%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET602+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 02:47:31 PM UTC 2026
% Result : Theorem 1.83s 1.28s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 15 unt; 1 def)
% Number of atoms : 30 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 4 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 14 !; 1 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).
fof(f6,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f8,conjecture,
! [X0] : difference(X0,X0) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_self_difference_is_empty_set) ).
fof(f9,negated_conjecture,
~ ! [X0] : difference(X0,X0) = empty_set,
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f11,plain,
? [X0] : empty_set != difference(X0,X0),
inference(ennf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( ( difference(X0,X1) != empty_set
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f20,plain,
empty_set != difference(sK1,sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f11]) ).
fof(f22,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f12]) ).
fof(f33,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f34,plain,
empty_set != difference(sK1,sK1),
inference(cnf_transformation,[],[f20]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( difference(X0,X1) = empty_set )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_61,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f33]) ).
tcf(c_62,negated_conjecture,
difference(sK1,sK1) != empty_set,
inference(cnf_transformation,[],[f34]) ).
tcf(c_336,definition,
iPr_def_10 = difference(sK1,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_337,negated_conjecture,
iPr_def_10 != empty_set,
inference(demodulation,[status(thm)],[c_62,c_336]) ).
tcf(c_618,plain,
! [X0: $i] : difference(X0,X0) = empty_set,
inference(superposition,[status(thm)],[c_61,c_49]) ).
tcf(c_620,plain,
empty_set = iPr_def_10,
inference(demodulation,[status(thm)],[c_336,c_618]) ).
tcf(c_624,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_337,c_620]) ).
tcf(c_625,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_624]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET602+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 11:24:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.42 % Proving...
% 1.83/1.28 % SZS status Started for theBenchmark.p
% 1.83/1.28 % SZS status Theorem for theBenchmark.p
% 1.83/1.28
% 1.83/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.83/1.28
% 1.83/1.28 % ------ iProver source info
% 1.83/1.28
% 1.83/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.83/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.83/1.28 % git: non_committed_changes: false
% 1.83/1.28
% 1.83/1.28 % ------ Parsing...
% 1.83/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.83/1.28
% 1.83/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.83/1.28
% 1.83/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.83/1.28
% 1.83/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.83/1.28 % ------ Proving...
% 1.83/1.28 % ------ Problem Properties
% 1.83/1.28
% 1.83/1.28 %
% 1.83/1.28 % clauses 13
% 1.83/1.28 % conjectures 1
% 1.83/1.28 % EPR 5
% 1.83/1.28 % Horn 11
% 1.83/1.28 % unary 4
% 1.83/1.28 % binary 6
% 1.83/1.28 % lits 25
% 1.83/1.28 % lits eq 5
% 1.83/1.28 % fd_pure 0
% 1.83/1.28 % fd_pseudo 0
% 1.83/1.28 % fd_cond 0
% 1.83/1.28 % fd_pseudo_cond 1
% 1.83/1.28 % AC symbols 0
% 1.83/1.28
% 1.83/1.28 % ------ Schedule dynamic 5 is on
% 1.83/1.28
% 1.83/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.83/1.28
% 1.83/1.28
% 1.83/1.28 % ------
% 1.83/1.28 % Current options:
% 1.83/1.28 % ------
% 1.83/1.28
% 1.83/1.28
% 1.83/1.28 %
% 1.83/1.28
% 1.83/1.28 % ------ Proving...
% 1.83/1.28 %
% 1.83/1.28
% 1.83/1.28 % SZS status Theorem for theBenchmark.p
% 1.83/1.28
% 1.83/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.83/1.28
% 1.83/1.28
%------------------------------------------------------------------------------