%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET247-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n018.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 02:47:01 PM UTC 2026
% Result : Unsatisfiable 10.81s 2.32s
% Output : CNFRefutation 10.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 68 ( 29 unt; 2 def)
% Number of atoms : 144 ( 37 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 88 ( 45 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 99 ( 0 sgn 99 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SET004-0.ax',restriction2) ).
fof(f67,axiom,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f122,negated_conjecture,
restrict(xr,x,null_class) != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_restriction_with_null_class3_1) ).
fof(f123,plain,
null_class != restrict(xr,x,null_class),
inference(reorient_equations,[],[f122]) ).
fof(f128,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f15,f128]) ).
fof(f140,plain,
! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(definition_unfolding,[],[f17,f128]) ).
fof(f143,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f186,plain,
null_class != intersection(xr,cross_product(x,null_class)),
inference(definition_unfolding,[],[f123,f28]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_165,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(cnf_transformation,[],[f143]) ).
tcf(c_214,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_255,negated_conjecture,
intersection(xr,cross_product(x,null_class)) != null_class,
inference(cnf_transformation,[],[f186]) ).
tcf(c_2974,definition,
iPr_def_10 = cross_product(x,null_class),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2975,definition,
iPr_def_11 = intersection(xr,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2976,negated_conjecture,
iPr_def_11 != null_class,
inference(demodulation,[status(thm)],[c_255,c_2974,c_2975]) ).
tcf(c_3847,plain,
! [X0: $i] : intersection(X0,iPr_def_10) = intersection(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_2974,c_185]) ).
tcf(c_3849,plain,
intersection(iPr_def_10,xr) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2975,c_3847]) ).
tcf(c_3884,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3849,c_180]) ).
tcf(c_3892,plain,
! [X0: $i] :
( subclass(iPr_def_11,X0)
| member(not_subclass_element(iPr_def_11,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_163,c_3884]) ).
tcf(c_3911,plain,
subclass(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_3892,c_164]) ).
tcf(c_3970,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_163,c_183]) ).
tcf(c_3971,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_214,c_183]) ).
tcf(c_3976,plain,
( ( complement(universal_class) = null_class )
| ~ member(regular(complement(universal_class)),universal_class) ),
inference(instantiation,[status(thm)],[c_3971]) ).
tcf(c_4022,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_165,c_162]) ).
tcf(c_4091,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_163,c_4022]) ).
tcf(c_4194,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ subclass(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3911,c_168]) ).
tcf(c_4555,plain,
! [X0: $i] : subclass(complement(universal_class),X0),
inference(superposition,[status(thm)],[c_4091,c_3970]) ).
tcf(c_4584,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,complement(universal_class)) ),
inference(superposition,[status(thm)],[c_4555,c_162]) ).
tcf(c_4598,plain,
! [X0: $i] :
( member(regular(complement(universal_class)),X0)
| ( complement(universal_class) = null_class ) ),
inference(superposition,[status(thm)],[c_214,c_4584]) ).
tcf(c_4601,plain,
( member(regular(complement(universal_class)),universal_class)
| ( complement(universal_class) = null_class ) ),
inference(instantiation,[status(thm)],[c_4598]) ).
tcf(c_4609,plain,
complement(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_4598,c_3976,c_4601]) ).
tcf(c_4612,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(demodulation,[status(thm)],[c_4584,c_4609]) ).
tcf(c_4613,plain,
! [X0: $i] : subclass(null_class,X0),
inference(demodulation,[status(thm)],[c_4555,c_4609]) ).
tcf(c_4623,plain,
! [X0: $i] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_4609,c_183]) ).
tcf(c_4630,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(global_subsumption_just,[status(thm)],[c_4612,c_4022,c_4612,c_4623]) ).
tcf(c_4745,plain,
! [X0: $i,X1: $i] :
( member(X1,null_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2974,c_174]) ).
tcf(c_4746,plain,
! [X0: $i,X1: $i] : ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_4745,c_4630]) ).
tcf(c_5322,plain,
! [X0: $i,X1: $i] :
( ( cross_product(X0,X1) = null_class )
| ( unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))) = regular(cross_product(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_214,c_176]) ).
tcf(c_9047,plain,
! [X0: $i,X1: $i] :
( ( cross_product(X0,X1) = null_class )
| ~ member(regular(cross_product(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5322,c_4746]) ).
tcf(c_15830,plain,
( ( cross_product(x,null_class) = null_class )
| ~ member(regular(iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2974,c_9047]) ).
tcf(c_15831,plain,
( ( null_class = iPr_def_10 )
| ~ member(regular(iPr_def_10),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_15830,c_2974]) ).
tcf(c_15843,plain,
null_class = iPr_def_10,
inference(superposition,[status(thm)],[c_214,c_15831]) ).
tcf(c_15913,plain,
! [X0: $i] : subclass(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_4613,c_15843]) ).
tcf(c_15927,plain,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_2976,c_15843]) ).
tcf(c_15928,plain,
~ subclass(iPr_def_10,iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_4194,c_15927]) ).
tcf(c_15948,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_15928,c_15913]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET247-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 10:24:49 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.12/0.45
% 0.12/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.45
% 0.12/0.45 % Detected problem language: tptp
% 0.18/0.46 % Proving...
% 10.81/2.32 % SZS status Started for theBenchmark.p
% 10.81/2.32 % SZS status Unsatisfiable for theBenchmark.p
% 10.81/2.32
% 10.81/2.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.81/2.32
% 10.81/2.32 % ------ iProver source info
% 10.81/2.32
% 10.81/2.32 % git: date: 2026-07-19 20:42:38 +0200
% 10.81/2.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.81/2.32 % git: non_committed_changes: false
% 10.81/2.32
% 10.81/2.32 % ------ Parsing...% successful
% 10.81/2.32
% 10.81/2.32
% 10.81/2.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.81/2.32
% 10.81/2.32 % ------ Preprocessing... sup_sim: 0 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: 3 0s sf_e pe_s pe_e %
% 10.81/2.32
% 10.81/2.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.81/2.32
% 10.81/2.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.81/2.32 % ------ Proving...
% 10.81/2.32 % ------ Problem Properties
% 10.81/2.32
% 10.81/2.32 %
% 10.81/2.32 % clauses 84
% 10.81/2.32 % conjectures 1
% 10.81/2.32 % EPR 13
% 10.81/2.32 % Horn 76
% 10.81/2.32 % unary 23
% 10.81/2.32 % binary 40
% 10.81/2.32 % lits 172
% 10.81/2.32 % lits eq 28
% 10.81/2.32 % fd_pure 0
% 10.81/2.32 % fd_pseudo 0
% 10.81/2.32 % fd_cond 3
% 10.81/2.32 % fd_pseudo_cond 7
% 10.81/2.32 % AC symbols 0
% 10.81/2.32
% 10.81/2.32 % ------ Schedule dynamic 5 is on
% 10.81/2.32
% 10.81/2.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.81/2.32
% 10.81/2.32
% 10.81/2.32 % ------
% 10.81/2.32 % Current options:
% 10.81/2.32 % ------
% 10.81/2.32
% 10.81/2.32
% 10.81/2.32 %
% 10.81/2.32
% 10.81/2.32 % ------ Proving...
% 10.81/2.32 %
% 10.81/2.32
% 10.81/2.32 % SZS status Unsatisfiable for theBenchmark.p
% 10.81/2.32
% 10.81/2.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.81/2.32
% 10.81/2.32
%------------------------------------------------------------------------------