%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU146+1 : TPTP v9.3.1. Released v3.3.0.
% 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 02:55:35 PM UTC 2026
% Result : Theorem 2.86s 1.30s
% Output : CNFRefutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 65 ( 12 unt; 1 def)
% Number of atoms : 198 ( 71 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 160 ( 58 ~; 81 |; 13 &)
% ( 5 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 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; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 1 sgn 66 !; 6 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f14,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f15,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f16,axiom,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f17,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f13]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
? [X0,X1] :
( subset(X0,singleton(X1))
<~> ( X0 = singleton(X1)
| X0 = empty_set ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f22,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(ennf_transformation,[],[f16]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f24,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( ~ subset(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f26,plain,
? [X0,X1] :
( ( subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ~ subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f27,plain,
? [X0,X1] :
( ( subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ~ subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
( ( subset(sK0,singleton(sK1))
| sK0 = singleton(sK1)
| empty_set = sK0 )
& ( ~ subset(sK0,singleton(sK1))
| ( sK0 != singleton(sK1)
& empty_set != sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f27]) ).
fof(f31,plain,
! [X0,X1] :
( ( empty_set != set_difference(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f35,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
( subset(sK0,singleton(sK1))
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
( ~ subset(sK0,singleton(sK1))
| sK0 != singleton(sK1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
( ~ subset(sK0,singleton(sK1))
| empty_set != sK0 ),
inference(cnf_transformation,[],[f28]) ).
fof(f45,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f17]) ).
fof(f46,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f47,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| subset(X0,set_difference(X1,singleton(X2)))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_57,negated_conjecture,
( ~ subset(sK0,singleton(sK1))
| ( empty_set != sK0 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_58,negated_conjecture,
( ~ subset(sK0,singleton(sK1))
| ( singleton(sK1) != sK0 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_59,negated_conjecture,
( subset(sK0,singleton(sK1))
| ( empty_set = sK0 )
| ( singleton(sK1) = sK0 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_62,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f45]) ).
tcf(c_63,plain,
! [X0: $i] : subset(empty_set,X0),
inference(cnf_transformation,[],[f46]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_66,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_432,definition,
iPr_def_10 = singleton(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_433,negated_conjecture,
( subset(sK0,iPr_def_10)
| ( iPr_def_10 = sK0 )
| ( empty_set = sK0 ) ),
inference(demodulation,[status(thm)],[c_59,c_432]) ).
tcf(c_434,negated_conjecture,
( ~ subset(sK0,iPr_def_10)
| ( iPr_def_10 != sK0 ) ),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_435,negated_conjecture,
( ~ subset(sK0,iPr_def_10)
| ( empty_set != sK0 ) ),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_802,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ~ in(sK1,X0) ),
inference(superposition,[status(thm)],[c_432,c_54]) ).
tcf(c_851,plain,
! [X0: $i] : set_difference(X0,X0) = empty_set,
inference(superposition,[status(thm)],[c_62,c_64]) ).
tcf(c_854,plain,
( ( sK0 = iPr_def_10 )
| ( empty_set = sK0 )
| ( set_difference(sK0,iPr_def_10) = empty_set ) ),
inference(superposition,[status(thm)],[c_433,c_64]) ).
tcf(c_873,plain,
( subset(sK0,iPr_def_10)
| ( sK0 = iPr_def_10 )
| ( empty_set = sK0 ) ),
inference(superposition,[status(thm)],[c_854,c_65]) ).
tcf(c_893,plain,
( ( sK0 = iPr_def_10 )
| ( empty_set = sK0 )
| ~ subset(iPr_def_10,sK0) ),
inference(superposition,[status(thm)],[c_873,c_50]) ).
tcf(c_907,plain,
! [X0: $i,X1: $i] :
( subset(X0,empty_set)
| in(X1,X0)
| ~ subset(X0,singleton(X1)) ),
inference(superposition,[status(thm)],[c_851,c_56]) ).
tcf(c_953,plain,
! [X0: $i] :
( subset(X0,empty_set)
| in(sK1,X0)
| ~ subset(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_432,c_907]) ).
tcf(c_969,plain,
( subset(sK0,empty_set)
| in(sK1,sK0)
| ( sK0 = iPr_def_10 )
| ( empty_set = sK0 ) ),
inference(superposition,[status(thm)],[c_873,c_953]) ).
tcf(c_1081,plain,
( subset(iPr_def_10,sK0)
| subset(sK0,empty_set)
| ( sK0 = iPr_def_10 )
| ( empty_set = sK0 ) ),
inference(superposition,[status(thm)],[c_969,c_802]) ).
tcf(c_1134,plain,
( ( empty_set = sK0 )
| ( sK0 = iPr_def_10 )
| subset(sK0,empty_set) ),
inference(global_subsumption_just,[status(thm)],[c_1081,c_893,c_1081]) ).
tcf(c_1135,plain,
( subset(sK0,empty_set)
| ( sK0 = iPr_def_10 )
| ( empty_set = sK0 ) ),
inference(renaming,[status(thm)],[c_1134]) ).
tcf(c_1144,plain,
( ( sK0 = iPr_def_10 )
| ( empty_set = sK0 ) ),
inference(superposition,[status(thm)],[c_1135,c_66]) ).
tcf(c_1158,plain,
( ( sK0 = iPr_def_10 )
| ~ subset(sK0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1144,c_435]) ).
tcf(c_1169,plain,
( ( sK0 = iPr_def_10 )
| ~ subset(empty_set,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1144,c_1158]) ).
tcf(c_1170,plain,
sK0 = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_1169,c_63]) ).
tcf(c_1173,plain,
( ~ subset(iPr_def_10,iPr_def_10)
| ( iPr_def_10 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_434,c_1170]) ).
tcf(c_1174,plain,
~ subset(iPr_def_10,iPr_def_10),
inference(equality_resolution_simp,[status(thm)],[c_1173]) ).
tcf(c_1175,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1174,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU146+1 : TPTP v9.3.1. Released v3.3.0.
% 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 12:56:43 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 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...
% 2.86/1.30 % SZS status Started for theBenchmark.p
% 2.86/1.30 % SZS status Theorem for theBenchmark.p
% 2.86/1.30
% 2.86/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.86/1.30
% 2.86/1.30 % ------ iProver source info
% 2.86/1.30
% 2.86/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.86/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.86/1.30 % git: non_committed_changes: false
% 2.86/1.30
% 2.86/1.30 % ------ Parsing...
% 2.86/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.86/1.30
% 2.86/1.30 % ------ 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 %
% 2.86/1.30
% 2.86/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.86/1.30
% 2.86/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.86/1.30 % ------ Proving...
% 2.86/1.30 % ------ Problem Properties
% 2.86/1.30
% 2.86/1.30 %
% 2.86/1.30 % clauses 17
% 2.86/1.30 % conjectures 3
% 2.86/1.30 % EPR 11
% 2.86/1.30 % Horn 15
% 2.86/1.30 % unary 6
% 2.86/1.30 % binary 8
% 2.86/1.30 % lits 31
% 2.86/1.30 % lits eq 9
% 2.86/1.30 % fd_pure 0
% 2.86/1.30 % fd_pseudo 0
% 2.86/1.30 % fd_cond 1
% 2.86/1.30 % fd_pseudo_cond 1
% 2.86/1.30 % AC symbols 0
% 2.86/1.30
% 2.86/1.30 % ------ Schedule dynamic 5 is on
% 2.86/1.30
% 2.86/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.86/1.30
% 2.86/1.30
% 2.86/1.30 % ------
% 2.86/1.30 % Current options:
% 2.86/1.30 % ------
% 2.86/1.30
% 2.86/1.30
% 2.86/1.30 %
% 2.86/1.30
% 2.86/1.30 % ------ Proving...
% 2.86/1.30 %
% 2.86/1.30
% 2.86/1.30 % SZS status Theorem for theBenchmark.p
% 2.86/1.30
% 2.86/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.86/1.30
% 2.86/1.30
%------------------------------------------------------------------------------