%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET094-7 : 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 : n020.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 02:46:33 PM UTC 2026
% Result : Unsatisfiable 1.11s 1.29s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 18 unt; 2 def)
% Number of atoms : 38 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 8 ~; 4 |; 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; 2 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f137,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f152,negated_conjecture,
singleton(member_of(x)) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_singletons1_1) ).
fof(f153,plain,
x = singleton(member_of(x)),
inference(reorient_equations,[],[f152]) ).
fof(f154,negated_conjecture,
member(y,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_singletons1_2) ).
fof(f155,negated_conjecture,
member_of(x) != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_singletons1_3) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f137,f12]) ).
fof(f231,plain,
x = unordered_pair(member_of(x),member_of(x)),
inference(definition_unfolding,[],[f153,f12]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_310,negated_conjecture,
unordered_pair(member_of(x),member_of(x)) = x,
inference(cnf_transformation,[],[f231]) ).
tcf(c_311,negated_conjecture,
member(y,x),
inference(cnf_transformation,[],[f154]) ).
tcf(c_312,negated_conjecture,
member_of(x) != y,
inference(cnf_transformation,[],[f155]) ).
tcf(c_3550,definition,
iPr_def_10 = member_of(x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3551,definition,
iPr_def_11 = unordered_pair(iPr_def_10,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3552,negated_conjecture,
iPr_def_10 != y,
inference(demodulation,[status(thm)],[c_312,c_3550]) ).
tcf(c_3553,negated_conjecture,
member(y,x),
inference(demodulation,[status(thm)],[c_311]) ).
tcf(c_3554,negated_conjecture,
iPr_def_11 = x,
inference(demodulation,[status(thm)],[c_310,c_3551]) ).
tcf(c_4670,plain,
member(y,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_3553,c_3554]) ).
tcf(c_4970,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3551,c_297]) ).
tcf(c_5033,plain,
y = iPr_def_10,
inference(superposition,[status(thm)],[c_4670,c_4970]) ).
tcf(c_5047,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_3552,c_5033]) ).
tcf(c_5049,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_5047]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET094-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 09:46:03 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 1.11/1.29 % SZS status Started for theBenchmark.p
% 1.11/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.11/1.29
% 1.11/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.11/1.29
% 1.11/1.29 % ------ iProver source info
% 1.11/1.29
% 1.11/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.11/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.11/1.29 % git: non_committed_changes: false
% 1.11/1.29
% 1.11/1.29 % ------ Parsing...% successful
% 1.11/1.29
% 1.11/1.29
% 1.11/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.11/1.29
% 1.11/1.29 % ------ 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 %
% 1.11/1.29
% 1.11/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.11/1.29
% 1.11/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.11/1.29 % ------ Proving...
% 1.11/1.29 % ------ Problem Properties
% 1.11/1.29
% 1.11/1.29 %
% 1.11/1.29 % clauses 113
% 1.11/1.29 % conjectures 3
% 1.11/1.29 % EPR 20
% 1.11/1.29 % Horn 93
% 1.11/1.29 % unary 29
% 1.11/1.29 % binary 53
% 1.11/1.29 % lits 235
% 1.11/1.29 % lits eq 58
% 1.11/1.29 % fd_pure 0
% 1.11/1.29 % fd_pseudo 0
% 1.11/1.29 % fd_cond 5
% 1.11/1.29 % fd_pseudo_cond 12
% 1.11/1.29 % AC symbols 0
% 1.11/1.29
% 1.11/1.29 % ------ Schedule dynamic 5 is on
% 1.11/1.29
% 1.11/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.11/1.29
% 1.11/1.29
% 1.11/1.29 % ------
% 1.11/1.29 % Current options:
% 1.11/1.29 % ------
% 1.11/1.29
% 1.11/1.29
% 1.11/1.29 %
% 1.11/1.29
% 1.11/1.29 % ------ Proving...
% 1.11/1.29 %
% 1.11/1.29
% 1.11/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.11/1.29
% 1.11/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.11/1.29
% 1.11/1.29
%------------------------------------------------------------------------------