%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM044-1 : 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 : n009.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 02:23:17 PM UTC 2026
% Result : Unsatisfiable 3.18s 1.18s
% Output : CNFRefutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 58 ( 26 unt; 5 def)
% Number of atoms : 133 ( 24 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 80 ( 42 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 73 ( 0 sgn 73 !; 0 ?; 40 :)
% 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(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
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(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f29,axiom,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction2) ).
fof(f67,axiom,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f123,axiom,
! [X0,X1] :
( subclass(restrict(X0,X1,X1),complement(identity_relation))
| ~ irreflexive(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',irreflexive1) ).
fof(f176,negated_conjecture,
irreflexive(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property6_1) ).
fof(f177,negated_conjecture,
restrict(intersection(x,identity_relation),y,y) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property6_2) ).
fof(f178,plain,
null_class != restrict(intersection(x,identity_relation),y,y),
inference(reorient_equations,[],[f177]) ).
fof(f202,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f245,plain,
! [X0,X1] :
( subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation))
| ~ irreflexive(X0,X1) ),
inference(definition_unfolding,[],[f123,f28]) ).
fof(f269,plain,
null_class != intersection(intersection(x,identity_relation),cross_product(y,y)),
inference(definition_unfolding,[],[f178,f28]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(cnf_transformation,[],[f202]) ).
tcf(c_261,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation))
| ~ irreflexive(X0,X1) ),
inference(cnf_transformation,[],[f245]) ).
tcf(c_344,negated_conjecture,
irreflexive(x,y),
inference(cnf_transformation,[],[f176]) ).
tcf(c_345,negated_conjecture,
intersection(intersection(x,identity_relation),cross_product(y,y)) != null_class,
inference(cnf_transformation,[],[f269]) ).
tcf(c_460,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation))
| ~ irreflexive(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_302]) ).
tcf(c_1723,plain,
intersection(cross_product(y,y),intersection(x,identity_relation)) != null_class,
inference(demodulation,[status(thm)],[c_345,c_232]) ).
tcf(c_2115,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation))
| ( X1 != y )
| ( X0 != x ) ),
inference(resolution_lifted,[status(thm)],[c_344,c_460]) ).
tcf(c_2116,plain,
subclass(intersection(x,cross_product(y,y)),complement(identity_relation)),
inference(unflattening,[status(thm)],[c_2115]) ).
tcf(c_4636,definition,
iPr_def_10 = cross_product(y,y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_4637,definition,
iPr_def_11 = intersection(x,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_4638,definition,
iPr_def_12 = complement(identity_relation),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_4639,definition,
iPr_def_13 = intersection(x,identity_relation),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_4640,definition,
iPr_def_14 = intersection(iPr_def_10,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_4641,plain,
subclass(iPr_def_11,iPr_def_12),
inference(demodulation,[status(thm)],[c_2116,c_4638,c_4636,c_4637]) ).
tcf(c_4642,plain,
iPr_def_14 != null_class,
inference(demodulation,[status(thm)],[c_1723,c_4639,c_4640]) ).
tcf(c_5846,plain,
! [X0: $i] : intersection(X0,iPr_def_10) = intersection(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_4636,c_232]) ).
tcf(c_5848,plain,
intersection(iPr_def_10,x) = iPr_def_11,
inference(demodulation,[status(thm)],[c_4637,c_5846]) ).
tcf(c_5936,plain,
! [X0: $i] :
( member(X0,x)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_4639,c_227]) ).
tcf(c_5940,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_4640,c_227]) ).
tcf(c_6063,plain,
! [X0: $i] :
( member(X0,identity_relation)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_4639,c_228]) ).
tcf(c_6068,plain,
! [X0: $i] :
( member(X0,iPr_def_13)
| ~ member(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_4640,c_228]) ).
tcf(c_6111,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_12)
| ~ member(X0,identity_relation) ),
inference(superposition,[status(thm)],[c_4638,c_230]) ).
tcf(c_6166,plain,
! [X0: $i] :
( subclass(iPr_def_14,X0)
| member(not_subclass_element(iPr_def_14,X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_210,c_6068]) ).
tcf(c_6294,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4641,c_209]) ).
tcf(c_6651,plain,
! [X0: $i] :
( subclass(iPr_def_14,X0)
| member(not_subclass_element(iPr_def_14,X0),identity_relation) ),
inference(superposition,[status(thm)],[c_6166,c_6063]) ).
tcf(c_6892,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,iPr_def_10)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_5848,c_229]) ).
tcf(c_7104,plain,
subclass(iPr_def_14,identity_relation),
inference(superposition,[status(thm)],[c_6651,c_211]) ).
tcf(c_7112,plain,
! [X0: $i] :
( member(X0,identity_relation)
| ~ member(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_7104,c_209]) ).
tcf(c_7119,plain,
! [X0: $i] : ~ member(X0,iPr_def_14),
inference(global_subsumption_just,[status(thm)],[c_7112,c_5940,c_5936,c_6068,c_6111,c_6294,c_6892,c_7112]) ).
tcf(c_7123,plain,
null_class = iPr_def_14,
inference(superposition,[status(thm)],[c_261,c_7119]) ).
tcf(c_7154,plain,
iPr_def_14 != iPr_def_14,
inference(demodulation,[status(thm)],[c_4642,c_7123]) ).
tcf(c_7155,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_7154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM044-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 02:45:13 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 3.18/1.18 % SZS status Started for theBenchmark.p
% 3.18/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.18/1.18
% 3.18/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.18/1.18
% 3.18/1.18 % ------ iProver source info
% 3.18/1.18
% 3.18/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.18/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.18/1.18 % git: non_committed_changes: false
% 3.18/1.18
% 3.18/1.18 % ------ Parsing...% successful
% 3.18/1.18
% 3.18/1.18
% 3.18/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.18/1.18
% 3.18/1.18 % ------ Preprocessing... sup_sim: 1 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 %
% 3.18/1.18
% 3.18/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.18/1.18
% 3.18/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.18/1.18 % ------ Proving...
% 3.18/1.18 % ------ Problem Properties
% 3.18/1.18
% 3.18/1.18 %
% 3.18/1.18 % clauses 121
% 3.18/1.18 % conjectures 0
% 3.18/1.18 % EPR 16
% 3.18/1.18 % Horn 109
% 3.18/1.18 % unary 32
% 3.18/1.18 % binary 58
% 3.18/1.18 % lits 255
% 3.18/1.18 % lits eq 45
% 3.18/1.18 % fd_pure 0
% 3.18/1.18 % fd_pseudo 0
% 3.18/1.18 % fd_cond 5
% 3.18/1.18 % fd_pseudo_cond 10
% 3.18/1.18 % AC symbols 0
% 3.18/1.18
% 3.18/1.18 % ------ Schedule dynamic 5 is on
% 3.18/1.18
% 3.18/1.18 % ------ no conjectures: strip conj schedule
% 3.18/1.18
% 3.18/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.18/1.18
% 3.18/1.18
% 3.18/1.18 % ------
% 3.18/1.18 % Current options:
% 3.18/1.18 % ------
% 3.18/1.18
% 3.18/1.18
% 3.18/1.18 %
% 3.18/1.18
% 3.18/1.18 % ------ Proving...
% 3.18/1.18 %
% 3.18/1.18
% 3.18/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.18/1.18
% 3.18/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.18/1.18
%------------------------------------------------------------------------------