TSTP Solution File: SEU267+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU267+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 12:39:50 EDT 2022
% Result : Theorem 0.84s 1.04s
% Output : CNFRefutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 23 unt; 0 def)
% Number of atoms : 125 ( 123 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 140 ( 67 ~; 50 |; 11 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 130 ( 14 sgn 58 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_mcart_1,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_first(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = C ) ) ) ).
fof(d2_mcart_1,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_second(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = D ) ) ) ).
fof(t7_mcart_1,conjecture,
! [A,B] :
( pair_first(ordered_pair(A,B)) = A
& pair_second(ordered_pair(A,B)) = B ) ).
fof(subgoal_0,plain,
! [A,B] : pair_first(ordered_pair(A,B)) = A,
inference(strip,[],[t7_mcart_1]) ).
fof(subgoal_1,plain,
! [A,B] :
( pair_first(ordered_pair(A,B)) = A
=> pair_second(ordered_pair(A,B)) = B ),
inference(strip,[],[t7_mcart_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] : pair_first(ordered_pair(A,B)) = A,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] : pair_first(ordered_pair(A,B)) != A,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
pair_first(ordered_pair(skolemFOFtoCNF_A_12,skolemFOFtoCNF_B_19)) != skolemFOFtoCNF_A_12,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] :
( ! [B] :
( B != pair_first(A)
<=> ? [C] :
( B != C
& ? [D] : A = ordered_pair(C,D) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(canonicalize,[],[d1_mcart_1]) ).
fof(normalize_0_3,plain,
! [A] :
( ! [B] :
( B != pair_first(A)
<=> ? [C] :
( B != C
& ? [D] : A = ordered_pair(C,D) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,B0,C,C0,D] :
( ( A != ordered_pair(B0,C0)
| B != skolemFOFtoCNF_C_1(A,B)
| B = pair_first(A) )
& ( A != ordered_pair(B0,C0)
| A = ordered_pair(skolemFOFtoCNF_C_1(A,B),skolemFOFtoCNF_D_7(A,B))
| B = pair_first(A) )
& ( A != ordered_pair(B0,C0)
| A != ordered_pair(C,D)
| B != pair_first(A)
| B = C ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,B0,C,C0,D] :
( A != ordered_pair(B0,C0)
| A != ordered_pair(C,D)
| B != pair_first(A)
| B = C ),
inference(conjunct,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
pair_first(ordered_pair(skolemFOFtoCNF_A_12,skolemFOFtoCNF_B_19)) != skolemFOFtoCNF_A_12,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( A != ordered_pair(B0,C0)
| A != ordered_pair(C,D)
| B != pair_first(A)
| B = C ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ordered_pair(B0,C0) != ordered_pair(B0,C0)
| ordered_pair(B0,C0) != ordered_pair(C,D)
| pair_first(ordered_pair(B0,C0)) != pair_first(ordered_pair(B0,C0))
| pair_first(ordered_pair(B0,C0)) = C ),
inference(subst,[],[refute_0_1:[bind(A,$fot(ordered_pair(B0,C0))),bind(B,$fot(pair_first(ordered_pair(B0,C0))))]]) ).
cnf(refute_0_3,plain,
ordered_pair(B0,C0) = ordered_pair(B0,C0),
introduced(tautology,[refl,[$fot(ordered_pair(B0,C0))]]) ).
cnf(refute_0_4,plain,
( ordered_pair(B0,C0) != ordered_pair(C,D)
| pair_first(ordered_pair(B0,C0)) != pair_first(ordered_pair(B0,C0))
| pair_first(ordered_pair(B0,C0)) = C ),
inference(resolve,[$cnf( $equal(ordered_pair(B0,C0),ordered_pair(B0,C0)) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
pair_first(ordered_pair(B0,C0)) = pair_first(ordered_pair(B0,C0)),
introduced(tautology,[refl,[$fot(pair_first(ordered_pair(B0,C0)))]]) ).
cnf(refute_0_6,plain,
( ordered_pair(B0,C0) != ordered_pair(C,D)
| pair_first(ordered_pair(B0,C0)) = C ),
inference(resolve,[$cnf( $equal(pair_first(ordered_pair(B0,C0)),pair_first(ordered_pair(B0,C0))) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( ordered_pair(C,D) != ordered_pair(C,D)
| pair_first(ordered_pair(C,D)) = C ),
inference(subst,[],[refute_0_6:[bind(B0,$fot(C)),bind(C0,$fot(D))]]) ).
cnf(refute_0_8,plain,
ordered_pair(C,D) = ordered_pair(C,D),
introduced(tautology,[refl,[$fot(ordered_pair(C,D))]]) ).
cnf(refute_0_9,plain,
pair_first(ordered_pair(C,D)) = C,
inference(resolve,[$cnf( $equal(ordered_pair(C,D),ordered_pair(C,D)) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
pair_first(ordered_pair(skolemFOFtoCNF_A_12,skolemFOFtoCNF_B_19)) = skolemFOFtoCNF_A_12,
inference(subst,[],[refute_0_9:[bind(C,$fot(skolemFOFtoCNF_A_12)),bind(D,$fot(skolemFOFtoCNF_B_19))]]) ).
cnf(refute_0_11,plain,
( pair_first(ordered_pair(skolemFOFtoCNF_A_12,skolemFOFtoCNF_B_19)) != skolemFOFtoCNF_A_12
| skolemFOFtoCNF_A_12 != skolemFOFtoCNF_A_12
| pair_first(ordered_pair(skolemFOFtoCNF_A_12,skolemFOFtoCNF_B_19)) = skolemFOFtoCNF_A_12 ),
introduced(tautology,[equality,[$cnf( ~ $equal(pair_first(ordered_pair(skolemFOFtoCNF_A_12,skolemFOFtoCNF_B_19)),skolemFOFtoCNF_A_12) ),[0],$fot(skolemFOFtoCNF_A_12)]]) ).
cnf(refute_0_12,plain,
( skolemFOFtoCNF_A_12 != skolemFOFtoCNF_A_12
| pair_first(ordered_pair(skolemFOFtoCNF_A_12,skolemFOFtoCNF_B_19)) = skolemFOFtoCNF_A_12 ),
inference(resolve,[$cnf( $equal(pair_first(ordered_pair(skolemFOFtoCNF_A_12,skolemFOFtoCNF_B_19)),skolemFOFtoCNF_A_12) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_A_12 != skolemFOFtoCNF_A_12,
inference(resolve,[$cnf( $equal(pair_first(ordered_pair(skolemFOFtoCNF_A_12,skolemFOFtoCNF_B_19)),skolemFOFtoCNF_A_12) )],[refute_0_12,refute_0_0]) ).
cnf(refute_0_14,plain,
skolemFOFtoCNF_A_12 = skolemFOFtoCNF_A_12,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_A_12)]]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_12,skolemFOFtoCNF_A_12) )],[refute_0_14,refute_0_13]) ).
fof(negate_1_0,plain,
~ ! [A,B] :
( pair_first(ordered_pair(A,B)) = A
=> pair_second(ordered_pair(A,B)) = B ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B] :
( pair_second(ordered_pair(A,B)) != B
& pair_first(ordered_pair(A,B)) = A ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( pair_second(ordered_pair(skolemFOFtoCNF_A_13,skolemFOFtoCNF_B_20)) != skolemFOFtoCNF_B_20
& pair_first(ordered_pair(skolemFOFtoCNF_A_13,skolemFOFtoCNF_B_20)) = skolemFOFtoCNF_A_13 ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
pair_second(ordered_pair(skolemFOFtoCNF_A_13,skolemFOFtoCNF_B_20)) != skolemFOFtoCNF_B_20,
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A] :
( ! [B] :
( B != pair_second(A)
<=> ? [C,D] :
( B != D
& A = ordered_pair(C,D) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(canonicalize,[],[d2_mcart_1]) ).
fof(normalize_1_4,plain,
! [A] :
( ! [B] :
( B != pair_second(A)
<=> ? [C,D] :
( B != D
& A = ordered_pair(C,D) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B,B0,C,C0,D] :
( ( A != ordered_pair(B0,C0)
| B != skolemFOFtoCNF_D_12(A,B)
| B = pair_second(A) )
& ( A != ordered_pair(B0,C0)
| A = ordered_pair(skolemFOFtoCNF_C_7(A,B),skolemFOFtoCNF_D_12(A,B))
| B = pair_second(A) )
& ( A != ordered_pair(B0,C0)
| A != ordered_pair(C,D)
| B != pair_second(A)
| B = D ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A,B,B0,C,C0,D] :
( A != ordered_pair(B0,C0)
| A != ordered_pair(C,D)
| B != pair_second(A)
| B = D ),
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
pair_second(ordered_pair(skolemFOFtoCNF_A_13,skolemFOFtoCNF_B_20)) != skolemFOFtoCNF_B_20,
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( A != ordered_pair(B0,C0)
| A != ordered_pair(C,D)
| B != pair_second(A)
| B = D ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( ordered_pair(B0,C0) != ordered_pair(B0,C0)
| ordered_pair(B0,C0) != ordered_pair(C,D)
| pair_second(ordered_pair(B0,C0)) != pair_second(ordered_pair(B0,C0))
| pair_second(ordered_pair(B0,C0)) = D ),
inference(subst,[],[refute_1_1:[bind(A,$fot(ordered_pair(B0,C0))),bind(B,$fot(pair_second(ordered_pair(B0,C0))))]]) ).
cnf(refute_1_3,plain,
ordered_pair(B0,C0) = ordered_pair(B0,C0),
introduced(tautology,[refl,[$fot(ordered_pair(B0,C0))]]) ).
cnf(refute_1_4,plain,
( ordered_pair(B0,C0) != ordered_pair(C,D)
| pair_second(ordered_pair(B0,C0)) != pair_second(ordered_pair(B0,C0))
| pair_second(ordered_pair(B0,C0)) = D ),
inference(resolve,[$cnf( $equal(ordered_pair(B0,C0),ordered_pair(B0,C0)) )],[refute_1_3,refute_1_2]) ).
cnf(refute_1_5,plain,
pair_second(ordered_pair(B0,C0)) = pair_second(ordered_pair(B0,C0)),
introduced(tautology,[refl,[$fot(pair_second(ordered_pair(B0,C0)))]]) ).
cnf(refute_1_6,plain,
( ordered_pair(B0,C0) != ordered_pair(C,D)
| pair_second(ordered_pair(B0,C0)) = D ),
inference(resolve,[$cnf( $equal(pair_second(ordered_pair(B0,C0)),pair_second(ordered_pair(B0,C0))) )],[refute_1_5,refute_1_4]) ).
cnf(refute_1_7,plain,
( ordered_pair(C,D) != ordered_pair(C,D)
| pair_second(ordered_pair(C,D)) = D ),
inference(subst,[],[refute_1_6:[bind(B0,$fot(C)),bind(C0,$fot(D))]]) ).
cnf(refute_1_8,plain,
ordered_pair(C,D) = ordered_pair(C,D),
introduced(tautology,[refl,[$fot(ordered_pair(C,D))]]) ).
cnf(refute_1_9,plain,
pair_second(ordered_pair(C,D)) = D,
inference(resolve,[$cnf( $equal(ordered_pair(C,D),ordered_pair(C,D)) )],[refute_1_8,refute_1_7]) ).
cnf(refute_1_10,plain,
pair_second(ordered_pair(skolemFOFtoCNF_A_13,skolemFOFtoCNF_B_20)) = skolemFOFtoCNF_B_20,
inference(subst,[],[refute_1_9:[bind(C,$fot(skolemFOFtoCNF_A_13)),bind(D,$fot(skolemFOFtoCNF_B_20))]]) ).
cnf(refute_1_11,plain,
( pair_second(ordered_pair(skolemFOFtoCNF_A_13,skolemFOFtoCNF_B_20)) != skolemFOFtoCNF_B_20
| skolemFOFtoCNF_B_20 != skolemFOFtoCNF_B_20
| pair_second(ordered_pair(skolemFOFtoCNF_A_13,skolemFOFtoCNF_B_20)) = skolemFOFtoCNF_B_20 ),
introduced(tautology,[equality,[$cnf( ~ $equal(pair_second(ordered_pair(skolemFOFtoCNF_A_13,skolemFOFtoCNF_B_20)),skolemFOFtoCNF_B_20) ),[0],$fot(skolemFOFtoCNF_B_20)]]) ).
cnf(refute_1_12,plain,
( skolemFOFtoCNF_B_20 != skolemFOFtoCNF_B_20
| pair_second(ordered_pair(skolemFOFtoCNF_A_13,skolemFOFtoCNF_B_20)) = skolemFOFtoCNF_B_20 ),
inference(resolve,[$cnf( $equal(pair_second(ordered_pair(skolemFOFtoCNF_A_13,skolemFOFtoCNF_B_20)),skolemFOFtoCNF_B_20) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
skolemFOFtoCNF_B_20 != skolemFOFtoCNF_B_20,
inference(resolve,[$cnf( $equal(pair_second(ordered_pair(skolemFOFtoCNF_A_13,skolemFOFtoCNF_B_20)),skolemFOFtoCNF_B_20) )],[refute_1_12,refute_1_0]) ).
cnf(refute_1_14,plain,
skolemFOFtoCNF_B_20 = skolemFOFtoCNF_B_20,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_B_20)]]) ).
cnf(refute_1_15,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_20,skolemFOFtoCNF_B_20) )],[refute_1_14,refute_1_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU267+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 22:15:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.84/1.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.84/1.04
% 0.84/1.04 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.84/1.04
%------------------------------------------------------------------------------