TSTP Solution File: SEU126+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU126+1 : 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 12:38:33 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 16 unt; 0 def)
% Number of atoms : 127 ( 49 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 126 ( 48 ~; 54 |; 11 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 76 ( 0 sgn 45 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(t12_xboole_1,conjecture,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ) ).
fof(subgoal_0,plain,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
inference(strip,[],[t12_xboole_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B,C] :
( C != set_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(canonicalize,[],[d2_xboole_0]) ).
fof(normalize_0_1,plain,
! [A,B,C] :
( C != set_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C,D] :
( ( C != set_union2(A,B)
| ~ in(D,A)
| in(D,C) )
& ( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),B)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) )
& ( C != set_union2(A,B)
| ~ in(D,C)
| in(D,A)
| in(D,B) )
& ( C = set_union2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B] :
( set_union2(A,B) != B
& subset(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != skolemFOFtoCNF_B
& subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C] :
( C = set_union2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_12,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_13,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != skolemFOFtoCNF_B,
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B)
| skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_2,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_4,plain,
( ~ in(X_80,skolemFOFtoCNF_A_2)
| ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| in(X_80,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_80))]]) ).
cnf(refute_0_5,plain,
( ~ in(X_80,skolemFOFtoCNF_A_2)
| in(X_80,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ in(skolemFOFtoCNF_D(X_215,skolemFOFtoCNF_A_2,X_215),skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_D(X_215,skolemFOFtoCNF_A_2,X_215),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_5:[bind(X_80,$fot(skolemFOFtoCNF_D(X_215,skolemFOFtoCNF_A_2,X_215)))]]) ).
cnf(refute_0_7,plain,
( C = set_union2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( X_215 = set_union2(X_215,skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_D(X_215,skolemFOFtoCNF_A_2,X_215),X_215)
| in(skolemFOFtoCNF_D(X_215,skolemFOFtoCNF_A_2,X_215),skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_215)),bind(B,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(X_215))]]) ).
cnf(refute_0_9,plain,
( X_215 = set_union2(X_215,skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_D(X_215,skolemFOFtoCNF_A_2,X_215),X_215)
| in(skolemFOFtoCNF_D(X_215,skolemFOFtoCNF_A_2,X_215),skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(X_215,skolemFOFtoCNF_A_2,X_215),skolemFOFtoCNF_A_2) )],[refute_0_8,refute_0_6]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_9:[bind(X_215,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_11,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_13,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_14,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( set_union2(A,B) != set_union2(B,A)
| set_union2(B,A) = set_union2(A,B) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(set_union2(A,B))),bind(Y,$fot(set_union2(B,A)))]]) ).
cnf(refute_0_16,plain,
set_union2(B,A) = set_union2(A,B),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_18,plain,
( set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| skolemFOFtoCNF_B != set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2)) ),[1],$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).
cnf(refute_0_19,plain,
( skolemFOFtoCNF_B != set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| in(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2)) )],[refute_0_10,refute_0_19]) ).
cnf(refute_0_21,plain,
set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_22,plain,
( skolemFOFtoCNF_B != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_23,plain,
skolemFOFtoCNF_B != set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
in(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_24,refute_0_1]) ).
cnf(refute_0_26,plain,
skolemFOFtoCNF_B = set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2)) )],[refute_0_25,refute_0_19]) ).
cnf(refute_0_27,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_26,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU126+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % 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 23:19:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.48
%------------------------------------------------------------------------------