%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET123-6 : 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 : n004.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 02:46:41 PM UTC 2026
% Result : Unsatisfiable 7.06s 1.75s
% Output : CNFRefutation 7.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 47 ( 26 unt; 5 def)
% Number of atoms : 112 ( 18 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 65 ( 32 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 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 : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?; 20 :)
% 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(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
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(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(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
fof(f101,axiom,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_set_builder) ).
fof(f102,negated_conjecture,
member(x,set_builder(y,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_1) ).
fof(f103,negated_conjecture,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_2) ).
fof(f104,negated_conjecture,
~ member(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_3) ).
fof(f110,plain,
! [X0,X1] : set_builder(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(X1))),
inference(definition_unfolding,[],[f101,f26,f12]) ).
fof(f154,plain,
member(x,complement(intersection(complement(unordered_pair(y,y)),complement(z)))),
inference(definition_unfolding,[],[f102,f110]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_147,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_219,negated_conjecture,
member(x,complement(intersection(complement(unordered_pair(y,y)),complement(z)))),
inference(cnf_transformation,[],[f154]) ).
tcf(c_220,negated_conjecture,
x != y,
inference(cnf_transformation,[],[f103]) ).
tcf(c_221,negated_conjecture,
~ member(x,z),
inference(cnf_transformation,[],[f104]) ).
tcf(c_2652,definition,
iPr_def_10 = unordered_pair(y,y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2653,definition,
iPr_def_11 = complement(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2654,definition,
iPr_def_12 = complement(z),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2655,definition,
iPr_def_13 = intersection(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2656,definition,
iPr_def_14 = complement(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2657,negated_conjecture,
~ member(x,z),
inference(demodulation,[status(thm)],[c_221]) ).
tcf(c_2658,negated_conjecture,
x != y,
inference(demodulation,[status(thm)],[c_220]) ).
tcf(c_2659,negated_conjecture,
member(x,iPr_def_14),
inference(demodulation,[status(thm)],[c_219,c_2654,c_2652,c_2653,c_2655,c_2656]) ).
tcf(c_3600,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_14)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_2656,c_165]) ).
tcf(c_3648,plain,
! [X0: $i] :
( member(x,X0)
| ~ subclass(iPr_def_14,X0) ),
inference(superposition,[status(thm)],[c_2659,c_144]) ).
tcf(c_3738,plain,
member(x,universal_class),
inference(superposition,[status(thm)],[c_147,c_3648]) ).
tcf(c_3804,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| member(X0,z)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2654,c_166]) ).
tcf(c_3805,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| member(X0,iPr_def_10)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2653,c_166]) ).
tcf(c_4065,plain,
! [X0: $i] :
( member(X0,iPr_def_13)
| ~ member(X0,iPr_def_12)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2655,c_164]) ).
tcf(c_4300,plain,
! [X0: $i] :
( ( X0 = y )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2652,c_151]) ).
tcf(c_4728,plain,
( member(x,iPr_def_12)
| member(x,z) ),
inference(superposition,[status(thm)],[c_3738,c_3804]) ).
tcf(c_4729,plain,
member(x,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_4728,c_2657]) ).
tcf(c_5165,plain,
( member(x,iPr_def_11)
| member(x,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3738,c_3805]) ).
tcf(c_8221,plain,
( member(x,iPr_def_13)
| member(x,iPr_def_10)
| ~ member(x,iPr_def_12) ),
inference(superposition,[status(thm)],[c_5165,c_4065]) ).
tcf(c_8222,plain,
( member(x,iPr_def_13)
| member(x,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8221,c_4729]) ).
tcf(c_8302,plain,
( member(x,iPr_def_10)
| ~ member(x,iPr_def_14) ),
inference(superposition,[status(thm)],[c_8222,c_3600]) ).
tcf(c_8305,plain,
member(x,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_8302,c_2659]) ).
tcf(c_8307,plain,
x = y,
inference(superposition,[status(thm)],[c_8305,c_4300]) ).
tcf(c_8308,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_8307,c_2658]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET123-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 09:57:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 7.06/1.75 % SZS status Started for theBenchmark.p
% 7.06/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 7.06/1.75
% 7.06/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.06/1.75
% 7.06/1.75 % ------ iProver source info
% 7.06/1.75
% 7.06/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 7.06/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.06/1.75 % git: non_committed_changes: false
% 7.06/1.75
% 7.06/1.75 % ------ Parsing...% successful
% 7.06/1.75
% 7.06/1.75
% 7.06/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.06/1.75
% 7.06/1.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 7.06/1.75
% 7.06/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.06/1.75
% 7.06/1.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.06/1.75 % ------ Proving...
% 7.06/1.75 % ------ Problem Properties
% 7.06/1.75
% 7.06/1.75 %
% 7.06/1.75 % clauses 75
% 7.06/1.75 % conjectures 3
% 7.06/1.75 % EPR 15
% 7.06/1.75 % Horn 67
% 7.06/1.75 % unary 23
% 7.06/1.75 % binary 32
% 7.06/1.75 % lits 153
% 7.06/1.75 % lits eq 26
% 7.06/1.75 % fd_pure 0
% 7.06/1.75 % fd_pseudo 0
% 7.06/1.75 % fd_cond 3
% 7.06/1.75 % fd_pseudo_cond 3
% 7.06/1.75 % AC symbols 0
% 7.06/1.75
% 7.06/1.75 % ------ Schedule dynamic 5 is on
% 7.06/1.75
% 7.06/1.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.06/1.75
% 7.06/1.75
% 7.06/1.75 % ------
% 7.06/1.75 % Current options:
% 7.06/1.75 % ------
% 7.06/1.75
% 7.06/1.75
% 7.06/1.75 %
% 7.06/1.75
% 7.06/1.75 % ------ Proving...
% 7.06/1.75 %
% 7.06/1.75
% 7.06/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 7.06/1.75
% 7.06/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.06/1.75
% 7.06/1.75
%------------------------------------------------------------------------------