%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET553-6 : 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 : n019.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 02:47:24 PM UTC 2026
% Result : Unsatisfiable 2.71s 1.09s
% Output : CNFRefutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 16
% Syntax : Number of formulae : 27 ( 19 unt; 9 def)
% Number of atoms : 61 ( 13 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 17 ( 9 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
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(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f81,axiom,
! [X0] : complement(domain_of(intersection(X0,identity_relation))) = diagonalise(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',diagonalisation) ).
fof(f82,axiom,
! [X0] : intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cantor_class) ).
fof(f122,negated_conjecture,
~ subclass(cantor(x),domain_of(x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cantor_class_alternate_defn_1) ).
fof(f135,plain,
! [X0] : cantor(X0) = intersection(domain_of(X0),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),X0),identity_relation)))),
inference(definition_unfolding,[],[f82,f81,f39]) ).
fof(f185,plain,
~ subclass(intersection(domain_of(x),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),x),identity_relation)))),domain_of(x)),
inference(definition_unfolding,[],[f122,f135]) ).
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_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_255,negated_conjecture,
~ subclass(intersection(domain_of(x),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),x),identity_relation)))),domain_of(x)),
inference(cnf_transformation,[],[f185]) ).
tcf(c_2974,definition,
iPr_def_10 = domain_of(x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2975,definition,
iPr_def_11 = cross_product(element_relation,universal_class),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2976,definition,
iPr_def_12 = flip(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2977,definition,
iPr_def_13 = domain_of(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2978,definition,
iPr_def_14 = compose(iPr_def_13,x),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2979,definition,
iPr_def_15 = intersection(iPr_def_14,identity_relation),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_2980,definition,
iPr_def_16 = domain_of(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_2981,definition,
iPr_def_17 = complement(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_2982,definition,
iPr_def_18 = intersection(iPr_def_10,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_2983,negated_conjecture,
~ subclass(iPr_def_18,iPr_def_10),
inference(demodulation,[status(thm)],[c_255,c_2975,c_2976,c_2977,c_2978,c_2979,c_2980,c_2981,c_2974,c_2982]) ).
tcf(c_3909,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_18) ),
inference(superposition,[status(thm)],[c_2982,c_180]) ).
tcf(c_4027,plain,
! [X0: $i] :
( subclass(iPr_def_18,X0)
| member(not_subclass_element(iPr_def_18,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_163,c_3909]) ).
tcf(c_4091,plain,
subclass(iPr_def_18,iPr_def_10),
inference(superposition,[status(thm)],[c_4027,c_164]) ).
tcf(c_4092,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4091,c_2983]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET553-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 11:16:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.71/1.09 % SZS status Started for theBenchmark.p
% 2.71/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 2.71/1.09
% 2.71/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.71/1.09
% 2.71/1.09 % ------ iProver source info
% 2.71/1.09
% 2.71/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 2.71/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.71/1.09 % git: non_committed_changes: false
% 2.71/1.09
% 2.71/1.09 % ------ Parsing...% successful
% 2.71/1.09
% 2.71/1.09
% 2.71/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.71/1.09
% 2.71/1.09 % ------ 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 %
% 2.71/1.09
% 2.71/1.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.71/1.09
% 2.71/1.09 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.71/1.09 % ------ Proving...
% 2.71/1.09 % ------ Problem Properties
% 2.71/1.09
% 2.71/1.09 %
% 2.71/1.09 % clauses 91
% 2.71/1.09 % conjectures 1
% 2.71/1.09 % EPR 13
% 2.71/1.09 % Horn 83
% 2.71/1.09 % unary 30
% 2.71/1.09 % binary 40
% 2.71/1.09 % lits 179
% 2.71/1.09 % lits eq 34
% 2.71/1.09 % fd_pure 0
% 2.71/1.09 % fd_pseudo 0
% 2.71/1.09 % fd_cond 3
% 2.71/1.09 % fd_pseudo_cond 7
% 2.71/1.09 % AC symbols 0
% 2.71/1.09
% 2.71/1.09 % ------ Schedule dynamic 5 is on
% 2.71/1.09
% 2.71/1.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.71/1.09
% 2.71/1.09
% 2.71/1.09 % ------
% 2.71/1.09 % Current options:
% 2.71/1.09 % ------
% 2.71/1.09
% 2.71/1.09
% 2.71/1.09 %
% 2.71/1.09
% 2.71/1.09 % ------ Proving...
% 2.71/1.09 %
% 2.71/1.09
% 2.71/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 2.71/1.09
% 2.71/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.71/1.09
% 2.71/1.09
%------------------------------------------------------------------------------