%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU154+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 : n010.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 02:55:38 PM UTC 2026
% Result : Theorem 2.27s 1.27s
% Output : CNFRefutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 67 ( 14 unt; 0 def)
% Number of atoms : 239 ( 71 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 287 ( 115 ~; 123 |; 39 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 122 ( 0 sgn 113 !; 9 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f13,conjecture,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f19,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f24,plain,
? [X0,X1] :
( ~ in(X0,X1)
& ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f32,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK1(X0,X1),X0)
& ~ in(sK1(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(rectify,[],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK2(X0,X1,X2),X2)
| ( in(sK2(X0,X1,X2),X1)
& in(sK2(X0,X1,X2),X0) ) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set )
& ( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f39,plain,
( ~ in(sK3,sK4)
& ~ disjoint(singleton(sK3),sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f24]) ).
fof(f47,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f30]) ).
fof(f48,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f57,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f37]) ).
fof(f58,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f37]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f37]) ).
fof(f61,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f64,plain,
~ in(sK3,sK4),
inference(cnf_transformation,[],[f39]) ).
fof(f65,plain,
~ disjoint(singleton(sK3),sK4),
inference(cnf_transformation,[],[f39]) ).
fof(f70,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f19]) ).
fof(f73,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f48]) ).
fof(f74,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f73]) ).
fof(f75,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f47]) ).
tcf(c_56,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f74]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_intersection2(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_71,negated_conjecture,
~ disjoint(singleton(sK3),sK4),
inference(cnf_transformation,[],[f65]) ).
tcf(c_72,negated_conjecture,
~ in(sK3,sK4),
inference(cnf_transformation,[],[f64]) ).
tcf(c_77,plain,
! [X0: $i] : subset(empty_set,X0),
inference(cnf_transformation,[],[f70]) ).
tcf(c_491,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_980,plain,
( disjoint(singleton(sK3),sK4)
| ( set_intersection2(singleton(sK3),sK4) != empty_set ) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_985,plain,
! [X0: $i,X1: $i] :
( in(sK3,sK4)
| ~ in(X0,X1)
| ( sK4 != X1 )
| ( sK3 != X0 ) ),
inference(instantiation,[status(thm)],[c_492]) ).
tcf(c_1008,plain,
( ( set_intersection2(singleton(sK3),sK4) = empty_set )
| ~ in(sK2(singleton(sK3),sK4,empty_set),sK4)
| ~ in(sK2(singleton(sK3),sK4,empty_set),empty_set)
| ~ in(sK2(singleton(sK3),sK4,empty_set),singleton(sK3)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_1009,plain,
( in(sK2(singleton(sK3),sK4,empty_set),empty_set)
| in(sK2(singleton(sK3),sK4,empty_set),singleton(sK3))
| ( set_intersection2(singleton(sK3),sK4) = empty_set ) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1010,plain,
( in(sK2(singleton(sK3),sK4,empty_set),sK4)
| in(sK2(singleton(sK3),sK4,empty_set),empty_set)
| ( set_intersection2(singleton(sK3),sK4) = empty_set ) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1015,plain,
! [X0: $i] :
( ( sK4 = X0 )
| ~ in(sK4,singleton(X0)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1058,plain,
( ( sK4 = sK4 )
| ~ in(sK4,singleton(sK4)) ),
inference(instantiation,[status(thm)],[c_1015]) ).
tcf(c_1081,plain,
! [X0: $i] :
( in(sK2(singleton(sK3),sK4,empty_set),X0)
| ~ subset(empty_set,X0)
| ~ in(sK2(singleton(sK3),sK4,empty_set),empty_set) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_1117,plain,
( in(sK3,sK4)
| ~ in(sK2(singleton(sK3),sK4,empty_set),sK4)
| ( sK4 != sK4 )
| ( sK3 != sK2(singleton(sK3),sK4,empty_set) ) ),
inference(instantiation,[status(thm)],[c_985]) ).
tcf(c_1193,plain,
in(sK4,singleton(sK4)),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_1196,plain,
! [X0: $i] :
( ( sK3 = sK2(singleton(sK3),sK4,empty_set) )
| ( sK3 != X0 )
| ( sK2(singleton(sK3),sK4,empty_set) != X0 ) ),
inference(instantiation,[status(thm)],[c_491]) ).
tcf(c_1198,plain,
in(sK3,singleton(sK3)),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_1290,plain,
( in(sK2(singleton(sK3),sK4,empty_set),sK4)
| ~ subset(empty_set,sK4)
| ~ in(sK2(singleton(sK3),sK4,empty_set),empty_set) ),
inference(instantiation,[status(thm)],[c_1081]) ).
tcf(c_1464,plain,
! [X0: $i] :
( ( sK3 = X0 )
| ~ in(sK3,singleton(X0)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1548,plain,
( ( sK3 = sK2(singleton(sK3),sK4,empty_set) )
| ( sK3 != sK3 )
| ( sK2(singleton(sK3),sK4,empty_set) != sK3 ) ),
inference(instantiation,[status(thm)],[c_1196]) ).
tcf(c_1635,plain,
subset(empty_set,sK4),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_1682,plain,
( in(sK2(singleton(sK3),sK4,empty_set),singleton(sK3))
| ~ subset(empty_set,singleton(sK3))
| ~ in(sK2(singleton(sK3),sK4,empty_set),empty_set) ),
inference(instantiation,[status(thm)],[c_1081]) ).
tcf(c_2009,plain,
( ( sK3 = sK3 )
| ~ in(sK3,singleton(sK3)) ),
inference(instantiation,[status(thm)],[c_1464]) ).
tcf(c_3220,plain,
( ( sK2(singleton(sK3),sK4,empty_set) = sK3 )
| ~ in(sK2(singleton(sK3),sK4,empty_set),singleton(sK3)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_3382,plain,
subset(empty_set,singleton(sK3)),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_3770,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3382,c_3220,c_2009,c_1682,c_1635,c_1548,c_1290,c_1198,c_1193,c_1117,c_1058,c_1008,c_1009,c_1010,c_980,c_71,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU154+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:58:45 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.38 Running first-order theorem proving
% 0.08/0.38 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
% 0.08/0.39
% 0.08/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.39
% 0.08/0.39 % Detected problem language: tptp
% 0.13/0.40 % Proving...
% 2.27/1.27 % SZS status Started for theBenchmark.p
% 2.27/1.27 % SZS status Theorem for theBenchmark.p
% 2.27/1.27
% 2.27/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.27/1.27
% 2.27/1.27 % ------ iProver source info
% 2.27/1.27
% 2.27/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.27/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.27/1.27 % git: non_committed_changes: false
% 2.27/1.27
% 2.27/1.27 % ------ Parsing...
% 2.27/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.27/1.27
% 2.27/1.27 % ------ 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 %
% 2.27/1.27
% 2.27/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.27/1.27
% 2.27/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.27/1.27 % ------ Proving...
% 2.27/1.27 % ------ Problem Properties
% 2.27/1.27
% 2.27/1.27 %
% 2.27/1.27 % clauses 27
% 2.27/1.27 % conjectures 2
% 2.27/1.27 % EPR 10
% 2.27/1.27 % Horn 23
% 2.27/1.27 % unary 10
% 2.27/1.27 % binary 9
% 2.27/1.27 % lits 53
% 2.27/1.27 % lits eq 13
% 2.27/1.27 % fd_pure 0
% 2.27/1.27 % fd_pseudo 0
% 2.27/1.27 % fd_cond 0
% 2.27/1.27 % fd_pseudo_cond 6
% 2.27/1.27 % AC symbols 0
% 2.27/1.27
% 2.27/1.27 % ------ Input Options Time Limit: Unbounded
% 2.27/1.27
% 2.27/1.27
% 2.27/1.27 % ------
% 2.27/1.27 % Current options:
% 2.27/1.27 % ------
% 2.27/1.27
% 2.27/1.27
% 2.27/1.27 %
% 2.27/1.27
% 2.27/1.27 % ------ Proving...
% 2.27/1.27 %
% 2.27/1.27
% 2.27/1.27 % SZS status Theorem for theBenchmark.p
% 2.27/1.27
% 2.27/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.27/1.27
% 2.27/1.27
%------------------------------------------------------------------------------