%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU145+2 : 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 : n008.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 36.23s 6.86s
% Output : CNFRefutation 36.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 82 ( 34 unt; 2 def)
% Number of atoms : 230 ( 38 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 205 ( 81 ~; 82 |; 33 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 142 ( 0 sgn 133 !; 9 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f10,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f29,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f31,conjecture,
! [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(f32,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f36,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f47,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f48,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f50,axiom,
! [X0,X1] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f61,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f64,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f65,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f82,plain,
? [X0,X1,X2] :
( subset(X0,X1)
& ~ subset(X0,set_difference(X1,singleton(X2)))
& ~ in(X2,X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f83,plain,
? [X0,X1,X2] :
( subset(X0,X1)
& ~ subset(X0,set_difference(X1,singleton(X2)))
& ~ in(X2,X0) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f106,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f107,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f106]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f118]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f119]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK3(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X1)
| in(sK3(X0,X1,X2),X0) )
& ( ~ in(sK3(X0,X1,X2),X2)
| ( ~ in(sK3(X0,X1,X2),X1)
& ~ in(sK3(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f120]) ).
fof(f134,plain,
! [X0,X1] :
( ( ~ subset(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f136,plain,
( subset(sK7,sK8)
& ~ subset(sK7,set_difference(sK8,singleton(sK9)))
& ~ in(sK9,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9)],[f83]) ).
fof(f144,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 )
& ( set_difference(X0,X1) != X0
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f148,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f152,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f107]) ).
fof(f165,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f196,plain,
! [X0,X1] :
( ~ subset(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f197,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f200,plain,
subset(sK7,sK8),
inference(cnf_transformation,[],[f136]) ).
fof(f201,plain,
~ subset(sK7,set_difference(sK8,singleton(sK9))),
inference(cnf_transformation,[],[f136]) ).
fof(f202,plain,
~ in(sK9,sK7),
inference(cnf_transformation,[],[f136]) ).
fof(f206,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f218,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f219,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f48]) ).
fof(f222,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f50]) ).
fof(f236,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f61]) ).
fof(f239,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f64]) ).
fof(f240,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f241,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
fof(f259,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f197,f236]) ).
fof(f260,plain,
! [X0,X1] :
( ~ subset(unordered_pair(X0,X0),X1)
| in(X0,X1) ),
inference(definition_unfolding,[],[f196,f236]) ).
fof(f261,plain,
~ subset(sK7,set_difference(sK8,unordered_pair(sK9,sK9))),
inference(definition_unfolding,[],[f201,f236]) ).
fof(f282,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f165]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f148]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f282]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f259]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ subset(unordered_pair(X0,X0),X1) ),
inference(cnf_transformation,[],[f260]) ).
tcf(c_104,negated_conjecture,
~ in(sK9,sK7),
inference(cnf_transformation,[],[f202]) ).
tcf(c_105,negated_conjecture,
~ subset(sK7,set_difference(sK8,unordered_pair(sK9,sK9))),
inference(cnf_transformation,[],[f261]) ).
tcf(c_106,negated_conjecture,
subset(sK7,sK8),
inference(cnf_transformation,[],[f200]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f219]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
inference(cnf_transformation,[],[f222]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f239]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = X0 )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_2094,definition,
iPr_def_10 = unordered_pair(sK9,sK9),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2095,definition,
iPr_def_11 = set_difference(sK8,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2096,negated_conjecture,
subset(sK7,sK8),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_2097,negated_conjecture,
~ subset(sK7,iPr_def_11),
inference(demodulation,[status(thm)],[c_105,c_2094,c_2095]) ).
tcf(c_2098,negated_conjecture,
~ in(sK9,sK7),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_3912,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ~ in(sK9,X0) ),
inference(superposition,[status(thm)],[c_2094,c_100]) ).
tcf(c_3924,plain,
! [X0: $i,X1: $i] : in(X0,set_union2(unordered_pair(X0,X0),X1)),
inference(superposition,[status(thm)],[c_141,c_101]) ).
tcf(c_4017,plain,
! [X0: $i] : in(sK9,set_union2(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_2094,c_3924]) ).
tcf(c_4029,plain,
! [X0: $i] : in(sK9,set_union2(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_52,c_4017]) ).
tcf(c_5262,plain,
! [X0: $i] :
( subset(set_difference(X0,iPr_def_10),iPr_def_11)
| ~ subset(X0,sK8) ),
inference(superposition,[status(thm)],[c_2095,c_122]) ).
tcf(c_5658,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| in(X0,set_difference(X2,X1))
| ~ in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_126,c_74]) ).
tcf(c_68627,plain,
! [X0: $i] :
( in(sK9,X0)
| in(sK9,set_difference(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_4029,c_5658]) ).
tcf(c_89833,plain,
! [X0: $i] :
( in(sK9,X0)
| subset(iPr_def_10,set_difference(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_68627,c_3912]) ).
tcf(c_93059,plain,
! [X0: $i] :
( in(sK9,X0)
| ( set_difference(iPr_def_10,X0) = iPr_def_10 )
| ~ subset(set_difference(iPr_def_10,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_89833,c_54]) ).
tcf(c_93089,plain,
! [X0: $i] :
( in(sK9,X0)
| ( set_difference(iPr_def_10,X0) = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_93059,c_123]) ).
tcf(c_102052,plain,
set_difference(iPr_def_10,sK7) = iPr_def_10,
inference(superposition,[status(thm)],[c_93089,c_2098]) ).
tcf(c_102275,plain,
disjoint(iPr_def_10,sK7),
inference(superposition,[status(thm)],[c_102052,c_142]) ).
tcf(c_102638,plain,
disjoint(sK7,iPr_def_10),
inference(superposition,[status(thm)],[c_102275,c_110]) ).
tcf(c_102662,plain,
set_difference(sK7,iPr_def_10) = sK7,
inference(superposition,[status(thm)],[c_102638,c_143]) ).
tcf(c_103350,plain,
( subset(sK7,iPr_def_11)
| ~ subset(sK7,sK8) ),
inference(superposition,[status(thm)],[c_102662,c_5262]) ).
tcf(c_103385,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_103350,c_2097,c_2096]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU145+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 12:57:10 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 36.23/6.86 % SZS status Started for theBenchmark.p
% 36.23/6.86 % SZS status Theorem for theBenchmark.p
% 36.23/6.86
% 36.23/6.86 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 36.23/6.86
% 36.23/6.86 % ------ iProver source info
% 36.23/6.86
% 36.23/6.86 % git: date: 2026-07-19 20:42:38 +0200
% 36.23/6.86 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 36.23/6.86 % git: non_committed_changes: false
% 36.23/6.86
% 36.23/6.86 % ------ Parsing...
% 36.23/6.86 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 36.23/6.86
% 36.23/6.86 % ------ Preprocessing... sup_sim: 3 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 %
% 36.23/6.86
% 36.23/6.86 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 36.23/6.86
% 36.23/6.86 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 36.23/6.86 % ------ Proving...
% 36.23/6.86 % ------ Problem Properties
% 36.23/6.86
% 36.23/6.86 %
% 36.23/6.86 % clauses 90
% 36.23/6.86 % conjectures 3
% 36.23/6.86 % EPR 24
% 36.23/6.86 % Horn 72
% 36.23/6.86 % unary 27
% 36.23/6.86 % binary 34
% 36.23/6.86 % lits 186
% 36.23/6.86 % lits eq 52
% 36.23/6.86 % fd_pure 0
% 36.23/6.86 % fd_pseudo 0
% 36.23/6.86 % fd_cond 3
% 36.23/6.86 % fd_pseudo_cond 19
% 36.23/6.86 % AC symbols 0
% 36.23/6.86
% 36.23/6.86 % ------ Schedule dynamic 5 is on
% 36.23/6.86
% 36.23/6.86 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 36.23/6.86
% 36.23/6.86
% 36.23/6.86 % ------
% 36.23/6.86 % Current options:
% 36.23/6.86 % ------
% 36.23/6.86
% 36.23/6.86
% 36.23/6.86 %
% 36.23/6.86
% 36.23/6.86 % ------ Proving...
% 36.23/6.86 %
% 36.23/6.86
% 36.23/6.86 % SZS status Theorem for theBenchmark.p
% 36.23/6.86
% 36.23/6.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 36.23/6.86
% 36.23/6.86
%------------------------------------------------------------------------------