%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM094-1 : 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 : n014.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 02:23:21 PM UTC 2026
% Result : Unsatisfiable 55.38s 10.28s
% Output : CNFRefutation 55.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 71 ( 21 unt; 0 def)
% Number of atoms : 158 ( 19 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 173 ( 86 ~; 87 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 93 !; 0 ?; 65 :)
% 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(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f6,axiom,
! [X0,X1] :
( subclass(X1,X0)
| X0 != X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',equal_implies_subclass2) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
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(f146,axiom,
! [X2,X0,X1] :
( subclass(X1,X2)
| ~ section(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',section1) ).
fof(f176,negated_conjecture,
well_ordering(xr,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sections_property3_1) ).
fof(f177,negated_conjecture,
section(xr,w,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sections_property3_2) ).
fof(f178,negated_conjecture,
~ member(least(xr,intersection(complement(w),y)),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sections_property3_3) ).
fof(f179,negated_conjecture,
y != w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sections_property3_4) ).
fof(f271,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f6]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_214,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_216,plain,
! [X0: $i] : subclass(X0,X0),
inference(cnf_transformation,[],[f271]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(least(X0,X3),X3)
| ~ subclass(X3,X1)
| ~ member(X2,X3)
| ~ well_ordering(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X1,X2)
| ~ section(X0,X1,X2) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_346,negated_conjecture,
well_ordering(xr,y),
inference(cnf_transformation,[],[f176]) ).
tcf(c_347,negated_conjecture,
section(xr,w,y),
inference(cnf_transformation,[],[f177]) ).
tcf(c_348,negated_conjecture,
~ member(least(xr,intersection(complement(w),y)),y),
inference(cnf_transformation,[],[f178]) ).
tcf(c_349,negated_conjecture,
y != w,
inference(cnf_transformation,[],[f179]) ).
tcf(c_484,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X1,X2)
| ~ section(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_320]) ).
tcf(c_2134,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X2,X1)
| ( X2 != w )
| ( X1 != y )
| ( X0 != xr ) ),
inference(resolution_lifted,[status(thm)],[c_347,c_484]) ).
tcf(c_2135,plain,
subclass(w,y),
inference(unflattening,[status(thm)],[c_2134]) ).
tcf(c_4854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( well_ordering(X0,X2)
| ~ well_ordering(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_6075,plain,
( ( y = w )
| ~ subclass(w,y)
| ~ subclass(y,w) ),
inference(instantiation,[status(thm)],[c_217]) ).
tcf(c_6101,plain,
! [X0: $i,X1: $i] :
( well_ordering(X0,X1)
| ~ well_ordering(xr,y)
| ( X1 != y )
| ( X0 != xr ) ),
inference(instantiation,[status(thm)],[c_4854]) ).
tcf(c_6134,plain,
( subclass(y,w)
| ~ member(not_subclass_element(y,w),w) ),
inference(instantiation,[status(thm)],[c_213]) ).
tcf(c_6135,plain,
( subclass(y,w)
| member(not_subclass_element(y,w),y) ),
inference(instantiation,[status(thm)],[c_212]) ).
tcf(c_6146,plain,
! [X0: $i] :
( ( X0 = y )
| ~ subclass(y,X0)
| ~ subclass(X0,y) ),
inference(instantiation,[status(thm)],[c_217]) ).
tcf(c_7959,plain,
! [X0: $i] :
( member(not_subclass_element(y,w),intersection(X0,y))
| ~ member(not_subclass_element(y,w),y)
| ~ member(not_subclass_element(y,w),X0) ),
inference(instantiation,[status(thm)],[c_231]) ).
tcf(c_7964,plain,
! [X0: $i] :
( member(not_subclass_element(y,w),X0)
| ~ subclass(y,X0)
| ~ member(not_subclass_element(y,w),y) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_7965,plain,
( member(not_subclass_element(y,w),universal_class)
| ~ subclass(y,universal_class)
| ~ member(not_subclass_element(y,w),y) ),
inference(instantiation,[status(thm)],[c_7964]) ).
tcf(c_8137,plain,
! [X0: $i] :
( ( X0 = xr )
| ~ subclass(xr,X0)
| ~ subclass(X0,xr) ),
inference(instantiation,[status(thm)],[c_217]) ).
tcf(c_8265,plain,
subclass(y,universal_class),
inference(instantiation,[status(thm)],[c_214]) ).
tcf(c_8866,plain,
! [X0: $i] :
( member(least(xr,intersection(complement(w),y)),y)
| ~ member(least(xr,intersection(complement(w),y)),intersection(X0,y)) ),
inference(instantiation,[status(thm)],[c_230]) ).
tcf(c_10404,plain,
( member(not_subclass_element(y,w),w)
| member(not_subclass_element(y,w),complement(w))
| ~ member(not_subclass_element(y,w),universal_class) ),
inference(instantiation,[status(thm)],[c_233]) ).
tcf(c_16404,plain,
( member(least(xr,intersection(complement(w),y)),y)
| ~ member(least(xr,intersection(complement(w),y)),intersection(complement(w),y)) ),
inference(instantiation,[status(thm)],[c_8866]) ).
tcf(c_16405,plain,
! [X0: $i,X1: $i] :
( member(least(xr,intersection(complement(w),y)),intersection(complement(w),y))
| ~ well_ordering(xr,X1)
| ~ subclass(intersection(complement(w),y),X1)
| ~ member(X0,intersection(complement(w),y)) ),
inference(instantiation,[status(thm)],[c_314]) ).
tcf(c_18018,plain,
( ( xr = xr )
| ~ subclass(xr,xr) ),
inference(instantiation,[status(thm)],[c_8137]) ).
tcf(c_18019,plain,
subclass(xr,xr),
inference(instantiation,[status(thm)],[c_216]) ).
tcf(c_21257,plain,
! [X0: $i] :
( well_ordering(xr,X0)
| ~ well_ordering(xr,y)
| ( xr != xr )
| ( X0 != y ) ),
inference(instantiation,[status(thm)],[c_6101]) ).
tcf(c_40019,plain,
! [X0: $i] :
( member(least(xr,intersection(complement(w),y)),intersection(complement(w),y))
| ~ well_ordering(xr,X0)
| ~ subclass(intersection(complement(w),y),X0)
| ~ member(not_subclass_element(y,w),intersection(complement(w),y)) ),
inference(instantiation,[status(thm)],[c_16405]) ).
tcf(c_40020,plain,
( member(not_subclass_element(y,w),intersection(complement(w),y))
| ~ member(not_subclass_element(y,w),y)
| ~ member(not_subclass_element(y,w),complement(w)) ),
inference(instantiation,[status(thm)],[c_7959]) ).
tcf(c_48619,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_212,c_230]) ).
tcf(c_48651,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X1),
inference(superposition,[status(thm)],[c_48619,c_213]) ).
tcf(c_48899,plain,
( ( y = w )
| ~ subclass(y,w) ),
inference(superposition,[status(thm)],[c_2135,c_217]) ).
tcf(c_48910,plain,
~ subclass(y,w),
inference(forward_subsumption_resolution,[status(thm)],[c_48899,c_349]) ).
tcf(c_49392,plain,
! [X0: $i,X1: $i] :
( member(least(xr,X1),X1)
| ~ subclass(X1,y)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_346,c_314]) ).
tcf(c_49459,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(least(xr,X0),X0)
| ~ subclass(X0,y) ),
inference(superposition,[status(thm)],[c_212,c_49392]) ).
tcf(c_49507,plain,
( member(least(xr,y),y)
| ~ subclass(y,y) ),
inference(superposition,[status(thm)],[c_49459,c_48910]) ).
tcf(c_49550,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,X2)
| member(least(xr,X0),X1)
| ~ subclass(X0,y)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_49459,c_211]) ).
tcf(c_49563,plain,
member(least(xr,y),y),
inference(forward_subsumption_resolution,[status(thm)],[c_49507,c_216]) ).
tcf(c_49626,plain,
! [X0: $i] :
( member(least(xr,y),X0)
| ~ subclass(y,X0) ),
inference(superposition,[status(thm)],[c_49563,c_211]) ).
tcf(c_49825,plain,
! [X0: $i] :
( subclass(intersection(complement(w),y),X0)
| ~ subclass(intersection(complement(w),y),y) ),
inference(superposition,[status(thm)],[c_49550,c_348]) ).
tcf(c_49849,plain,
! [X0: $i] : subclass(intersection(complement(w),y),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_49825,c_48651]) ).
tcf(c_54150,plain,
! [X0: $i] :
( member(least(xr,X0),X0)
| ~ subclass(y,X0)
| ~ subclass(X0,y) ),
inference(superposition,[status(thm)],[c_49626,c_49392]) ).
tcf(c_54204,plain,
! [X0: $i] :
( ~ subclass(X0,y)
| ~ subclass(y,X0) ),
inference(global_subsumption_just,[status(thm)],[c_54150,c_346,c_349,c_348,c_2135,c_6075,c_6135,c_6134,c_6146,c_7965,c_8265,c_10404,c_16404,c_18018,c_18019,c_21257,c_40019,c_40020,c_49849]) ).
tcf(c_54205,plain,
! [X0: $i] :
( ~ subclass(y,X0)
| ~ subclass(X0,y) ),
inference(renaming,[status(thm)],[c_54204]) ).
tcf(c_54211,plain,
~ subclass(y,y),
inference(superposition,[status(thm)],[c_216,c_54205]) ).
tcf(c_54245,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_54211,c_216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM094-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.64 % Computer : n014.cluster.edu
% 0.16/0.64 % Model : x86_64 x86_64
% 0.16/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.64 % Memory : 8046.5625MB
% 0.16/0.64 % OS : Linux 6.8.0-71-generic
% 0.16/0.64 % CPULimit : 300
% 0.16/0.64 % WCLimit : 300
% 0.16/0.64 % DateTime : Thu Sep 24 02:53:34 UTC 2026
% 0.16/0.65 % CPUTime :
% 0.16/0.65 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.21/0.70 Running first-order theorem proving
% 0.21/0.70 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
% 0.21/0.72
% 0.21/0.72 % ======== iProver multi-core TPTP/SMT =========
% 0.21/0.72
% 0.21/0.72 % Detected problem language: tptp
% 0.21/0.73 % Proving...
% 55.38/10.28 % SZS status Started for theBenchmark.p
% 55.38/10.28 % SZS status Unsatisfiable for theBenchmark.p
% 55.38/10.28
% 55.38/10.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 55.38/10.28
% 55.38/10.28 % ------ iProver source info
% 55.38/10.28
% 55.38/10.28 % git: date: 2026-07-19 20:42:38 +0200
% 55.38/10.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 55.38/10.28 % git: non_committed_changes: false
% 55.38/10.28
% 55.38/10.28 % ------ Parsing...% successful
% 55.38/10.28
% 55.38/10.28
% 55.38/10.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 55.38/10.28
% 55.38/10.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 55.38/10.28
% 55.38/10.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 55.38/10.28
% 55.38/10.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 55.38/10.28 % ------ Proving...
% 55.38/10.28 % ------ Problem Properties
% 55.38/10.28
% 55.38/10.28 %
% 55.38/10.28 % clauses 119
% 55.38/10.28 % conjectures 3
% 55.38/10.28 % EPR 17
% 55.38/10.28 % Horn 107
% 55.38/10.28 % unary 30
% 55.38/10.28 % binary 58
% 55.38/10.28 % lits 253
% 55.38/10.28 % lits eq 40
% 55.38/10.28 % fd_pure 0
% 55.38/10.28 % fd_pseudo 0
% 55.38/10.28 % fd_cond 5
% 55.38/10.28 % fd_pseudo_cond 10
% 55.38/10.28 % AC symbols 0
% 55.38/10.28
% 55.38/10.28 % ------ Input Options Time Limit: Unbounded
% 55.38/10.28
% 55.38/10.28
% 55.38/10.28 % ------
% 55.38/10.28 % Current options:
% 55.38/10.28 % ------
% 55.38/10.28
% 55.38/10.28
% 55.38/10.28 %
% 55.38/10.28
% 55.38/10.28 % ------ Proving...
% 55.38/10.28 %
% 55.38/10.28
% 55.38/10.28 % SZS status Unsatisfiable for theBenchmark.p
% 55.38/10.28
% 55.38/10.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 55.38/10.28
% 55.38/10.28
%------------------------------------------------------------------------------