%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET157-6 : 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 : 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 02:46:47 PM UTC 2026
% Result : Unsatisfiable 15.14s 3.30s
% Output : CNFRefutation 17.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of formulae : 86 ( 37 unt; 5 def)
% Number of atoms : 221 ( 31 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 124 ( 60 ~; 64 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 85 !; 0 ?; 61 :)
% 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(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
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,
union(x,y) = universal_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_complement_is_unique_1) ).
fof(f123,plain,
universal_class = union(x,y),
inference(reorient_equations,[],[f122]) ).
fof(f124,negated_conjecture,
intersection(x,y) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_complement_is_unique_2) ).
fof(f125,plain,
null_class = intersection(x,y),
inference(reorient_equations,[],[f124]) ).
fof(f126,negated_conjecture,
complement(x) != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_complement_is_unique_3) ).
fof(f127,plain,
y != complement(x),
inference(reorient_equations,[],[f126]) ).
fof(f190,plain,
universal_class = complement(intersection(complement(x),complement(y))),
inference(definition_unfolding,[],[f123,f26]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_167,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_216,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_257,negated_conjecture,
complement(intersection(complement(x),complement(y))) = universal_class,
inference(cnf_transformation,[],[f190]) ).
tcf(c_258,negated_conjecture,
intersection(x,y) = null_class,
inference(cnf_transformation,[],[f125]) ).
tcf(c_259,negated_conjecture,
complement(x) != y,
inference(cnf_transformation,[],[f127]) ).
tcf(c_2988,definition,
iPr_def_10 = complement(x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2989,definition,
iPr_def_11 = intersection(x,y),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2990,definition,
iPr_def_12 = complement(y),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2991,definition,
iPr_def_13 = intersection(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2992,definition,
iPr_def_14 = complement(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2993,negated_conjecture,
iPr_def_10 != y,
inference(demodulation,[status(thm)],[c_259,c_2988]) ).
tcf(c_2994,negated_conjecture,
iPr_def_11 = null_class,
inference(demodulation,[status(thm)],[c_258,c_2989]) ).
tcf(c_2995,negated_conjecture,
iPr_def_14 = universal_class,
inference(demodulation,[status(thm)],[c_257,c_2990,c_2991,c_2992]) ).
tcf(c_3860,plain,
! [X0: $i] : subclass(X0,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_167,c_2995]) ).
tcf(c_3898,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_216,c_2994]) ).
tcf(c_4103,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_165,c_185]) ).
tcf(c_4110,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_14)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_2992,c_185]) ).
tcf(c_4463,plain,
! [X0: $i,X1: $i] :
( member(X0,iPr_def_14)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_3860,c_164]) ).
tcf(c_4521,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_186,c_2995]) ).
tcf(c_4534,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(X1))
| member(not_subclass_element(X0,complement(X1)),X1)
| ~ member(not_subclass_element(X0,complement(X1)),iPr_def_14) ),
inference(superposition,[status(thm)],[c_4521,c_166]) ).
tcf(c_4604,plain,
( ( iPr_def_10 = y )
| ~ subclass(iPr_def_10,y)
| ~ subclass(y,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_170]) ).
tcf(c_4641,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),iPr_def_14) ),
inference(superposition,[status(thm)],[c_165,c_4463]) ).
tcf(c_4849,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,y)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_2989,c_184]) ).
tcf(c_5793,plain,
! [X0: $i] :
( member(X0,x)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2989,c_182]) ).
tcf(c_5946,plain,
! [X0: $i] : ~ member(X0,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_4110,c_4463]) ).
tcf(c_5948,plain,
iPr_def_11 = iPr_def_13,
inference(superposition,[status(thm)],[c_3898,c_5946]) ).
tcf(c_5953,plain,
! [X0: $i] : ~ member(X0,iPr_def_11),
inference(demodulation,[status(thm)],[c_5946,c_5948]) ).
tcf(c_5954,plain,
intersection(iPr_def_10,iPr_def_12) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2991,c_5948]) ).
tcf(c_6650,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,iPr_def_12)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_5954,c_184]) ).
tcf(c_6653,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_12)
| ~ member(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6650,c_5953]) ).
tcf(c_7384,plain,
! [X0: $i] : ~ member(X0,iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_5793,c_5953]) ).
tcf(c_9345,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(X1))
| member(not_subclass_element(X0,complement(X1)),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4534,c_4641]) ).
tcf(c_10296,plain,
! [X0: $i] :
( subclass(iPr_def_10,X0)
| ~ member(not_subclass_element(iPr_def_10,X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_165,c_6653]) ).
tcf(c_12023,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,y)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_2989,c_184]) ).
tcf(c_12044,plain,
! [X0: $i] :
( ~ member(X0,y)
| ~ member(X0,x) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12023,c_7384]) ).
tcf(c_12380,plain,
! [X0: $i] :
( subclass(X0,complement(x))
| member(not_subclass_element(X0,iPr_def_10),x) ),
inference(superposition,[status(thm)],[c_2988,c_9345]) ).
tcf(c_12381,plain,
! [X0: $i] :
( subclass(X0,complement(y))
| member(not_subclass_element(X0,iPr_def_12),y) ),
inference(superposition,[status(thm)],[c_2990,c_9345]) ).
tcf(c_12414,plain,
subclass(iPr_def_10,complement(iPr_def_12)),
inference(superposition,[status(thm)],[c_9345,c_10296]) ).
tcf(c_12422,plain,
! [X0: $i] :
( subclass(X0,iPr_def_12)
| member(not_subclass_element(X0,iPr_def_12),y) ),
inference(light_normalisation,[status(thm)],[c_12381,c_2990]) ).
tcf(c_12425,plain,
! [X0: $i] :
( subclass(X0,iPr_def_10)
| member(not_subclass_element(X0,iPr_def_10),x) ),
inference(light_normalisation,[status(thm)],[c_12380,c_2988]) ).
tcf(c_12641,plain,
( ( complement(iPr_def_12) = iPr_def_10 )
| ~ subclass(complement(iPr_def_12),iPr_def_10) ),
inference(superposition,[status(thm)],[c_12414,c_170]) ).
tcf(c_13244,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0)
| ~ member(not_subclass_element(complement(complement(X0)),X1),iPr_def_14) ),
inference(superposition,[status(thm)],[c_4521,c_4103]) ).
tcf(c_13437,plain,
! [X0: $i] :
( ~ member(X0,x)
| ~ member(X0,y) ),
inference(global_subsumption_just,[status(thm)],[c_4849,c_12044]) ).
tcf(c_13438,plain,
! [X0: $i] :
( ~ member(X0,y)
| ~ member(X0,x) ),
inference(renaming,[status(thm)],[c_13437]) ).
tcf(c_13443,plain,
! [X0: $i] :
( subclass(x,X0)
| ~ member(not_subclass_element(x,X0),y) ),
inference(superposition,[status(thm)],[c_165,c_13438]) ).
tcf(c_13460,plain,
! [X0: $i] :
( subclass(X0,iPr_def_10)
| ~ member(not_subclass_element(X0,iPr_def_10),y) ),
inference(superposition,[status(thm)],[c_12425,c_13438]) ).
tcf(c_13646,plain,
subclass(x,iPr_def_12),
inference(superposition,[status(thm)],[c_12422,c_13443]) ).
tcf(c_13653,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_13646,c_164]) ).
tcf(c_13688,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13244,c_4641]) ).
tcf(c_13699,plain,
! [X0: $i] : subclass(complement(complement(X0)),X0),
inference(superposition,[status(thm)],[c_13688,c_166]) ).
tcf(c_14340,plain,
subclass(complement(iPr_def_12),y),
inference(superposition,[status(thm)],[c_2990,c_13699]) ).
tcf(c_14404,plain,
! [X0: $i] :
( subclass(X0,iPr_def_10)
| member(not_subclass_element(X0,iPr_def_10),iPr_def_12) ),
inference(superposition,[status(thm)],[c_12425,c_13653]) ).
tcf(c_15211,plain,
subclass(complement(iPr_def_12),iPr_def_10),
inference(superposition,[status(thm)],[c_14404,c_4103]) ).
tcf(c_15216,plain,
complement(iPr_def_12) = iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_12641,c_15211]) ).
tcf(c_15218,plain,
subclass(iPr_def_10,y),
inference(demodulation,[status(thm)],[c_14340,c_15216]) ).
tcf(c_15223,plain,
( ( y = iPr_def_10 )
| ~ subclass(y,iPr_def_10) ),
inference(superposition,[status(thm)],[c_15218,c_170]) ).
tcf(c_15709,plain,
~ subclass(y,iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_15223,c_2993,c_4604,c_15218]) ).
tcf(c_21378,plain,
subclass(y,iPr_def_10),
inference(superposition,[status(thm)],[c_165,c_13460]) ).
tcf(c_21384,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_21378,c_15709]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET157-6 : 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 : n009.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 10:03:59 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...
% 15.14/3.30 % SZS status Started for theBenchmark.p
% 15.14/3.30 % SZS status Unsatisfiable for theBenchmark.p
% 15.14/3.30
% 15.14/3.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.14/3.30
% 15.14/3.30 % ------ iProver source info
% 15.14/3.30
% 15.14/3.30 % git: date: 2026-07-19 20:42:38 +0200
% 15.14/3.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.14/3.30 % git: non_committed_changes: false
% 15.14/3.30
% 15.14/3.30 % ------ Parsing...% successful
% 15.14/3.30
% 15.14/3.30
% 15.14/3.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.14/3.30
% 15.14/3.30 % ------ 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 %
% 15.14/3.30
% 15.14/3.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.14/3.30
% 15.14/3.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 15.14/3.30 % ------ Proving...
% 15.14/3.30 % ------ Problem Properties
% 15.14/3.30
% 15.14/3.30 %
% 15.14/3.30 % clauses 89
% 15.14/3.30 % conjectures 3
% 15.14/3.30 % EPR 15
% 15.14/3.30 % Horn 81
% 15.14/3.30 % unary 28
% 15.14/3.30 % binary 40
% 15.14/3.30 % lits 177
% 15.14/3.30 % lits eq 33
% 15.14/3.30 % fd_pure 0
% 15.14/3.30 % fd_pseudo 0
% 15.14/3.30 % fd_cond 3
% 15.14/3.30 % fd_pseudo_cond 7
% 15.14/3.30 % AC symbols 0
% 15.14/3.30
% 15.14/3.30 % ------ Schedule dynamic 5 is on
% 15.14/3.30
% 15.14/3.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 15.14/3.30
% 15.14/3.30
% 15.14/3.30 % ------
% 15.14/3.30 % Current options:
% 15.14/3.30 % ------
% 15.14/3.30
% 15.14/3.30
% 15.14/3.30 %
% 15.14/3.30
% 15.14/3.30 % ------ Proving...
% 15.14/3.30 %
% 15.14/3.30
% 15.14/3.30 % SZS status Unsatisfiable for theBenchmark.p
% 15.14/3.30
% 15.14/3.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.99/3.30
% 17.99/3.30
%------------------------------------------------------------------------------