TSTP Solution File: SET988+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET988+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 : 600s
% DateTime : Tue Jul 19 03:38:48 EDT 2022
% Result : Theorem 0.22s 0.48s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 8 unt; 0 def)
% Number of atoms : 131 ( 44 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 145 ( 56 ~; 29 |; 41 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 112 ( 2 sgn 74 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t2_funct_1,conjecture,
! [A] :
( ( ! [B] :
~ ( in(B,A)
& ! [C,D] : ordered_pair(C,D) != B )
& ! [B,C,D] :
( ( in(ordered_pair(B,C),A)
& in(ordered_pair(B,D),A) )
=> C = D ) )
=> ( relation(A)
& function(A) ) ) ).
fof(d1_funct_1,axiom,
! [A] :
( function(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(B,C),A)
& in(ordered_pair(B,D),A) )
=> C = D ) ) ).
fof(d1_relat_1,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( in(B,A)
& ! [C,D] : B != ordered_pair(C,D) ) ) ).
fof(subgoal_0,plain,
! [A] :
( ( ! [B] :
~ ( in(B,A)
& ! [C,D] : ordered_pair(C,D) != B )
& ! [B,C,D] :
( ( in(ordered_pair(B,C),A)
& in(ordered_pair(B,D),A) )
=> C = D ) )
=> relation(A) ),
inference(strip,[],[t2_funct_1]) ).
fof(subgoal_1,plain,
! [A] :
( ( ! [B] :
~ ( in(B,A)
& ! [C,D] : ordered_pair(C,D) != B )
& ! [B,C,D] :
( ( in(ordered_pair(B,C),A)
& in(ordered_pair(B,D),A) )
=> C = D )
& relation(A) )
=> function(A) ),
inference(strip,[],[t2_funct_1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ( ! [B] :
~ ( in(B,A)
& ! [C,D] : ordered_pair(C,D) != B )
& ! [B,C,D] :
( ( in(ordered_pair(B,C),A)
& in(ordered_pair(B,D),A) )
=> C = D ) )
=> relation(A) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] :
( ~ relation(A)
<=> ? [B] :
( in(B,A)
& ! [C,D] : B != ordered_pair(C,D) ) ),
inference(canonicalize,[],[d1_relat_1]) ).
fof(normalize_0_1,plain,
! [A] :
( ~ relation(A)
<=> ? [B] :
( in(B,A)
& ! [C,D] : B != ordered_pair(C,D) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C,D] :
( ( skolemFOFtoCNF_B_4(A) != ordered_pair(C,D)
| relation(A) )
& ( in(skolemFOFtoCNF_B_4(A),A)
| relation(A) )
& ( ~ in(B,A)
| ~ relation(A)
| B = ordered_pair(skolemFOFtoCNF_C_1(B),skolemFOFtoCNF_D_1(B)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,C,D] :
( skolemFOFtoCNF_B_4(A) != ordered_pair(C,D)
| relation(A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] :
( in(skolemFOFtoCNF_B_4(A),A)
| relation(A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
? [A] :
( ~ relation(A)
& ! [B] :
( ~ in(B,A)
| ? [C,D] : ordered_pair(C,D) = B )
& ! [B,C,D] :
( ~ in(ordered_pair(B,C),A)
| ~ in(ordered_pair(B,D),A)
| C = D ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_6,plain,
! [A] :
( ~ function(A)
<=> ? [B,C,D] :
( C != D
& in(ordered_pair(B,C),A)
& in(ordered_pair(B,D),A) ) ),
inference(canonicalize,[],[d1_funct_1]) ).
fof(normalize_0_7,plain,
! [A] :
( ~ function(A)
<=> ? [B,C,D] :
( C != D
& in(ordered_pair(B,C),A)
& in(ordered_pair(B,D),A) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [A] :
( ~ relation(A)
& function(A)
& ! [B] :
( ~ in(B,A)
| ? [C,D] : ordered_pair(C,D) = B ) ),
inference(simplify,[],[normalize_0_5,normalize_0_7]) ).
fof(normalize_0_9,plain,
( ~ relation(skolemFOFtoCNF_A_6)
& function(skolemFOFtoCNF_A_6)
& ! [B] :
( ~ in(B,skolemFOFtoCNF_A_6)
| ? [C,D] : ordered_pair(C,D) = B ) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B] :
( ~ in(B,skolemFOFtoCNF_A_6)
| ? [C,D] : ordered_pair(C,D) = B ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B] :
( ~ in(B,skolemFOFtoCNF_A_6)
| ? [C,D] : ordered_pair(C,D) = B ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B] :
( ~ in(B,skolemFOFtoCNF_A_6)
| ordered_pair(skolemFOFtoCNF_C_2(B),skolemFOFtoCNF_D_2(B)) = B ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
~ relation(skolemFOFtoCNF_A_6),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( skolemFOFtoCNF_B_4(A) != ordered_pair(C,D)
| relation(A) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( skolemFOFtoCNF_B_4(X_70) != ordered_pair(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_D_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)))
| relation(X_70) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_70)),bind(C,$fot(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)))),bind(D,$fot(skolemFOFtoCNF_D_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6))))]]) ).
cnf(refute_0_2,plain,
( in(skolemFOFtoCNF_B_4(A),A)
| relation(A) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( in(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6),skolemFOFtoCNF_A_6)
| relation(skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_4,plain,
( ~ in(B,skolemFOFtoCNF_A_6)
| ordered_pair(skolemFOFtoCNF_C_2(B),skolemFOFtoCNF_D_2(B)) = B ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_5,plain,
( ~ in(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6),skolemFOFtoCNF_A_6)
| ordered_pair(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_D_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6))) = skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)))]]) ).
cnf(refute_0_6,plain,
( ordered_pair(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_D_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6))) = skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)
| relation(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6),skolemFOFtoCNF_A_6) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
~ relation(skolemFOFtoCNF_A_6),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_8,plain,
ordered_pair(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_D_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6))) = skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_6) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ordered_pair(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_D_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6))) != skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_B_4(X_70) != skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_B_4(X_70) = ordered_pair(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_D_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_B_4(X_70),ordered_pair(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_D_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)))) ),[1],$fot(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_B_4(X_70) != skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)
| skolemFOFtoCNF_B_4(X_70) = ordered_pair(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_D_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6))) ),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_D_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6))),skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( skolemFOFtoCNF_B_4(X_70) != skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)
| relation(X_70) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_4(X_70),ordered_pair(skolemFOFtoCNF_C_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_D_2(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)))) )],[refute_0_10,refute_0_1]) ).
cnf(refute_0_12,plain,
( skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6) != skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)
| relation(skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_0_11:[bind(X_70,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6) = skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_14,plain,
relation(skolemFOFtoCNF_A_6),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_4(skolemFOFtoCNF_A_6)) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_6) )],[refute_0_14,refute_0_7]) ).
fof(negate_1_0,plain,
~ ! [A] :
( ( ! [B] :
~ ( in(B,A)
& ! [C,D] : ordered_pair(C,D) != B )
& ! [B,C,D] :
( ( in(ordered_pair(B,C),A)
& in(ordered_pair(B,D),A) )
=> C = D )
& relation(A) )
=> function(A) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A] :
( ~ function(A)
& relation(A)
& ! [B] :
( ~ in(B,A)
| ? [C,D] : ordered_pair(C,D) = B )
& ! [B,C,D] :
( ~ in(ordered_pair(B,C),A)
| ~ in(ordered_pair(B,D),A)
| C = D ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [A] :
( ~ function(A)
<=> ? [B,C,D] :
( C != D
& in(ordered_pair(B,C),A)
& in(ordered_pair(B,D),A) ) ),
inference(canonicalize,[],[d1_funct_1]) ).
fof(normalize_1_2,plain,
! [A] :
( ~ function(A)
<=> ? [B,C,D] :
( C != D
& in(ordered_pair(B,C),A)
& in(ordered_pair(B,D),A) ) ),
inference(specialize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
$false,
inference(simplify,[],[normalize_1_0,normalize_1_2]) ).
cnf(refute_1_0,plain,
$false,
inference(canonicalize,[],[normalize_1_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET988+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 15:01:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.48
% 0.22/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.22/0.49
%------------------------------------------------------------------------------