%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU162+3 : 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 : n009.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 02:55:41 PM UTC 2026
% Result : Theorem 2.00s 1.30s
% Output : CNFRefutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 10 unt; 2 def)
% Number of atoms : 120 ( 31 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 36 ~; 33 |; 4 &)
% ( 3 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 43 !; 4 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f6,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f7,conjecture,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f11,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f13,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f14,plain,
? [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<~> ~ in(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f17,plain,
? [X0,X1] :
( ( set_difference(X0,singleton(X1)) = X0
| ~ in(X1,X0) )
& ( set_difference(X0,singleton(X1)) != X0
| in(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f18,plain,
( ( sK2 = set_difference(sK2,singleton(sK3))
| ~ in(sK3,sK2) )
& ( sK2 != set_difference(sK2,singleton(sK3))
| in(sK3,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 )
& ( set_difference(X0,X1) != X0
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f21,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f25,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f26,plain,
( sK2 = set_difference(sK2,singleton(sK3))
| ~ in(sK3,sK2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
( sK2 != set_difference(sK2,singleton(sK3))
| in(sK3,sK2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_55,negated_conjecture,
( in(sK3,sK2)
| ( set_difference(sK2,singleton(sK3)) != sK2 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_56,negated_conjecture,
( ( set_difference(sK2,singleton(sK3)) = sK2 )
| ~ in(sK3,sK2) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = X0 )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_296,definition,
iPr_def_10 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_297,definition,
iPr_def_11 = set_difference(sK2,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_298,negated_conjecture,
( ( iPr_def_11 = sK2 )
| ~ in(sK3,sK2) ),
inference(demodulation,[status(thm)],[c_56,c_296,c_297]) ).
tcf(c_299,negated_conjecture,
( in(sK3,sK2)
| ( iPr_def_11 != sK2 ) ),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_580,plain,
! [X0: $i] :
( disjoint(iPr_def_10,X0)
| in(sK3,X0) ),
inference(superposition,[status(thm)],[c_296,c_51]) ).
tcf(c_609,plain,
! [X0: $i] :
( ~ disjoint(iPr_def_10,X0)
| ~ in(sK3,X0) ),
inference(superposition,[status(thm)],[c_296,c_50]) ).
tcf(c_617,plain,
( disjoint(sK2,iPr_def_10)
| ( sK2 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_297,c_57]) ).
tcf(c_625,plain,
! [X0: $i] :
( in(sK3,X0)
| ( set_difference(iPr_def_10,X0) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_580,c_58]) ).
tcf(c_684,plain,
( ( sK2 = iPr_def_11 )
| ( set_difference(iPr_def_10,sK2) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_625,c_298]) ).
tcf(c_698,plain,
( disjoint(iPr_def_10,sK2)
| ( sK2 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_684,c_57]) ).
tcf(c_706,plain,
( disjoint(sK2,iPr_def_10)
| ( sK2 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_698,c_54]) ).
tcf(c_710,plain,
disjoint(sK2,iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_706,c_617,c_706]) ).
tcf(c_712,plain,
set_difference(sK2,iPr_def_10) = sK2,
inference(superposition,[status(thm)],[c_710,c_58]) ).
tcf(c_713,plain,
disjoint(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_710,c_54]) ).
tcf(c_714,plain,
sK2 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_712,c_297]) ).
tcf(c_717,plain,
( in(sK3,iPr_def_11)
| ( iPr_def_11 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_299,c_714]) ).
tcf(c_719,plain,
in(sK3,iPr_def_11),
inference(equality_resolution_simp,[status(thm)],[c_717]) ).
tcf(c_722,plain,
~ disjoint(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_719,c_609]) ).
tcf(c_724,plain,
disjoint(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_713,c_714]) ).
tcf(c_725,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_724,c_722]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU162+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 13:00:15 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.45 % Proving...
% 2.00/1.30 % SZS status Started for theBenchmark.p
% 2.00/1.30 % SZS status Theorem for theBenchmark.p
% 2.00/1.30
% 2.00/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.00/1.30
% 2.00/1.30 % ------ iProver source info
% 2.00/1.30
% 2.00/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.00/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.00/1.30 % git: non_committed_changes: false
% 2.00/1.30
% 2.00/1.30 % ------ Parsing...
% 2.00/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.00/1.30
% 2.00/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.00/1.30
% 2.00/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.00/1.30
% 2.00/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.00/1.30 % ------ Proving...
% 2.00/1.30 % ------ Problem Properties
% 2.00/1.30
% 2.00/1.30 %
% 2.00/1.30 % clauses 11
% 2.00/1.30 % conjectures 2
% 2.00/1.30 % EPR 5
% 2.00/1.30 % Horn 10
% 2.00/1.30 % unary 3
% 2.00/1.30 % binary 8
% 2.00/1.30 % lits 19
% 2.00/1.30 % lits eq 7
% 2.00/1.30 % fd_pure 0
% 2.00/1.30 % fd_pseudo 0
% 2.00/1.30 % fd_cond 0
% 2.00/1.30 % fd_pseudo_cond 0
% 2.00/1.30 % AC symbols 0
% 2.00/1.30
% 2.00/1.30 % ------ Schedule dynamic 5 is on
% 2.00/1.30
% 2.00/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.00/1.30
% 2.00/1.30
% 2.00/1.30 % ------
% 2.00/1.30 % Current options:
% 2.00/1.30 % ------
% 2.00/1.30
% 2.00/1.30
% 2.00/1.30 %
% 2.00/1.30
% 2.00/1.30 % ------ Proving...
% 2.00/1.30 %
% 2.00/1.30
% 2.00/1.30 % SZS status Theorem for theBenchmark.p
% 2.00/1.30
% 2.00/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.00/1.30
% 2.00/1.30
%------------------------------------------------------------------------------