%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET604+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 2.34s 1.31s
% Output : CNFRefutation 2.34s
% 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] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_subset) ).
fof(f2,axiom,
! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).
fof(f9,conjecture,
! [X0] : difference(empty_set,X0) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_no_difference_with_empty_set) ).
fof(f10,negated_conjecture,
~ ! [X0] : difference(empty_set,X0) = empty_set,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
? [X0] : empty_set != difference(empty_set,X0),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( ( empty_set != difference(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f21,plain,
empty_set != difference(empty_set,sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f12]) ).
fof(f22,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = difference(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f36,plain,
empty_set != difference(empty_set,sK1),
inference(cnf_transformation,[],[f21]) ).
tcf(c_49,plain,
! [X0: $i] : subset(empty_set,X0),
inference(cnf_transformation,[],[f22]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( difference(X0,X1) = empty_set )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_63,negated_conjecture,
difference(empty_set,sK1) != empty_set,
inference(cnf_transformation,[],[f36]) ).
tcf(c_345,definition,
iPr_def_10 = difference(empty_set,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_346,negated_conjecture,
iPr_def_10 != empty_set,
inference(demodulation,[status(thm)],[c_63,c_345]) ).
tcf(c_643,plain,
! [X0: $i] : difference(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_49,c_50]) ).
tcf(c_645,plain,
empty_set = iPr_def_10,
inference(demodulation,[status(thm)],[c_345,c_643]) ).
tcf(c_649,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_346,c_645]) ).
tcf(c_650,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_649]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET604+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n011.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
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 11:25:14 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...
% 2.34/1.31 % SZS status Started for theBenchmark.p
% 2.34/1.31 % SZS status Theorem for theBenchmark.p
% 2.34/1.31
% 2.34/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.34/1.31
% 2.34/1.31 % ------ iProver source info
% 2.34/1.31
% 2.34/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 2.34/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.34/1.31 % git: non_committed_changes: false
% 2.34/1.31
% 2.34/1.31 % ------ Parsing...
% 2.34/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.34/1.31
% 2.34/1.31 % ------ 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 %
% 2.34/1.31
% 2.34/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.34/1.31
% 2.34/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.34/1.31 % ------ Proving...
% 2.34/1.31 % ------ Problem Properties
% 2.34/1.31
% 2.34/1.31 %
% 2.34/1.31 % clauses 14
% 2.34/1.31 % conjectures 1
% 2.34/1.31 % EPR 6
% 2.34/1.31 % Horn 12
% 2.34/1.31 % unary 5
% 2.34/1.31 % binary 6
% 2.34/1.31 % lits 26
% 2.34/1.31 % lits eq 5
% 2.34/1.31 % fd_pure 0
% 2.34/1.31 % fd_pseudo 0
% 2.34/1.31 % fd_cond 0
% 2.34/1.31 % fd_pseudo_cond 1
% 2.34/1.31 % AC symbols 0
% 2.34/1.31
% 2.34/1.31 % ------ Schedule dynamic 5 is on
% 2.34/1.31
% 2.34/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.34/1.31
% 2.34/1.31
% 2.34/1.31 % ------
% 2.34/1.31 % Current options:
% 2.34/1.31 % ------
% 2.34/1.31
% 2.34/1.31
% 2.34/1.31 %
% 2.34/1.31
% 2.34/1.31 % ------ Proving...
% 2.34/1.31 %
% 2.34/1.31
% 2.34/1.31 % SZS status Theorem for theBenchmark.p
% 2.34/1.31
% 2.34/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.34/1.31
% 2.34/1.31
%------------------------------------------------------------------------------