%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET987+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 02:49:16 PM UTC 2026
% Result : Theorem 1.61s 1.18s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 16 unt; 2 def)
% Number of atoms : 41 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 17 ~; 3 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 22 ( 0 sgn 20 !; 2 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,conjecture,
! [X0,X1] :
( ~ in(X0,X1)
=> set_difference(set_union2(X1,singleton(X0)),singleton(X0)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] :
( ~ in(X0,X1)
=> set_difference(set_union2(X1,singleton(X0)),singleton(X0)) = X1 ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f11,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f13,plain,
! [X0,X1] :
( ~ in(X1,X0)
=> set_difference(X0,singleton(X1)) = X0 ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f17,plain,
? [X0,X1] :
( ~ in(X0,X1)
& set_difference(set_union2(X1,singleton(X0)),singleton(X0)) != X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f18,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(ennf_transformation,[],[f13]) ).
fof(f21,plain,
( ~ in(sK2,sK3)
& sK3 != set_difference(set_union2(sK3,singleton(sK2)),singleton(sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f17]) ).
fof(f29,plain,
~ in(sK2,sK3),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
sK3 != set_difference(set_union2(sK3,singleton(sK2)),singleton(sK2)),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[],[f10]) ).
fof(f32,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_56,negated_conjecture,
set_difference(set_union2(sK3,singleton(sK2)),singleton(sK2)) != sK3,
inference(cnf_transformation,[],[f30]) ).
tcf(c_57,negated_conjecture,
~ in(sK2,sK3),
inference(cnf_transformation,[],[f29]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[],[f31]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( set_difference(X0,singleton(X1)) = X0 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_110,plain,
set_difference(sK3,singleton(sK2)) != sK3,
inference(demodulation,[status(thm)],[c_56,c_58]) ).
tcf(c_118,definition,
iPr_def_10 = singleton(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_119,definition,
iPr_def_11 = set_difference(sK3,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_120,plain,
iPr_def_11 != sK3,
inference(demodulation,[status(thm)],[c_110,c_118,c_119]) ).
tcf(c_121,negated_conjecture,
~ in(sK2,sK3),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_290,plain,
set_difference(sK3,singleton(sK2)) = sK3,
inference(superposition,[status(thm)],[c_59,c_121]) ).
tcf(c_291,plain,
sK3 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_290,c_118,c_119]) ).
tcf(c_295,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_120,c_291]) ).
tcf(c_297,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET987+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n002.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 12:33:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 1.61/1.18 % SZS status Started for theBenchmark.p
% 1.61/1.18 % SZS status Theorem for theBenchmark.p
% 1.61/1.18
% 1.61/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.61/1.18
% 1.61/1.18 % ------ iProver source info
% 1.61/1.18
% 1.61/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 1.61/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.61/1.18 % git: non_committed_changes: false
% 1.61/1.18
% 1.61/1.18 % ------ Parsing...
% 1.61/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.61/1.18
% 1.61/1.18 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.61/1.18
% 1.61/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.61/1.18
% 1.61/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.61/1.18 % ------ Proving...
% 1.61/1.18 % ------ Problem Properties
% 1.61/1.18
% 1.61/1.18 %
% 1.61/1.18 % clauses 13
% 1.61/1.18 % conjectures 1
% 1.61/1.18 % EPR 5
% 1.61/1.18 % Horn 12
% 1.61/1.18 % unary 9
% 1.61/1.18 % binary 4
% 1.61/1.18 % lits 17
% 1.61/1.18 % lits eq 7
% 1.61/1.18 % fd_pure 0
% 1.61/1.18 % fd_pseudo 0
% 1.61/1.18 % fd_cond 0
% 1.61/1.18 % fd_pseudo_cond 0
% 1.61/1.18 % AC symbols 0
% 1.61/1.18
% 1.61/1.18 % ------ Schedule dynamic 5 is on
% 1.61/1.18
% 1.61/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.61/1.18
% 1.61/1.18
% 1.61/1.18 % ------
% 1.61/1.18 % Current options:
% 1.61/1.18 % ------
% 1.61/1.18
% 1.61/1.18
% 1.61/1.18 %
% 1.61/1.18
% 1.61/1.18 % ------ Proving...
% 1.61/1.18 %
% 1.61/1.18
% 1.61/1.18 % SZS status Theorem for theBenchmark.p
% 1.61/1.18
% 1.61/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.61/1.18
% 1.61/1.18
%------------------------------------------------------------------------------