TSTP Solution File: SEU121+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU121+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 12:38:30 EDT 2022
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 71 ( 27 ~; 26 |; 11 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 26 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(t1_xboole_1,conjecture,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ),
inference(strip,[],[t1_xboole_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B,C] :
( ~ subset(A,C)
& subset(A,B)
& subset(B,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3)
& subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
& subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_3) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_3),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
! [A,B] :
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_9,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_10,plain,
~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3)
| subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_C_3))]]) ).
cnf(refute_0_2,plain,
subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_3),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ in(X_177,skolemFOFtoCNF_B_1)
| ~ subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_3)
| in(X_177,skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(skolemFOFtoCNF_C_3)),bind(C,$fot(X_177))]]) ).
cnf(refute_0_5,plain,
( ~ in(X_177,skolemFOFtoCNF_B_1)
| in(X_177,skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_3) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_194),skolemFOFtoCNF_B_1)
| in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_194),skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_0_5:[bind(X_177,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_194)))]]) ).
cnf(refute_0_7,plain,
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,B),skolemFOFtoCNF_A_2)
| subset(skolemFOFtoCNF_A_2,B) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_9,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,plain,
( ~ in(X_177,skolemFOFtoCNF_A_2)
| ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| in(X_177,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(X_177))]]) ).
cnf(refute_0_11,plain,
( ~ in(X_177,skolemFOFtoCNF_A_2)
| in(X_177,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,B),skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,B),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_11:[bind(X_177,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,B)))]]) ).
cnf(refute_0_13,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,B),skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_A_2,B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,B),skolemFOFtoCNF_A_2) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_194),skolemFOFtoCNF_B_1)
| subset(skolemFOFtoCNF_A_2,X_194) ),
inference(subst,[],[refute_0_13:[bind(B,$fot(X_194))]]) ).
cnf(refute_0_15,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_194),skolemFOFtoCNF_C_3)
| subset(skolemFOFtoCNF_A_2,X_194) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,X_194),skolemFOFtoCNF_B_1) )],[refute_0_14,refute_0_6]) ).
cnf(refute_0_16,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3)
| subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_0_15:[bind(X_194,$fot(skolemFOFtoCNF_C_3))]]) ).
cnf(refute_0_17,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3) )],[refute_0_16,refute_0_1]) ).
cnf(refute_0_18,plain,
~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3) )],[refute_0_17,refute_0_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.10 % Problem : SEU121+2 : TPTP v8.1.0. Released v3.3.0.
% 0.01/0.10 % Command : metis --show proof --show saturation %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Sun Jun 19 11:43:18 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.38
%------------------------------------------------------------------------------