%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.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 02:49:15 PM UTC 2026
% Result : Theorem 1.90s 1.29s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 104 ( 28 unt; 2 def)
% Number of atoms : 268 ( 124 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 262 ( 109 ~; 120 |; 25 &)
% ( 4 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 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; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 171 ( 0 sgn 159 !; 12 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
<=> ( X1 = empty_set
| X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
=> ( ( X1 = X3
& X0 = X2 )
| X1 = empty_set
| X0 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
=> ( ( X1 = X3
& X0 = X2 )
| X1 = empty_set
| X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f15,plain,
? [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
& ( X1 != X3
| X0 != X2 )
& empty_set != X1
& empty_set != X0 ),
inference(ennf_transformation,[],[f12]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
& ( X1 != X3
| X0 != X2 )
& empty_set != X1
& empty_set != X0 ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f13]) ).
fof(f18,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f19,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK0(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f19]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ( empty_set != cartesian_product2(X0,X1)
| X1 = empty_set
| X0 = empty_set )
& ( ( empty_set != X1
& empty_set != X0 )
| cartesian_product2(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f26,plain,
! [X0,X1] :
( ( empty_set != cartesian_product2(X0,X1)
| X1 = empty_set
| X0 = empty_set )
& ( ( empty_set != X1
& empty_set != X0 )
| cartesian_product2(X0,X1) = empty_set ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
( cartesian_product2(sK5,sK6) = cartesian_product2(sK3,sK4)
& ( sK4 != sK6
| sK3 != sK5 )
& empty_set != sK4
& empty_set != sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f16]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X0,X1] :
( ( ( in(sK7(X0,X1),X0)
| in(sK7(X0,X1),X1) )
& ( ~ in(sK7(X0,X1),X0)
| ~ in(sK7(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f28]) ).
fof(f31,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f32,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0] :
( in(sK0(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X0,X1] :
( empty_set != cartesian_product2(X0,X1)
| empty_set = X1
| empty_set = X0 ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X0,X1] :
( empty_set != X1
| empty_set = cartesian_product2(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f45,plain,
cartesian_product2(sK5,sK6) = cartesian_product2(sK3,sK4),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
( sK4 != sK6
| sK3 != sK5 ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
empty_set != sK4,
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
empty_set != sK3,
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
! [X0,X1] :
( in(sK7(X0,X1),X0)
| in(sK7(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f50,plain,
! [X0,X1] :
( ~ in(sK7(X0,X1),X0)
| ~ in(sK7(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f39,f34]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f38,f34]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f37,f34]) ).
fof(f55,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f32]) ).
fof(f57,plain,
! [X0] : empty_set = cartesian_product2(X0,empty_set),
inference(equality_resolution,[],[f43]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_51,plain,
! [X0: $i] :
( in(sK0(X0),X0)
| ( X0 = empty_set ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_52,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f55]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_61,plain,
! [X0: $i] : cartesian_product2(X0,empty_set) = empty_set,
inference(cnf_transformation,[],[f57]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ( X0 = empty_set )
| ( cartesian_product2(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_63,negated_conjecture,
empty_set != sK3,
inference(cnf_transformation,[],[f48]) ).
tcf(c_64,negated_conjecture,
empty_set != sK4,
inference(cnf_transformation,[],[f47]) ).
tcf(c_65,negated_conjecture,
( ( sK4 != sK6 )
| ( sK3 != sK5 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_66,negated_conjecture,
cartesian_product2(sK3,sK4) = cartesian_product2(sK5,sK6),
inference(cnf_transformation,[],[f45]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK7(X0,X1),X1)
| ~ in(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1),X1)
| in(sK7(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_70,plain,
cartesian_product2(empty_set,empty_set) = empty_set,
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_76,plain,
( ( empty_set = empty_set )
| ( cartesian_product2(empty_set,empty_set) != empty_set ) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(demodulation,[status(thm)],[c_57,c_50]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(demodulation,[status(thm)],[c_56,c_50]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_55,c_50]) ).
tcf(c_228,definition,
iPr_def_10 = cartesian_product2(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_229,definition,
iPr_def_11 = cartesian_product2(sK5,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_230,negated_conjecture,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_66,c_229,c_228]) ).
tcf(c_232,negated_conjecture,
empty_set != sK4,
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_233,negated_conjecture,
empty_set != sK3,
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_456,plain,
cartesian_product2(sK5,sK6) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_229,c_230]) ).
tcf(c_484,plain,
! [X0: $i] :
( in(sK7(X0,empty_set),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_68,c_52]) ).
tcf(c_531,plain,
! [X0: $i,X1: $i] :
( in(X1,sK6)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_456,c_161]) ).
tcf(c_532,plain,
! [X0: $i,X1: $i] :
( in(X1,sK4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_228,c_161]) ).
tcf(c_568,plain,
! [X0: $i,X1: $i] :
( in(X0,sK5)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_456,c_168]) ).
tcf(c_569,plain,
! [X0: $i,X1: $i] :
( in(X0,sK3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_228,c_168]) ).
tcf(c_598,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10)
| ~ in(X1,sK6)
| ~ in(X0,sK5) ),
inference(superposition,[status(thm)],[c_456,c_187]) ).
tcf(c_599,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10)
| ~ in(X1,sK4)
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_228,c_187]) ).
tcf(c_656,plain,
! [X0: $i,X1: $i] :
( in(X0,sK3)
| ~ in(X1,sK6)
| ~ in(X0,sK5) ),
inference(superposition,[status(thm)],[c_598,c_569]) ).
tcf(c_658,plain,
! [X0: $i,X1: $i] :
( in(X1,sK4)
| ~ in(X1,sK6)
| ~ in(X0,sK5) ),
inference(superposition,[status(thm)],[c_598,c_532]) ).
tcf(c_676,plain,
! [X0: $i] :
( ( empty_set = sK3 )
| ( sK3 != X0 )
| ( empty_set != X0 ) ),
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_677,plain,
( ( empty_set = sK3 )
| ( sK3 != empty_set )
| ( empty_set != empty_set ) ),
inference(instantiation,[status(thm)],[c_676]) ).
tcf(c_678,plain,
! [X0: $i] :
( ( empty_set = sK4 )
| ( sK4 != X0 )
| ( empty_set != X0 ) ),
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_691,plain,
! [X0: $i] :
( in(X0,sK3)
| ( empty_set = sK6 )
| ~ in(X0,sK5) ),
inference(superposition,[status(thm)],[c_484,c_656]) ).
tcf(c_713,plain,
! [X0: $i,X1: $i] :
( in(sK7(sK6,X1),sK4)
| in(sK7(sK6,X1),X1)
| ( X1 = sK6 )
| ~ in(X0,sK5) ),
inference(superposition,[status(thm)],[c_68,c_658]) ).
tcf(c_793,plain,
! [X0: $i] :
( in(sK7(X0,sK5),sK3)
| in(sK7(X0,sK5),X0)
| ( empty_set = sK6 )
| ( X0 = sK5 ) ),
inference(superposition,[status(thm)],[c_68,c_691]) ).
tcf(c_890,plain,
( in(sK0(sK3),sK3)
| ( sK3 = empty_set ) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_1482,plain,
( in(sK7(sK3,sK5),sK3)
| ( sK3 = sK5 )
| ( empty_set = sK6 ) ),
inference(equality_factoring,[status(thm)],[c_793]) ).
tcf(c_1592,plain,
! [X0: $i,X1: $i] :
( in(X0,sK5)
| ~ in(X1,sK4)
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_599,c_568]) ).
tcf(c_1594,plain,
! [X0: $i,X1: $i] :
( in(X1,sK6)
| ~ in(X1,sK4)
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_599,c_531]) ).
tcf(c_1617,plain,
( ( empty_set = sK4 )
| ( sK4 != sK6 )
| ( empty_set != sK6 ) ),
inference(instantiation,[status(thm)],[c_678]) ).
tcf(c_1664,plain,
! [X0: $i] :
( in(X0,sK5)
| ( empty_set = sK4 )
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_484,c_1592]) ).
tcf(c_1674,plain,
! [X0: $i] :
( in(X0,sK5)
| ~ in(X0,sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1664,c_232]) ).
tcf(c_1684,plain,
( in(sK0(sK3),sK5)
| ( empty_set = sK3 ) ),
inference(superposition,[status(thm)],[c_51,c_1674]) ).
tcf(c_1686,plain,
! [X0: $i] :
( in(sK7(sK3,X0),sK5)
| in(sK7(sK3,X0),X0)
| ( X0 = sK3 ) ),
inference(superposition,[status(thm)],[c_68,c_1674]) ).
tcf(c_1698,plain,
in(sK0(sK3),sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_1684,c_233]) ).
tcf(c_1790,plain,
! [X0: $i] :
( in(sK7(sK6,X0),sK4)
| in(sK7(sK6,X0),X0)
| ( X0 = sK6 ) ),
inference(superposition,[status(thm)],[c_1698,c_713]) ).
tcf(c_1797,plain,
( in(sK0(sK3),sK3)
| ( empty_set = sK6 ) ),
inference(superposition,[status(thm)],[c_1698,c_691]) ).
tcf(c_1938,plain,
in(sK0(sK3),sK3),
inference(global_subsumption_just,[status(thm)],[c_1797,c_63,c_70,c_76,c_677,c_890]) ).
tcf(c_2300,plain,
( in(sK7(sK3,sK5),sK5)
| ( sK3 = sK5 ) ),
inference(equality_factoring,[status(thm)],[c_1686]) ).
tcf(c_2424,plain,
( in(sK7(sK6,sK4),sK4)
| ( sK4 = sK6 ) ),
inference(equality_factoring,[status(thm)],[c_1790]) ).
tcf(c_2620,plain,
( ( sK3 = sK5 )
| ~ in(sK7(sK3,sK5),sK3) ),
inference(superposition,[status(thm)],[c_2300,c_67]) ).
tcf(c_2639,plain,
in(sK7(sK6,sK4),sK4),
inference(global_subsumption_just,[status(thm)],[c_2424,c_64,c_65,c_1482,c_1617,c_2424,c_2620]) ).
tcf(c_2642,plain,
( ( sK4 = sK6 )
| ~ in(sK7(sK6,sK4),sK6) ),
inference(superposition,[status(thm)],[c_2639,c_67]) ).
tcf(c_2884,plain,
~ in(sK7(sK6,sK4),sK6),
inference(global_subsumption_just,[status(thm)],[c_2642,c_64,c_65,c_1482,c_1617,c_2620,c_2642]) ).
tcf(c_2913,plain,
! [X0: $i] :
( in(sK7(sK6,sK4),sK6)
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_2639,c_1594]) ).
tcf(c_2914,plain,
! [X0: $i] : ~ in(X0,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_2913,c_2884]) ).
tcf(c_2915,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1938,c_2914]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n014.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:30:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.90/1.29 % SZS status Started for theBenchmark.p
% 1.90/1.29 % SZS status Theorem for theBenchmark.p
% 1.90/1.29
% 1.90/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.90/1.29
% 1.90/1.29 % ------ iProver source info
% 1.90/1.29
% 1.90/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.90/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.90/1.29 % git: non_committed_changes: false
% 1.90/1.29
% 1.90/1.29 % ------ Parsing...
% 1.90/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.90/1.29
% 1.90/1.29 % ------ Preprocessing... sup_sim: 4 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.90/1.29
% 1.90/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.90/1.29
% 1.90/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.90/1.29 % ------ Proving...
% 1.90/1.29 % ------ Problem Properties
% 1.90/1.29
% 1.90/1.29 %
% 1.90/1.29 % clauses 22
% 1.90/1.29 % conjectures 4
% 1.90/1.29 % EPR 9
% 1.90/1.29 % Horn 19
% 1.90/1.29 % unary 13
% 1.90/1.29 % binary 5
% 1.90/1.29 % lits 35
% 1.90/1.29 % lits eq 16
% 1.90/1.29 % fd_pure 0
% 1.90/1.29 % fd_pseudo 0
% 1.90/1.29 % fd_cond 2
% 1.90/1.29 % fd_pseudo_cond 2
% 1.90/1.29 % AC symbols 0
% 1.90/1.29
% 1.90/1.29 % ------ Schedule dynamic 5 is on
% 1.90/1.29
% 1.90/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.90/1.29
% 1.90/1.29
% 1.90/1.29 % ------
% 1.90/1.29 % Current options:
% 1.90/1.29 % ------
% 1.90/1.29
% 1.90/1.29
% 1.90/1.29 %
% 1.90/1.29
% 1.90/1.29 % ------ Proving...
% 1.90/1.29 %
% 1.90/1.29
% 1.90/1.29 % SZS status Theorem for theBenchmark.p
% 1.90/1.29
% 1.90/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.90/1.29
% 1.90/1.29
%------------------------------------------------------------------------------