TSTP Solution File: SEU166+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU166+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 03:04:48 EDT 2024
% Result : Theorem 43.04s 6.73s
% Output : CNFRefutation 43.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 10
% Syntax : Number of formulae : 79 ( 13 unt; 0 def)
% Number of atoms : 284 ( 56 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 339 ( 134 ~; 142 |; 51 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 208 ( 1 sgn 125 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,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(f13,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f14,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
inference(negated_conjecture,[],[f14]) ).
fof(f16,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f13]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ( ~ subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) )
& subset(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| ~ in(X3,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) ) )
& ( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK0(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK0(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) )
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK0(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) )
=> ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
& in(sK2(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) )
=> ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
& in(sK4(X0,X1,X8),X1)
& in(sK3(X0,X1,X8),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK0(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
& in(sK2(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) ) )
& ( ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
& in(sK4(X0,X1,X8),X1)
& in(sK3(X0,X1,X8),X0) )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f24,f23,f22]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f27,f28]) ).
fof(f34,plain,
( ? [X0,X1,X2] :
( ( ~ subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) )
& subset(X0,X1) )
=> ( ( ~ subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))
| ~ subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)) )
& subset(sK8,sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
( ( ~ subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))
| ~ subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)) )
& subset(sK8,sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f19,f34]) ).
fof(f38,plain,
! [X2,X0,X1,X8] :
( in(sK3(X0,X1,X8),X0)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
! [X2,X0,X1,X8] :
( in(sK4(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f47,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f48,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f49,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f53,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f16]) ).
fof(f54,plain,
subset(sK8,sK9),
inference(cnf_transformation,[],[f35]) ).
fof(f55,plain,
( ~ subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))
| ~ subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f58,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| unordered_pair(unordered_pair(X9,X10),singleton(X9)) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f41,f49]) ).
fof(f59,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f40,f49]) ).
fof(f61,plain,
! [X2,X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),X2)
| ~ in(X10,X1)
| ~ in(X9,X0)
| cartesian_product2(X0,X1) != X2 ),
inference(equality_resolution,[],[f58]) ).
fof(f62,plain,
! [X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),cartesian_product2(X0,X1))
| ~ in(X10,X1)
| ~ in(X9,X0) ),
inference(equality_resolution,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f59]) ).
fof(f64,plain,
! [X0,X1,X8] :
( in(sK4(X0,X1,X8),X1)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f39]) ).
fof(f65,plain,
! [X0,X1,X8] :
( in(sK3(X0,X1,X8),X0)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f38]) ).
cnf(c_55,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),cartesian_product2(X1,X3)) ),
inference(cnf_transformation,[],[f62]) ).
cnf(c_56,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| unordered_pair(unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0)),singleton(sK3(X1,X2,X0))) = X0 ),
inference(cnf_transformation,[],[f63]) ).
cnf(c_57,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| in(sK4(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_58,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| in(sK3(X1,X2,X0),X1) ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_59,plain,
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_60,plain,
( in(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
cnf(c_61,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f46]) ).
cnf(c_65,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f53]) ).
cnf(c_66,negated_conjecture,
( ~ subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))
| ~ subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_67,negated_conjecture,
subset(sK8,sK9),
inference(cnf_transformation,[],[f54]) ).
cnf(c_68,plain,
subset(sK10,sK10),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_567,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| ~ subset(X2,X3)
| in(sK4(X1,X2,X0),X3) ),
inference(superposition,[status(thm)],[c_57,c_61]) ).
cnf(c_579,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| ~ subset(X1,X3)
| in(sK3(X1,X2,X0),X3) ),
inference(superposition,[status(thm)],[c_58,c_61]) ).
cnf(c_593,plain,
( unordered_pair(unordered_pair(sK3(X0,X1,sK5(cartesian_product2(X0,X1),X2)),sK4(X0,X1,sK5(cartesian_product2(X0,X1),X2))),singleton(sK3(X0,X1,sK5(cartesian_product2(X0,X1),X2)))) = sK5(cartesian_product2(X0,X1),X2)
| subset(cartesian_product2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_60,c_56]) ).
cnf(c_1469,plain,
( ~ subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| unordered_pair(unordered_pair(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)))),singleton(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))))) = sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) ),
inference(superposition,[status(thm)],[c_593,c_66]) ).
cnf(c_1477,plain,
( unordered_pair(unordered_pair(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)))),singleton(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))))) = sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))
| unordered_pair(unordered_pair(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)))),singleton(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))))) = sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)) ),
inference(superposition,[status(thm)],[c_593,c_1469]) ).
cnf(c_1481,plain,
( ~ in(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),X0)
| ~ in(sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),X1)
| unordered_pair(unordered_pair(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)))),singleton(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))))) = sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_1477,c_55]) ).
cnf(c_1553,plain,
( ~ in(sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),X0)
| ~ in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,sK8))
| unordered_pair(unordered_pair(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)))),singleton(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))))) = sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,X0)) ),
inference(superposition,[status(thm)],[c_58,c_1481]) ).
cnf(c_1578,plain,
( ~ in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,sK8))
| ~ subset(sK8,X0)
| unordered_pair(unordered_pair(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)))),singleton(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))))) = sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,X0)) ),
inference(superposition,[status(thm)],[c_567,c_1553]) ).
cnf(c_1650,plain,
( ~ subset(sK8,X0)
| unordered_pair(unordered_pair(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)))),singleton(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))))) = sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,X0))
| subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) ),
inference(superposition,[status(thm)],[c_60,c_1578]) ).
cnf(c_1709,plain,
( ~ subset(sK8,sK9)
| unordered_pair(unordered_pair(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)))),singleton(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))))) = sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) ),
inference(superposition,[status(thm)],[c_1650,c_59]) ).
cnf(c_1716,plain,
( unordered_pair(unordered_pair(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)))),singleton(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))))) = sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) ),
inference(global_subsumption_just,[status(thm)],[c_1709,c_67,c_1709]) ).
cnf(c_1745,plain,
( ~ subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))
| unordered_pair(unordered_pair(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)))),singleton(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))))) = sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)) ),
inference(superposition,[status(thm)],[c_1716,c_66]) ).
cnf(c_1753,plain,
unordered_pair(unordered_pair(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)))),singleton(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))))) = sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),
inference(superposition,[status(thm)],[c_593,c_1745]) ).
cnf(c_1757,plain,
( ~ in(sK3(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),X0)
| ~ in(sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),X1)
| in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_1753,c_55]) ).
cnf(c_1819,plain,
( ~ in(sK4(sK8,sK10,sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10))),X0)
| ~ in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(sK8,sK10))
| ~ subset(sK8,X1)
| in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(X1,X0)) ),
inference(superposition,[status(thm)],[c_579,c_1757]) ).
cnf(c_1882,plain,
( ~ in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(sK8,sK10))
| ~ subset(sK8,X0)
| in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(X0,sK10)) ),
inference(superposition,[status(thm)],[c_57,c_1819]) ).
cnf(c_1917,plain,
( ~ subset(sK8,X0)
| in(sK5(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),cartesian_product2(X0,sK10))
| subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)) ),
inference(superposition,[status(thm)],[c_60,c_1882]) ).
cnf(c_1985,plain,
( ~ subset(sK8,sK9)
| subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)) ),
inference(superposition,[status(thm)],[c_1917,c_59]) ).
cnf(c_1992,plain,
subset(cartesian_product2(sK8,sK10),cartesian_product2(sK9,sK10)),
inference(global_subsumption_just,[status(thm)],[c_1985,c_67,c_1985]) ).
cnf(c_2023,plain,
unordered_pair(unordered_pair(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)))),singleton(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))))) = sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),
inference(superposition,[status(thm)],[c_1992,c_1469]) ).
cnf(c_2028,plain,
( ~ in(sK3(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),X0)
| ~ in(sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),X1)
| in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_2023,c_55]) ).
cnf(c_2117,plain,
( ~ in(sK4(sK10,sK8,sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9))),X0)
| ~ in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,sK8))
| ~ subset(sK10,X1)
| in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(X1,X0)) ),
inference(superposition,[status(thm)],[c_579,c_2028]) ).
cnf(c_2142,plain,
( ~ in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,sK8))
| ~ subset(sK10,X0)
| in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(X0,sK8)) ),
inference(superposition,[status(thm)],[c_57,c_2117]) ).
cnf(c_2143,plain,
( ~ in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,sK8))
| ~ subset(sK10,X0)
| ~ subset(sK8,X1)
| in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_567,c_2117]) ).
cnf(c_2181,plain,
( ~ subset(sK10,X0)
| in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(X0,sK8))
| subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) ),
inference(superposition,[status(thm)],[c_60,c_2142]) ).
cnf(c_2184,plain,
( ~ subset(sK10,sK10)
| in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(sK10,sK8))
| subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) ),
inference(instantiation,[status(thm)],[c_2181]) ).
cnf(c_2194,plain,
( ~ subset(sK10,X0)
| ~ subset(sK8,X1)
| in(sK5(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)),cartesian_product2(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_2143,c_67,c_68,c_66,c_1985,c_2143,c_2184]) ).
cnf(c_2199,plain,
( ~ subset(sK10,sK10)
| ~ subset(sK8,sK9)
| subset(cartesian_product2(sK10,sK8),cartesian_product2(sK10,sK9)) ),
inference(superposition,[status(thm)],[c_2194,c_59]) ).
cnf(c_2207,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2199,c_1985,c_66,c_68,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU166+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 17:32:01 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 43.04/6.73 % SZS status Started for theBenchmark.p
% 43.04/6.73 % SZS status Theorem for theBenchmark.p
% 43.04/6.73
% 43.04/6.73 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 43.04/6.73
% 43.04/6.73 ------ iProver source info
% 43.04/6.73
% 43.04/6.73 git: date: 2024-05-02 19:28:25 +0000
% 43.04/6.73 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 43.04/6.73 git: non_committed_changes: false
% 43.04/6.73
% 43.04/6.73 ------ Parsing...
% 43.04/6.73 ------ Clausification by vclausify_rel & Parsing by iProver...
% 43.04/6.73
% 43.04/6.73 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 43.04/6.73
% 43.04/6.73 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 43.04/6.73
% 43.04/6.73 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 43.04/6.73 ------ Proving...
% 43.04/6.73 ------ Problem Properties
% 43.04/6.73
% 43.04/6.73
% 43.04/6.73 clauses 19
% 43.04/6.73 conjectures 2
% 43.04/6.73 EPR 6
% 43.04/6.73 Horn 15
% 43.04/6.73 unary 6
% 43.04/6.73 binary 7
% 43.04/6.73 lits 40
% 43.04/6.73 lits eq 8
% 43.04/6.73 fd_pure 0
% 43.04/6.73 fd_pseudo 0
% 43.04/6.73 fd_cond 0
% 43.04/6.73 fd_pseudo_cond 4
% 43.04/6.73 AC symbols 0
% 43.04/6.73
% 43.04/6.73 ------ Input Options Time Limit: Unbounded
% 43.04/6.73
% 43.04/6.73
% 43.04/6.73 ------
% 43.04/6.73 Current options:
% 43.04/6.73 ------
% 43.04/6.73
% 43.04/6.73
% 43.04/6.73
% 43.04/6.73
% 43.04/6.73 ------ Proving...
% 43.04/6.73
% 43.04/6.73
% 43.04/6.73 % SZS status Theorem for theBenchmark.p
% 43.04/6.73
% 43.04/6.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 43.04/6.73
% 43.04/6.73
%------------------------------------------------------------------------------