%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM066-1 : 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 : n026.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 02:23:19 PM UTC 2026
% Result : Unsatisfiable 4.63s 1.31s
% Output : CNFRefutation 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 16 unt; 0 def)
% Number of atoms : 90 ( 4 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 108 ( 57 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 57 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
fof(f20,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',element_relation3) ).
fof(f137,axiom,
! [X2,X3,X0,X1] :
( member(least(X0,X2),X2)
| ~ member(X3,X2)
| ~ subclass(X2,X1)
| ~ well_ordering(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',well_ordering3) ).
fof(f140,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X3,least(X0,X2)),X0)
| ~ member(X3,X2)
| ~ subclass(X2,X1)
| ~ well_ordering(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',well_ordering5) ).
fof(f176,negated_conjecture,
well_ordering(element_relation,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_1) ).
fof(f177,negated_conjecture,
subclass(u,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_2) ).
fof(f178,negated_conjecture,
member(v,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_3) ).
fof(f179,negated_conjecture,
member(v,least(element_relation,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_4) ).
tcf(c_211,negated_conjecture,
well_ordering(element_relation,y),
inference(cnf_transformation,[],[f176]) ).
tcf(c_212,negated_conjecture,
subclass(u,y),
inference(cnf_transformation,[],[f177]) ).
tcf(c_213,negated_conjecture,
member(v,u),
inference(cnf_transformation,[],[f178]) ).
tcf(c_214,negated_conjecture,
member(v,least(element_relation,u)),
inference(cnf_transformation,[],[f179]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_224,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X0,X2)
| ~ subclass(X2,X3)
| ~ well_ordering(X1,X3)
| ~ member(ordered_pair(X0,least(X1,X2)),X1) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(least(X0,X2),X2)
| ~ member(X3,X2)
| ~ subclass(X2,X1)
| ~ well_ordering(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(least(X0,X2),X2)
| ~ member(X3,X2)
| ~ subclass(X2,X1)
| ( X1 != y )
| ( X0 != element_relation ) ),
inference(resolution_lifted,[status(thm)],[c_211,c_227]) ).
tcf(c_742,plain,
! [X0: $i,X1: $i] :
( member(least(element_relation,X1),X1)
| ~ subclass(X1,y)
| ~ member(X0,X1) ),
inference(unflattening,[status(thm)],[c_741]) ).
tcf(c_765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X2,X3)
| ~ subclass(X3,X1)
| ~ member(ordered_pair(X2,least(X0,X3)),X0)
| ( X1 != y )
| ( X0 != element_relation ) ),
inference(resolution_lifted,[status(thm)],[c_211,c_226]) ).
tcf(c_766,plain,
! [X0: $i,X1: $i] :
( ~ subclass(X1,y)
| ~ member(X0,X1)
| ~ member(ordered_pair(X0,least(element_relation,X1)),element_relation) ),
inference(unflattening,[status(thm)],[c_765]) ).
tcf(c_1631,plain,
( member(least(element_relation,u),u)
| ~ subclass(u,y) ),
inference(superposition,[status(thm)],[c_213,c_742]) ).
tcf(c_1633,plain,
member(least(element_relation,u),u),
inference(forward_subsumption_resolution,[status(thm)],[c_1631,c_212]) ).
tcf(c_1690,plain,
! [X0: $i] :
( member(X0,y)
| ~ member(X0,u) ),
inference(superposition,[status(thm)],[c_212,c_225]) ).
tcf(c_1691,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_224,c_225]) ).
tcf(c_1710,plain,
member(v,y),
inference(superposition,[status(thm)],[c_213,c_1690]) ).
tcf(c_1712,plain,
member(least(element_relation,u),y),
inference(superposition,[status(thm)],[c_1633,c_1690]) ).
tcf(c_1872,plain,
member(v,universal_class),
inference(superposition,[status(thm)],[c_1710,c_1691]) ).
tcf(c_1873,plain,
member(least(element_relation,u),universal_class),
inference(superposition,[status(thm)],[c_1712,c_1691]) ).
tcf(c_1969,plain,
! [X0: $i] :
( ~ subclass(u,y)
| ~ member(X0,u)
| ~ member(ordered_pair(X0,least(element_relation,u)),element_relation) ),
inference(instantiation,[status(thm)],[c_766]) ).
tcf(c_2032,plain,
( member(ordered_pair(v,least(element_relation,u)),element_relation)
| ~ member(v,least(element_relation,u))
| ~ member(ordered_pair(v,least(element_relation,u)),cross_product(universal_class,universal_class)) ),
inference(instantiation,[status(thm)],[c_215]) ).
tcf(c_2371,plain,
( ~ member(v,u)
| ~ subclass(u,y)
| ~ member(ordered_pair(v,least(element_relation,u)),element_relation) ),
inference(instantiation,[status(thm)],[c_1969]) ).
tcf(c_2381,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(ordered_pair(v,X0),cross_product(X2,X1))
| ~ member(v,X2)
| ~ member(X0,X1) ),
inference(instantiation,[status(thm)],[c_229]) ).
tcf(c_5949,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(v,least(element_relation,u)),cross_product(X1,X0))
| ~ member(v,X1)
| ~ member(least(element_relation,u),X0) ),
inference(instantiation,[status(thm)],[c_2381]) ).
tcf(c_5950,plain,
( member(ordered_pair(v,least(element_relation,u)),cross_product(universal_class,universal_class))
| ~ member(v,universal_class)
| ~ member(least(element_relation,u),universal_class) ),
inference(instantiation,[status(thm)],[c_5949]) ).
tcf(c_5951,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5950,c_2371,c_2032,c_1873,c_1872,c_214,c_212,c_213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM066-1 : 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 : n026.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 02:51:24 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...
% 4.63/1.31 % SZS status Started for theBenchmark.p
% 4.63/1.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.63/1.31
% 4.63/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.63/1.31
% 4.63/1.31 % ------ iProver source info
% 4.63/1.31
% 4.63/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.63/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.63/1.31 % git: non_committed_changes: false
% 4.63/1.31
% 4.63/1.31 % ------ Parsing...% successful
% 4.63/1.31
% 4.63/1.31
% 4.63/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.63/1.31
% 4.63/1.31 % ------ Preprocessing... sup_sim: 4 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.63/1.31
% 4.63/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.63/1.31
% 4.63/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.63/1.31 % ------ Proving...
% 4.63/1.31 % ------ Problem Properties
% 4.63/1.31
% 4.63/1.31 %
% 4.63/1.31 % clauses 33
% 4.63/1.31 % conjectures 3
% 4.63/1.31 % EPR 6
% 4.63/1.31 % Horn 29
% 4.63/1.31 % unary 8
% 4.63/1.31 % binary 9
% 4.63/1.31 % lits 78
% 4.63/1.31 % lits eq 7
% 4.63/1.31 % fd_pure 0
% 4.63/1.31 % fd_pseudo 0
% 4.63/1.31 % fd_cond 2
% 4.63/1.31 % fd_pseudo_cond 1
% 4.63/1.31 % AC symbols 0
% 4.63/1.31
% 4.63/1.31 % ------ Schedule dynamic 5 is on
% 4.63/1.31
% 4.63/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.63/1.31
% 4.63/1.31
% 4.63/1.31 % ------
% 4.63/1.31 % Current options:
% 4.63/1.31 % ------
% 4.63/1.31
% 4.63/1.31
% 4.63/1.31 %
% 4.63/1.31
% 4.63/1.31 % ------ Proving...
% 4.63/1.31 %
% 4.63/1.31
% 4.63/1.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.63/1.31
% 4.63/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.63/1.32
% 4.63/1.32
%------------------------------------------------------------------------------