%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET916+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 : 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 02:49:06 PM UTC 2026
% Result : Theorem 0.81s 1.20s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 8 unt; 0 def)
% Number of atoms : 207 ( 71 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 261 ( 101 ~; 99 |; 57 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 118 ( 0 sgn 106 !; 12 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f10,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f11,conjecture,
! [X0,X1,X2] :
~ ( ~ disjoint(unordered_pair(X0,X2),X1)
& ~ in(X2,X1)
& ~ in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( ~ disjoint(unordered_pair(X0,X2),X1)
& ~ in(X2,X1)
& ~ in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X3] : in(X3,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f17,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ( ? [X2] : in(X2,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ~ disjoint(unordered_pair(X0,X2),X1)
& ~ in(X2,X1)
& ~ in(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| sK0(X0,X1,X2) = X1
| sK0(X0,X1,X2) = X0 )
& ( ~ in(sK0(X0,X1,X2),X2)
| ( sK0(X0,X1,X2) != X1
& sK0(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f21]) ).
fof(f23,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,[],[f5]) ).
fof(f24,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,[],[f23]) ).
fof(f25,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,[],[f24]) ).
fof(f26,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(sK1(X0,X1,X2),X2)
| ( in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) ) )
& ( ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f25]) ).
fof(f29,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ( in(sK4(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f17]) ).
fof(f30,plain,
( ~ disjoint(unordered_pair(sK5,sK7),sK6)
& ~ in(sK7,sK6)
& ~ in(sK5,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f18]) ).
fof(f34,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| ~ in(X4,X2)
| X1 = X4
| X0 = X4 ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f51,plain,
! [X0,X1] :
( in(sK4(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
~ disjoint(unordered_pair(sK5,sK7),sK6),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
~ in(sK7,sK6),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
~ in(sK5,sK6),
inference(cnf_transformation,[],[f30]) ).
fof(f59,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f34]) ).
fof(f61,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f41]) ).
fof(f62,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f40]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK4(X0,X1),set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_70,negated_conjecture,
~ in(sK5,sK6),
inference(cnf_transformation,[],[f54]) ).
tcf(c_71,negated_conjecture,
~ in(sK7,sK6),
inference(cnf_transformation,[],[f53]) ).
tcf(c_72,negated_conjecture,
~ disjoint(unordered_pair(sK5,sK7),sK6),
inference(cnf_transformation,[],[f52]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_68,c_62]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK4(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_68,c_63]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_68,c_62]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK4(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_68,c_63]) ).
tcf(c_353,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(unordered_pair(X0,X1),X2)
| ( sK4(unordered_pair(X0,X1),X2) = X1 )
| ( sK4(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_235,c_57]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(unordered_pair(X0,X1),X2)
| ( sK4(unordered_pair(X0,X1),X2) = X1 )
| ( sK4(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_345,c_57]) ).
tcf(c_766,plain,
( ( sK4(unordered_pair(sK5,sK7),sK6) = sK7 )
| ( sK4(unordered_pair(sK5,sK7),sK6) = sK5 ) ),
inference(superposition,[status(thm)],[c_353,c_72]) ).
tcf(c_1498,plain,
( ( sK4(unordered_pair(sK5,sK7),sK6) = sK7 )
| ( sK4(unordered_pair(sK5,sK7),sK6) = sK5 ) ),
inference(superposition,[status(thm)],[c_600,c_72]) ).
tcf(c_3317,plain,
( in(sK7,sK6)
| disjoint(unordered_pair(sK5,sK7),sK6)
| ( sK4(unordered_pair(sK5,sK7),sK6) = sK5 ) ),
inference(superposition,[status(thm)],[c_766,c_236]) ).
tcf(c_6584,plain,
sK4(unordered_pair(sK5,sK7),sK6) = sK5,
inference(global_subsumption_just,[status(thm)],[c_1498,c_71,c_72,c_3317]) ).
tcf(c_6596,plain,
( in(sK5,sK6)
| disjoint(unordered_pair(sK5,sK7),sK6) ),
inference(superposition,[status(thm)],[c_6584,c_346]) ).
tcf(c_6598,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6596,c_72,c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET916+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:22:14 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 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...
% 0.81/1.20 % SZS status Started for theBenchmark.p
% 0.81/1.20 % SZS status Theorem for theBenchmark.p
% 0.81/1.20
% 0.81/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.81/1.20
% 0.81/1.20 % ------ iProver source info
% 0.81/1.20
% 0.81/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 0.81/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.81/1.20 % git: non_committed_changes: false
% 0.81/1.20
% 0.81/1.20 % ------ Parsing...
% 0.81/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.81/1.20 % ------ Proving...
% 0.81/1.20 % ------ Problem Properties
% 0.81/1.20
% 0.81/1.20 %
% 0.81/1.20 % clauses 24
% 0.81/1.20 % conjectures 3
% 0.81/1.20 % EPR 6
% 0.81/1.20 % Horn 19
% 0.81/1.20 % unary 10
% 0.81/1.20 % binary 6
% 0.81/1.20 % lits 48
% 0.81/1.20 % lits eq 15
% 0.81/1.20 % fd_pure 0
% 0.81/1.20 % fd_pseudo 0
% 0.81/1.20 % fd_cond 0
% 0.81/1.20 % fd_pseudo_cond 6
% 0.81/1.20 % AC symbols 0
% 0.81/1.20
% 0.81/1.20 % ------ Input Options Time Limit: Unbounded
% 0.81/1.20
% 0.81/1.20
% 0.81/1.20 % ------
% 0.81/1.20 % Current options:
% 0.81/1.20 % ------
% 0.81/1.20
% 0.81/1.20
% 0.81/1.20 %
% 0.81/1.20
% 0.81/1.20 % ------ Proving...
% 0.81/1.20 %
% 0.81/1.20
% 0.81/1.20 % ------ Proving...
% 0.81/1.20 %
% 0.81/1.20
% 0.81/1.20 % ------ Proving...
% 0.81/1.20 %
% 0.81/1.20
% 0.81/1.20 % SZS status Theorem for theBenchmark.p
% 0.81/1.20
% 0.81/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.81/1.21
% 0.81/1.21
%------------------------------------------------------------------------------