TSTP Solution File: GRP657+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP657+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 : Sat Jul 16 10:44:36 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 72 ( 43 unt; 0 def)
% Number of atoms : 110 ( 109 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 82 ( 44 ~; 35 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% Number of variables : 143 ( 0 sgn 33 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f02,axiom,
! [B,A] : ld(A,mult(A,B)) = B ).
fof(f03,axiom,
! [B,A] : mult(rd(A,B),B) = A ).
fof(f04,axiom,
! [B,A] : rd(mult(A,B),B) = A ).
fof(f05,axiom,
! [C,B,A] : mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)) ).
fof(goals,conjecture,
? [X0] :
! [X1] :
( mult(X1,X0) = X1
& mult(X0,X1) = X1 ) ).
fof(subgoal_0,plain,
? [X0] :
! [X1] :
( mult(X1,X0) = X1
& mult(X0,X1) = X1 ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ? [X0] :
! [X1] :
( mult(X1,X0) = X1
& mult(X0,X1) = X1 ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X0] :
( ? [X1] : mult(X0,X1) != X1
| ? [X1] : mult(X1,X0) != X1 ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X0] :
( ? [X1] : mult(X0,X1) != X1
| ? [X1] : mult(X1,X0) != X1 ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0] :
( mult(X0,skolemFOFtoCNF_X1(X0)) != skolemFOFtoCNF_X1(X0)
| mult(skolemFOFtoCNF_X1_1(X0),X0) != skolemFOFtoCNF_X1_1(X0) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] : rd(mult(A,B),B) = A,
inference(canonicalize,[],[f04]) ).
fof(normalize_0_4,plain,
! [A,B] : rd(mult(A,B),B) = A,
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C] : mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)),
inference(canonicalize,[],[f05]) ).
fof(normalize_0_6,plain,
! [A,B,C] : mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(canonicalize,[],[f03]) ).
fof(normalize_0_8,plain,
! [A,B] : mult(rd(A,B),B) = A,
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] : ld(A,mult(A,B)) = B,
inference(canonicalize,[],[f02]) ).
fof(normalize_0_10,plain,
! [A,B] : ld(A,mult(A,B)) = B,
inference(specialize,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( mult(X0,skolemFOFtoCNF_X1(X0)) != skolemFOFtoCNF_X1(X0)
| mult(skolemFOFtoCNF_X1_1(X0),X0) != skolemFOFtoCNF_X1_1(X0) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( mult(ld(X_60,X_60),skolemFOFtoCNF_X1(ld(X_60,X_60))) != skolemFOFtoCNF_X1(ld(X_60,X_60))
| mult(skolemFOFtoCNF_X1_1(ld(X_60,X_60)),ld(X_60,X_60)) != skolemFOFtoCNF_X1_1(ld(X_60,X_60)) ),
inference(subst,[],[refute_0_0:[bind(X0,$fot(ld(X_60,X_60)))]]) ).
cnf(refute_0_2,plain,
rd(mult(A,B),B) = A,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
rd(mult(A,mult(X_40,A)),mult(X_40,A)) = A,
inference(subst,[],[refute_0_2:[bind(B,$fot(mult(X_40,A)))]]) ).
cnf(refute_0_4,plain,
rd(mult(mult(X_13,X_14),mult(X_15,X_13)),mult(X_15,X_13)) = mult(X_13,X_14),
inference(subst,[],[refute_0_2:[bind(A,$fot(mult(X_13,X_14))),bind(B,$fot(mult(X_15,X_13)))]]) ).
cnf(refute_0_5,plain,
mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
mult(mult(X_13,X_14),mult(X_15,X_13)) = mult(X_13,mult(mult(X_14,X_15),X_13)),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_13)),bind(B,$fot(X_14)),bind(C,$fot(X_15))]]) ).
cnf(refute_0_7,plain,
( mult(mult(X_13,X_14),mult(X_15,X_13)) != mult(X_13,mult(mult(X_14,X_15),X_13))
| rd(mult(mult(X_13,X_14),mult(X_15,X_13)),mult(X_15,X_13)) != mult(X_13,X_14)
| rd(mult(X_13,mult(mult(X_14,X_15),X_13)),mult(X_15,X_13)) = mult(X_13,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(mult(X_13,X_14),mult(X_15,X_13)),mult(X_15,X_13)),mult(X_13,X_14)) ),[0,0],$fot(mult(X_13,mult(mult(X_14,X_15),X_13)))]]) ).
cnf(refute_0_8,plain,
( rd(mult(mult(X_13,X_14),mult(X_15,X_13)),mult(X_15,X_13)) != mult(X_13,X_14)
| rd(mult(X_13,mult(mult(X_14,X_15),X_13)),mult(X_15,X_13)) = mult(X_13,X_14) ),
inference(resolve,[$cnf( $equal(mult(mult(X_13,X_14),mult(X_15,X_13)),mult(X_13,mult(mult(X_14,X_15),X_13))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
rd(mult(X_13,mult(mult(X_14,X_15),X_13)),mult(X_15,X_13)) = mult(X_13,X_14),
inference(resolve,[$cnf( $equal(rd(mult(mult(X_13,X_14),mult(X_15,X_13)),mult(X_15,X_13)),mult(X_13,X_14)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
rd(mult(X_19,mult(mult(rd(A,X_21),X_21),X_19)),mult(X_21,X_19)) = mult(X_19,rd(A,X_21)),
inference(subst,[],[refute_0_9:[bind(X_13,$fot(X_19)),bind(X_14,$fot(rd(A,X_21))),bind(X_15,$fot(X_21))]]) ).
cnf(refute_0_11,plain,
mult(rd(A,B),B) = A,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_12,plain,
mult(rd(A,X_21),X_21) = A,
inference(subst,[],[refute_0_11:[bind(B,$fot(X_21))]]) ).
cnf(refute_0_13,plain,
( mult(rd(A,X_21),X_21) != A
| rd(mult(X_19,mult(mult(rd(A,X_21),X_21),X_19)),mult(X_21,X_19)) != mult(X_19,rd(A,X_21))
| rd(mult(X_19,mult(A,X_19)),mult(X_21,X_19)) = mult(X_19,rd(A,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(X_19,mult(mult(rd(A,X_21),X_21),X_19)),mult(X_21,X_19)),mult(X_19,rd(A,X_21))) ),[0,0,1,0],$fot(A)]]) ).
cnf(refute_0_14,plain,
( rd(mult(X_19,mult(mult(rd(A,X_21),X_21),X_19)),mult(X_21,X_19)) != mult(X_19,rd(A,X_21))
| rd(mult(X_19,mult(A,X_19)),mult(X_21,X_19)) = mult(X_19,rd(A,X_21)) ),
inference(resolve,[$cnf( $equal(mult(rd(A,X_21),X_21),A) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
rd(mult(X_19,mult(A,X_19)),mult(X_21,X_19)) = mult(X_19,rd(A,X_21)),
inference(resolve,[$cnf( $equal(rd(mult(X_19,mult(mult(rd(A,X_21),X_21),X_19)),mult(X_21,X_19)),mult(X_19,rd(A,X_21))) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
rd(mult(A,mult(X_40,A)),mult(X_40,A)) = mult(A,rd(X_40,X_40)),
inference(subst,[],[refute_0_15:[bind(A,$fot(X_40)),bind(X_19,$fot(A)),bind(X_21,$fot(X_40))]]) ).
cnf(refute_0_17,plain,
( rd(mult(A,mult(X_40,A)),mult(X_40,A)) != A
| rd(mult(A,mult(X_40,A)),mult(X_40,A)) != mult(A,rd(X_40,X_40))
| mult(A,rd(X_40,X_40)) = A ),
introduced(tautology,[equality,[$cnf( $equal(rd(mult(A,mult(X_40,A)),mult(X_40,A)),A) ),[0],$fot(mult(A,rd(X_40,X_40)))]]) ).
cnf(refute_0_18,plain,
( rd(mult(A,mult(X_40,A)),mult(X_40,A)) != A
| mult(A,rd(X_40,X_40)) = A ),
inference(resolve,[$cnf( $equal(rd(mult(A,mult(X_40,A)),mult(X_40,A)),mult(A,rd(X_40,X_40))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
mult(A,rd(X_40,X_40)) = A,
inference(resolve,[$cnf( $equal(rd(mult(A,mult(X_40,A)),mult(X_40,A)),A) )],[refute_0_3,refute_0_18]) ).
cnf(refute_0_20,plain,
ld(A,mult(A,B)) = B,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_21,plain,
ld(A,mult(A,rd(X_44,X_44))) = rd(X_44,X_44),
inference(subst,[],[refute_0_20:[bind(B,$fot(rd(X_44,X_44)))]]) ).
cnf(refute_0_22,plain,
mult(A,rd(X_44,X_44)) = A,
inference(subst,[],[refute_0_19:[bind(X_40,$fot(X_44))]]) ).
cnf(refute_0_23,plain,
( ld(A,mult(A,rd(X_44,X_44))) != rd(X_44,X_44)
| mult(A,rd(X_44,X_44)) != A
| ld(A,A) = rd(X_44,X_44) ),
introduced(tautology,[equality,[$cnf( $equal(ld(A,mult(A,rd(X_44,X_44))),rd(X_44,X_44)) ),[0,1],$fot(A)]]) ).
cnf(refute_0_24,plain,
( ld(A,mult(A,rd(X_44,X_44))) != rd(X_44,X_44)
| ld(A,A) = rd(X_44,X_44) ),
inference(resolve,[$cnf( $equal(mult(A,rd(X_44,X_44)),A) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
ld(A,A) = rd(X_44,X_44),
inference(resolve,[$cnf( $equal(ld(A,mult(A,rd(X_44,X_44))),rd(X_44,X_44)) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
ld(X_47,X_47) = rd(X_40,X_40),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_47)),bind(X_44,$fot(X_40))]]) ).
cnf(refute_0_27,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_28,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_29,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( ld(X_47,X_47) != rd(X_40,X_40)
| rd(X_40,X_40) = ld(X_47,X_47) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(ld(X_47,X_47))),bind(Y,$fot(rd(X_40,X_40)))]]) ).
cnf(refute_0_31,plain,
rd(X_40,X_40) = ld(X_47,X_47),
inference(resolve,[$cnf( $equal(ld(X_47,X_47),rd(X_40,X_40)) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
( mult(A,rd(X_40,X_40)) != A
| rd(X_40,X_40) != ld(X_47,X_47)
| mult(A,ld(X_47,X_47)) = A ),
introduced(tautology,[equality,[$cnf( $equal(mult(A,rd(X_40,X_40)),A) ),[0,1],$fot(ld(X_47,X_47))]]) ).
cnf(refute_0_33,plain,
( mult(A,rd(X_40,X_40)) != A
| mult(A,ld(X_47,X_47)) = A ),
inference(resolve,[$cnf( $equal(rd(X_40,X_40),ld(X_47,X_47)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
mult(A,ld(X_47,X_47)) = A,
inference(resolve,[$cnf( $equal(mult(A,rd(X_40,X_40)),A) )],[refute_0_19,refute_0_33]) ).
cnf(refute_0_35,plain,
mult(skolemFOFtoCNF_X1_1(ld(X_60,X_60)),ld(X_60,X_60)) = skolemFOFtoCNF_X1_1(ld(X_60,X_60)),
inference(subst,[],[refute_0_34:[bind(A,$fot(skolemFOFtoCNF_X1_1(ld(X_60,X_60)))),bind(X_47,$fot(X_60))]]) ).
cnf(refute_0_36,plain,
( mult(skolemFOFtoCNF_X1_1(ld(X_60,X_60)),ld(X_60,X_60)) != skolemFOFtoCNF_X1_1(ld(X_60,X_60))
| skolemFOFtoCNF_X1_1(ld(X_60,X_60)) != skolemFOFtoCNF_X1_1(ld(X_60,X_60))
| mult(skolemFOFtoCNF_X1_1(ld(X_60,X_60)),ld(X_60,X_60)) = skolemFOFtoCNF_X1_1(ld(X_60,X_60)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(skolemFOFtoCNF_X1_1(ld(X_60,X_60)),ld(X_60,X_60)),skolemFOFtoCNF_X1_1(ld(X_60,X_60))) ),[0],$fot(skolemFOFtoCNF_X1_1(ld(X_60,X_60)))]]) ).
cnf(refute_0_37,plain,
( skolemFOFtoCNF_X1_1(ld(X_60,X_60)) != skolemFOFtoCNF_X1_1(ld(X_60,X_60))
| mult(skolemFOFtoCNF_X1_1(ld(X_60,X_60)),ld(X_60,X_60)) = skolemFOFtoCNF_X1_1(ld(X_60,X_60)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X1_1(ld(X_60,X_60)),ld(X_60,X_60)),skolemFOFtoCNF_X1_1(ld(X_60,X_60))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( mult(ld(X_60,X_60),skolemFOFtoCNF_X1(ld(X_60,X_60))) != skolemFOFtoCNF_X1(ld(X_60,X_60))
| skolemFOFtoCNF_X1_1(ld(X_60,X_60)) != skolemFOFtoCNF_X1_1(ld(X_60,X_60)) ),
inference(resolve,[$cnf( $equal(mult(skolemFOFtoCNF_X1_1(ld(X_60,X_60)),ld(X_60,X_60)),skolemFOFtoCNF_X1_1(ld(X_60,X_60))) )],[refute_0_37,refute_0_1]) ).
cnf(refute_0_39,plain,
skolemFOFtoCNF_X1_1(ld(X_60,X_60)) = skolemFOFtoCNF_X1_1(ld(X_60,X_60)),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X1_1(ld(X_60,X_60)))]]) ).
cnf(refute_0_40,plain,
mult(ld(X_60,X_60),skolemFOFtoCNF_X1(ld(X_60,X_60))) != skolemFOFtoCNF_X1(ld(X_60,X_60)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1_1(ld(X_60,X_60)),skolemFOFtoCNF_X1_1(ld(X_60,X_60))) )],[refute_0_39,refute_0_38]) ).
cnf(refute_0_41,plain,
mult(rd(B,B),B) = B,
inference(subst,[],[refute_0_11:[bind(A,$fot(B))]]) ).
cnf(refute_0_42,plain,
ld(X_47,X_47) = rd(B,B),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_47)),bind(X_44,$fot(B))]]) ).
cnf(refute_0_43,plain,
( ld(X_47,X_47) != rd(B,B)
| rd(B,B) = ld(X_47,X_47) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(ld(X_47,X_47))),bind(Y,$fot(rd(B,B)))]]) ).
cnf(refute_0_44,plain,
rd(B,B) = ld(X_47,X_47),
inference(resolve,[$cnf( $equal(ld(X_47,X_47),rd(B,B)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( mult(rd(B,B),B) != B
| rd(B,B) != ld(X_47,X_47)
| mult(ld(X_47,X_47),B) = B ),
introduced(tautology,[equality,[$cnf( $equal(mult(rd(B,B),B),B) ),[0,0],$fot(ld(X_47,X_47))]]) ).
cnf(refute_0_46,plain,
( mult(rd(B,B),B) != B
| mult(ld(X_47,X_47),B) = B ),
inference(resolve,[$cnf( $equal(rd(B,B),ld(X_47,X_47)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
mult(ld(X_47,X_47),B) = B,
inference(resolve,[$cnf( $equal(mult(rd(B,B),B),B) )],[refute_0_41,refute_0_46]) ).
cnf(refute_0_48,plain,
mult(ld(X_60,X_60),skolemFOFtoCNF_X1(ld(X_60,X_60))) = skolemFOFtoCNF_X1(ld(X_60,X_60)),
inference(subst,[],[refute_0_47:[bind(B,$fot(skolemFOFtoCNF_X1(ld(X_60,X_60)))),bind(X_47,$fot(X_60))]]) ).
cnf(refute_0_49,plain,
( mult(ld(X_60,X_60),skolemFOFtoCNF_X1(ld(X_60,X_60))) != skolemFOFtoCNF_X1(ld(X_60,X_60))
| skolemFOFtoCNF_X1(ld(X_60,X_60)) != skolemFOFtoCNF_X1(ld(X_60,X_60))
| mult(ld(X_60,X_60),skolemFOFtoCNF_X1(ld(X_60,X_60))) = skolemFOFtoCNF_X1(ld(X_60,X_60)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(ld(X_60,X_60),skolemFOFtoCNF_X1(ld(X_60,X_60))),skolemFOFtoCNF_X1(ld(X_60,X_60))) ),[0],$fot(skolemFOFtoCNF_X1(ld(X_60,X_60)))]]) ).
cnf(refute_0_50,plain,
( skolemFOFtoCNF_X1(ld(X_60,X_60)) != skolemFOFtoCNF_X1(ld(X_60,X_60))
| mult(ld(X_60,X_60),skolemFOFtoCNF_X1(ld(X_60,X_60))) = skolemFOFtoCNF_X1(ld(X_60,X_60)) ),
inference(resolve,[$cnf( $equal(mult(ld(X_60,X_60),skolemFOFtoCNF_X1(ld(X_60,X_60))),skolemFOFtoCNF_X1(ld(X_60,X_60))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
skolemFOFtoCNF_X1(ld(X_60,X_60)) != skolemFOFtoCNF_X1(ld(X_60,X_60)),
inference(resolve,[$cnf( $equal(mult(ld(X_60,X_60),skolemFOFtoCNF_X1(ld(X_60,X_60))),skolemFOFtoCNF_X1(ld(X_60,X_60))) )],[refute_0_50,refute_0_40]) ).
cnf(refute_0_52,plain,
skolemFOFtoCNF_X1(ld(X_60,X_60)) = skolemFOFtoCNF_X1(ld(X_60,X_60)),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X1(ld(X_60,X_60)))]]) ).
cnf(refute_0_53,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1(ld(X_60,X_60)),skolemFOFtoCNF_X1(ld(X_60,X_60))) )],[refute_0_52,refute_0_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP657+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n029.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 : Mon Jun 13 16:43:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43
% 0.18/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.44
%------------------------------------------------------------------------------