element_of_collection(X0,top_of_basis(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_41) ).
fof(f9,axiom,
! [X2,X0,X1] :
( subset_sets(X0,union_of_members(X2))
| ~ element_of_collection(X1,X2)
| ~ subset_sets(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_20) ).
fof(f10,axiom,
! [X2,X0,X1] :
( element_of_collection(X2,X1)
| ~ element_of_collection(X2,X0)
| ~ subset_collections(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_21) ).
fof(f11,negated_conjecture,
subset_collections(g,top_of_basis(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_2) ).
fof(f12,negated_conjecture,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_3) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( element_of_set(X0,f1(X1,X0))
| ~ element_of_set(X0,union_of_members(X1)) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( element_of_collection(f1(X1,X0),X1)
| ~ element_of_set(X0,union_of_members(X1)) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( element_of_set(X2,f10(X1,X0,X2))
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( element_of_collection(f10(X1,X0,X2),X1)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset_sets(f10(X1,X0,X2),X0)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( element_of_collection(X1,top_of_basis(X0))
| element_of_set(f11(X0,X1),X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( element_of_collection(X1,top_of_basis(X0))
| ~ subset_sets(X2,X1)
| ~ element_of_collection(X2,X0)
| ~ element_of_set(f11(X0,X1),X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset_sets(X2,union_of_members(X1))
| ~ subset_sets(X2,X0)
| ~ element_of_collection(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( element_of_collection(X0,X2)
| ~ subset_collections(X1,X2)
| ~ element_of_collection(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_71,negated_conjecture,
subset_collections(g,top_of_basis(f)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,negated_conjecture,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_141,plain,
! [X0: $i] :
( element_of_collection(X0,top_of_basis(f))
| ~ element_of_collection(X0,g) ),
inference(resolution,[status(thm)],[c_70,c_71]) ).
tcf(c_207,plain,
! [X0_iProver_element_of_collection_1: iProver_element_of_collection_1] :
( element_of_collection(X0_iProver_element_of_collection_1,top_of_basis(f))
| ~ element_of_collection(X0_iProver_element_of_collection_1,g) ),
inference(subtyping,[status(esa)],[c_141]) ).
tcf(c_208,negated_conjecture,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
inference(subtyping,[status(esa)],[c_72]) ).
tcf(c_209,plain,
! [X0_iProver_element_of_collection_1: iProver_element_of_collection_1,X0_iProver_top_of_basis_1: iProver_top_of_basis_1,X1_iProver_element_of_collection_1: iProver_element_of_collection_1] :
( subset_sets(X1_iProver_element_of_collection_1,union_of_members(X0_iProver_top_of_basis_1))
| ~ subset_sets(X1_iProver_element_of_collection_1,X0_iProver_element_of_collection_1)
| ~ element_of_collection(X0_iProver_element_of_collection_1,X0_iProver_top_of_basis_1) ),
inference(subtyping,[status(esa)],[c_69]) ).
tcf(c_211,plain,
! [X0_iProver_element_of_collection_1: iProver_element_of_collection_1,X0_iProver_top_of_basis_1: iProver_top_of_basis_1,X1_iProver_element_of_collection_1: iProver_element_of_collection_1] :
( element_of_collection(X0_iProver_element_of_collection_1,top_of_basis(X0_iProver_top_of_basis_1))
| ~ subset_sets(X1_iProver_element_of_collection_1,X0_iProver_element_of_collection_1)
| ~ element_of_collection(X1_iProver_element_of_collection_1,X0_iProver_top_of_basis_1)
| ~ element_of_set(f11(X0_iProver_top_of_basis_1,X0_iProver_element_of_collection_1),X1_iProver_element_of_collection_1) ),
inference(subtyping,[status(esa)],[c_67]) ).
tcf(c_212,plain,
! [X0_iProver_element_of_collection_1: iProver_element_of_collection_1,X0_iProver_top_of_basis_1: iProver_top_of_basis_1] :
( element_of_collection(X0_iProver_element_of_collection_1,top_of_basis(X0_iProver_top_of_basis_1))
| element_of_set(f11(X0_iProver_top_of_basis_1,X0_iProver_element_of_collection_1),X0_iProver_element_of_collection_1) ),
inference(subtyping,[status(esa)],[c_66]) ).
tcf(c_213,plain,
! [X0_iProver_element_of_collection_1: iProver_element_of_collection_1,X0_iProver_top_of_basis_1: iProver_top_of_basis_1,X0_iProver_element_of_set_1: iProver_element_of_set_1] :
( subset_sets(f10(X0_iProver_top_of_basis_1,X0_iProver_element_of_collection_1,X0_iProver_element_of_set_1),X0_iProver_element_of_collection_1)
| ~ element_of_set(X0_iProver_element_of_set_1,X0_iProver_element_of_collection_1)
| ~ element_of_collection(X0_iProver_element_of_collection_1,top_of_basis(X0_iProver_top_of_basis_1)) ),
inference(subtyping,[status(esa)],[c_65]) ).
tcf(c_214,plain,
! [X0_iProver_element_of_collection_1: iProver_element_of_collection_1,X0_iProver_top_of_basis_1: iProver_top_of_basis_1,X0_iProver_element_of_set_1: iProver_element_of_set_1] :
( element_of_collection(f10(X0_iProver_top_of_basis_1,X0_iProver_element_of_collection_1,X0_iProver_element_of_set_1),X0_iProver_top_of_basis_1)
| ~ element_of_set(X0_iProver_element_of_set_1,X0_iProver_element_of_collection_1)
| ~ element_of_collection(X0_iProver_element_of_collection_1,top_of_basis(X0_iProver_top_of_basis_1)) ),
inference(subtyping,[status(esa)],[c_64]) ).
tcf(c_215,plain,
! [X0_iProver_element_of_collection_1: iProver_element_of_collection_1,X0_iProver_top_of_basis_1: iProver_top_of_basis_1,X0_iProver_element_of_set_1: iProver_element_of_set_1] :
( element_of_set(X0_iProver_element_of_set_1,f10(X0_iProver_top_of_basis_1,X0_iProver_element_of_collection_1,X0_iProver_element_of_set_1))
| ~ element_of_set(X0_iProver_element_of_set_1,X0_iProver_element_of_collection_1)
| ~ element_of_collection(X0_iProver_element_of_collection_1,top_of_basis(X0_iProver_top_of_basis_1)) ),
inference(subtyping,[status(esa)],[c_63]) ).
tcf(c_216,plain,
! [X0_iProver_top_of_basis_1: iProver_top_of_basis_1,X0_iProver_element_of_set_1: iProver_element_of_set_1] :
( element_of_collection(f1(X0_iProver_top_of_basis_1,X0_iProver_element_of_set_1),X0_iProver_top_of_basis_1)
| ~ element_of_set(X0_iProver_element_of_set_1,union_of_members(X0_iProver_top_of_basis_1)) ),
inference(subtyping,[status(esa)],[c_62]) ).
tcf(c_217,plain,
! [X0_iProver_top_of_basis_1: iProver_top_of_basis_1,X0_iProver_element_of_set_1: iProver_element_of_set_1] :
( element_of_set(X0_iProver_element_of_set_1,f1(X0_iProver_top_of_basis_1,X0_iProver_element_of_set_1))
| ~ element_of_set(X0_iProver_element_of_set_1,union_of_members(X0_iProver_top_of_basis_1)) ),
inference(subtyping,[status(esa)],[c_61]) ).
tcf(c_257,plain,
! [X0_iProver_element_of_collection_1: iProver_element_of_collection_1] :
( ~ element_of_collection(X0_iProver_element_of_collection_1,f)
| ~ subset_sets(X0_iProver_element_of_collection_1,union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),X0_iProver_element_of_collection_1) ),
inference(resolution,[status(thm)],[c_211,c_208]) ).
tcf(c_264,plain,
! [X0_iProver_element_of_collection_1: iProver_element_of_collection_1,X1_iProver_element_of_collection_1: iProver_element_of_collection_1] :
( ~ element_of_collection(X1_iProver_element_of_collection_1,g)
| ~ element_of_collection(X0_iProver_element_of_collection_1,f)
| ~ subset_sets(X0_iProver_element_of_collection_1,X1_iProver_element_of_collection_1)
| ~ element_of_set(f11(f,union_of_members(g)),X0_iProver_element_of_collection_1) ),
inference(resolution,[status(thm)],[c_257,c_209]) ).
tcf(c_267,plain,
( element_of_collection(union_of_members(g),top_of_basis(f))
| element_of_set(f11(f,union_of_members(g)),union_of_members(g)) ),
inference(instantiation,[status(thm)],[c_212]) ).
tcf(c_279,plain,
! [X0_iProver_element_of_collection_1: iProver_element_of_collection_1,X0_iProver_top_of_basis_1: iProver_top_of_basis_1,X0_iProver_element_of_set_1: iProver_element_of_set_1] :
( ~ element_of_collection(X0_iProver_element_of_collection_1,g)
| ~ element_of_set(X0_iProver_element_of_set_1,X0_iProver_element_of_collection_1)
| ~ element_of_collection(X0_iProver_element_of_collection_1,top_of_basis(X0_iProver_top_of_basis_1))
| ~ element_of_collection(f10(X0_iProver_top_of_basis_1,X0_iProver_element_of_collection_1,X0_iProver_element_of_set_1),f)
| ~ element_of_set(f11(f,union_of_members(g)),f10(X0_iProver_top_of_basis_1,X0_iProver_element_of_collection_1,X0_iProver_element_of_set_1)) ),
inference(resolution,[status(thm)],[c_264,c_213]) ).
tcf(c_319,plain,
! [X0_iProver_element_of_collection_1: iProver_element_of_collection_1,X0_iProver_element_of_set_1: iProver_element_of_set_1] :
( ~ element_of_collection(X0_iProver_element_of_collection_1,g)
| ~ element_of_set(X0_iProver_element_of_set_1,X0_iProver_element_of_collection_1)
| ~ element_of_collection(X0_iProver_element_of_collection_1,top_of_basis(f))
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,X0_iProver_element_of_collection_1,X0_iProver_element_of_set_1)) ),
inference(resolution,[status(thm)],[c_279,c_214]) ).
tcf(c_321,plain,
! [X0_iProver_element_of_collection_1: iProver_element_of_collection_1,X0_iProver_element_of_set_1: iProver_element_of_set_1] :
( ~ element_of_collection(X0_iProver_element_of_collection_1,g)
| ~ element_of_set(X0_iProver_element_of_set_1,X0_iProver_element_of_collection_1)
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,X0_iProver_element_of_collection_1,X0_iProver_element_of_set_1)) ),
inference(global_subsumption_just,[status(thm)],[c_319,c_207,c_319]) ).
tcf(c_329,plain,
! [X0_iProver_element_of_set_1: iProver_element_of_set_1,X1_iProver_element_of_set_1: iProver_element_of_set_1] :
( ~ element_of_set(X0_iProver_element_of_set_1,union_of_members(g))
| ~ element_of_set(X1_iProver_element_of_set_1,f1(g,X0_iProver_element_of_set_1))
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,X0_iProver_element_of_set_1),X1_iProver_element_of_set_1)) ),
inference(resolution,[status(thm)],[c_321,c_216]) ).
tcf(c_347,plain,
! [X0_iProver_element_of_set_1: iProver_element_of_set_1] :
( ~ element_of_set(X0_iProver_element_of_set_1,union_of_members(g))
| ~ element_of_collection(f1(g,X0_iProver_element_of_set_1),top_of_basis(f))
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,X0_iProver_element_of_set_1)) ),
inference(resolution,[status(thm)],[c_329,c_215]) ).
tcf(c_358,plain,
! [X0_iProver_element_of_set_1: iProver_element_of_set_1] :
( ~ element_of_set(X0_iProver_element_of_set_1,union_of_members(g))
| ~ element_of_collection(f1(g,X0_iProver_element_of_set_1),g)
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,X0_iProver_element_of_set_1)) ),
inference(resolution,[status(thm)],[c_347,c_207]) ).
tcf(c_365,plain,
! [X0_iProver_element_of_set_1: iProver_element_of_set_1] :
( ~ element_of_set(X0_iProver_element_of_set_1,union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,X0_iProver_element_of_set_1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_358,c_216]) ).
tcf(c_376,plain,
~ element_of_set(f11(f,union_of_members(g)),union_of_members(g)),
inference(resolution,[status(thm)],[c_365,c_217]) ).
tcf(c_377,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_376,c_267,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 04:06:28 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 3.51/1.30 % SZS status Started for theBenchmark.p
% 3.51/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.51/1.30
% 3.51/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.51/1.30
% 3.51/1.30 % ------ iProver source info
% 3.51/1.30
% 3.51/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.51/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.51/1.30 % git: non_committed_changes: false
% 3.51/1.30
% 3.51/1.30 % ------ Parsing...% successful
% 3.51/1.30
% 3.51/1.30
% 3.51/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.51/1.30
% 3.51/1.30 % ------ 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 %
% 3.51/1.30
% 3.51/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.51/1.30 % ------ Proving...
% 3.51/1.30 % ------ Problem Properties
% 3.51/1.30
% 3.51/1.30 %
% 3.51/1.30 % clauses 11
% 3.51/1.30 % conjectures 1
% 3.51/1.30 % EPR 1
% 3.51/1.30 % Horn 9
% 3.51/1.30 % unary 1
% 3.51/1.30 % binary 4
% 3.51/1.30 % lits 28
% 3.51/1.30 % lits eq 0
% 3.51/1.30 % fd_pure 0
% 3.51/1.30 % fd_pseudo 0
% 3.51/1.30 % fd_cond 0
% 3.51/1.30 % fd_pseudo_cond 0
% 3.51/1.30 % AC symbols 0
% 3.51/1.30
% 3.51/1.30 % ------ Input Options Time Limit: Unbounded
% 3.51/1.30
% 3.51/1.30
% 3.51/1.30 % ------
% 3.51/1.30 % Current options:
% 3.51/1.30 % ------
% 3.51/1.30
% 3.51/1.30
% 3.51/1.30 %
% 3.51/1.30
% 3.51/1.30 % ------ Proving...
% 3.51/1.30 %
% 3.51/1.30
% 3.51/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.51/1.30
% 3.51/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.51/1.30
% 3.51/1.30
%------------------------------------------------------------------------------