%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET078-7 : 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 : n015.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 02:46:28 PM UTC 2026
% Result : Unsatisfiable 3.47s 1.30s
% Output : CNFRefutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 17 ( 14 unt; 2 def)
% Number of atoms : 31 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f120,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f133,negated_conjecture,
~ member(singleton(y),unordered_pair(x,singleton(y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_singletons_are_sets_1) ).
fof(f194,plain,
~ member(unordered_pair(y,y),unordered_pair(x,unordered_pair(y,y))),
inference(definition_unfolding,[],[f133,f12,f12]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f11]) ).
tcf(c_261,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f120]) ).
tcf(c_274,negated_conjecture,
~ member(unordered_pair(y,y),unordered_pair(x,unordered_pair(y,y))),
inference(cnf_transformation,[],[f194]) ).
tcf(c_3179,definition,
iPr_def_10 = unordered_pair(y,y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3180,definition,
iPr_def_11 = unordered_pair(x,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3181,negated_conjecture,
~ member(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_274,c_3180,c_3179]) ).
tcf(c_4151,plain,
member(iPr_def_10,universal_class),
inference(superposition,[status(thm)],[c_3179,c_180]) ).
tcf(c_4154,plain,
unordered_pair(iPr_def_10,x) = iPr_def_11,
inference(demodulation,[status(thm)],[c_3180,c_261]) ).
tcf(c_4233,plain,
( member(iPr_def_10,iPr_def_11)
| ~ member(iPr_def_10,universal_class) ),
inference(superposition,[status(thm)],[c_4154,c_178]) ).
tcf(c_4234,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4233,c_3181,c_4151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET078-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n015.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % 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 09:41:25 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 3.47/1.30 % SZS status Started for theBenchmark.p
% 3.47/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.47/1.30
% 3.47/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.47/1.30
% 3.47/1.30 % ------ iProver source info
% 3.47/1.30
% 3.47/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.47/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.47/1.30 % git: non_committed_changes: false
% 3.47/1.30
% 3.47/1.30 % ------ Parsing...% successful
% 3.47/1.30
% 3.47/1.30
% 3.47/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.47/1.30
% 3.47/1.30 % ------ 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 %
% 3.47/1.30
% 3.47/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.47/1.30
% 3.47/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.47/1.30 % ------ Proving...
% 3.47/1.30 % ------ Problem Properties
% 3.47/1.30
% 3.47/1.30 %
% 3.47/1.30 % clauses 96
% 3.47/1.30 % conjectures 1
% 3.47/1.30 % EPR 18
% 3.47/1.30 % Horn 82
% 3.47/1.30 % unary 25
% 3.47/1.30 % binary 43
% 3.47/1.30 % lits 201
% 3.47/1.30 % lits eq 38
% 3.47/1.30 % fd_pure 0
% 3.47/1.30 % fd_pseudo 0
% 3.47/1.30 % fd_cond 5
% 3.47/1.30 % fd_pseudo_cond 8
% 3.47/1.30 % AC symbols 0
% 3.47/1.30
% 3.47/1.30 % ------ Schedule dynamic 5 is on
% 3.47/1.30
% 3.47/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.47/1.30
% 3.47/1.30
% 3.47/1.30 % ------
% 3.47/1.30 % Current options:
% 3.47/1.30 % ------
% 3.47/1.30
% 3.47/1.30
% 3.47/1.30 %
% 3.47/1.30
% 3.47/1.30 % ------ Proving...
% 3.47/1.30 %
% 3.47/1.30
% 3.47/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.47/1.30
% 3.47/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.47/1.30
% 3.47/1.30
%------------------------------------------------------------------------------