TSTP Solution File: SYN072-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN072-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 : Thu Jul 21 08:59:17 EDT 2022
% Result : Unsatisfiable 0.20s 0.39s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 20
% Syntax : Number of clauses : 68 ( 13 unt; 25 nHn; 60 RR)
% Number of literals : 151 ( 112 equ; 58 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_1,axiom,
( X = c
| X = d ) ).
cnf(clause_2,axiom,
big_p(a) ).
cnf(clause_3,axiom,
big_p(b) ).
cnf(clause_4,axiom,
a != b ).
cnf(prove_this,negated_conjecture,
~ big_p(e) ).
cnf(refute_0_0,plain,
( e = c
| e = d ),
inference(subst,[],[clause_1:[bind(X,$fot(e))]]) ).
cnf(refute_0_1,plain,
( e != d
| ~ big_p(d)
| big_p(e) ),
introduced(tautology,[equality,[$cnf( ~ big_p(e) ),[0],$fot(d)]]) ).
cnf(refute_0_2,plain,
( ~ big_p(d)
| e = c
| big_p(e) ),
inference(resolve,[$cnf( $equal(e,d) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ big_p(d)
| e = c ),
inference(resolve,[$cnf( big_p(e) )],[refute_0_2,prove_this]) ).
cnf(refute_0_4,plain,
( e != c
| ~ big_p(c)
| big_p(e) ),
introduced(tautology,[equality,[$cnf( ~ big_p(e) ),[0],$fot(c)]]) ).
cnf(refute_0_5,plain,
( ~ big_p(c)
| e = d
| big_p(e) ),
inference(resolve,[$cnf( $equal(e,c) )],[refute_0_0,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ big_p(c)
| e = d ),
inference(resolve,[$cnf( big_p(e) )],[refute_0_5,prove_this]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_0_9,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( X != c
| c = X ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(X)),bind(Y,$fot(c))]]) ).
cnf(refute_0_11,plain,
( X = d
| c = X ),
inference(resolve,[$cnf( $equal(X,c) )],[clause_1,refute_0_10]) ).
cnf(refute_0_12,plain,
( c != X
| ~ big_p(X)
| big_p(c) ),
introduced(tautology,[equality,[$cnf( ~ big_p(c) ),[0],$fot(X)]]) ).
cnf(refute_0_13,plain,
( ~ big_p(X)
| X = d
| big_p(c) ),
inference(resolve,[$cnf( $equal(c,X) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ big_p(X)
| X = d
| e = d ),
inference(resolve,[$cnf( big_p(c) )],[refute_0_13,refute_0_6]) ).
cnf(refute_0_15,plain,
( ~ big_p(b)
| b = d
| e = d ),
inference(subst,[],[refute_0_14:[bind(X,$fot(b))]]) ).
cnf(refute_0_16,plain,
( b = d
| e = d ),
inference(resolve,[$cnf( big_p(b) )],[clause_3,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ big_p(d)
| b = d
| big_p(e) ),
inference(resolve,[$cnf( $equal(e,d) )],[refute_0_16,refute_0_1]) ).
cnf(refute_0_18,plain,
( ~ big_p(d)
| b = d ),
inference(resolve,[$cnf( big_p(e) )],[refute_0_17,prove_this]) ).
cnf(refute_0_19,plain,
( X_0 = c
| X_0 = d ),
inference(subst,[],[clause_1:[bind(X,$fot(X_0))]]) ).
cnf(refute_0_20,plain,
( X_0 != c
| c = X_0 ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(X_0)),bind(Y,$fot(c))]]) ).
cnf(refute_0_21,plain,
( X_0 = d
| c = X_0 ),
inference(resolve,[$cnf( $equal(X_0,c) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( X != c
| c != X_0
| X = X_0 ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,X_0) ),[0],$fot(c)]]) ).
cnf(refute_0_23,plain,
( X != c
| X = X_0
| X_0 = d ),
inference(resolve,[$cnf( $equal(c,X_0) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( X = X_0
| X = d
| X_0 = d ),
inference(resolve,[$cnf( $equal(X,c) )],[clause_1,refute_0_23]) ).
cnf(refute_0_25,plain,
( X_4 = d
| a = X_4
| a = d ),
inference(subst,[],[refute_0_24:[bind(X,$fot(a)),bind(X_0,$fot(X_4))]]) ).
cnf(refute_0_26,plain,
( X_4 != b
| a != X_4
| a = b ),
introduced(tautology,[equality,[$cnf( $equal(a,X_4) ),[1],$fot(b)]]) ).
cnf(refute_0_27,plain,
( X_4 != b
| X_4 = d
| a = b
| a = d ),
inference(resolve,[$cnf( $equal(a,X_4) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( X_4 != b
| X_4 = d
| a = d ),
inference(resolve,[$cnf( $equal(a,b) )],[refute_0_27,clause_4]) ).
cnf(refute_0_29,plain,
( b != b
| a = d
| b = d ),
inference(subst,[],[refute_0_28:[bind(X_4,$fot(b))]]) ).
cnf(refute_0_30,plain,
b = b,
introduced(tautology,[refl,[$fot(b)]]) ).
cnf(refute_0_31,plain,
( a = d
| b = d ),
inference(resolve,[$cnf( $equal(b,b) )],[refute_0_30,refute_0_29]) ).
cnf(refute_0_32,plain,
( a != d
| d = a ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(a)),bind(Y,$fot(d))]]) ).
cnf(refute_0_33,plain,
( b = d
| d = a ),
inference(resolve,[$cnf( $equal(a,d) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( d != a
| ~ big_p(a)
| big_p(d) ),
introduced(tautology,[equality,[$cnf( ~ big_p(d) ),[0],$fot(a)]]) ).
cnf(refute_0_35,plain,
( ~ big_p(a)
| b = d
| big_p(d) ),
inference(resolve,[$cnf( $equal(d,a) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ big_p(a)
| b = d ),
inference(resolve,[$cnf( big_p(d) )],[refute_0_35,refute_0_18]) ).
cnf(refute_0_37,plain,
b = d,
inference(resolve,[$cnf( big_p(a) )],[clause_2,refute_0_36]) ).
cnf(refute_0_38,plain,
( b != d
| d = b ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(b)),bind(Y,$fot(d))]]) ).
cnf(refute_0_39,plain,
d = b,
inference(resolve,[$cnf( $equal(b,d) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( d != b
| ~ big_p(b)
| big_p(d) ),
introduced(tautology,[equality,[$cnf( ~ big_p(d) ),[0],$fot(b)]]) ).
cnf(refute_0_41,plain,
( ~ big_p(b)
| big_p(d) ),
inference(resolve,[$cnf( $equal(d,b) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ big_p(b)
| e = c ),
inference(resolve,[$cnf( big_p(d) )],[refute_0_41,refute_0_3]) ).
cnf(refute_0_43,plain,
e = c,
inference(resolve,[$cnf( big_p(b) )],[clause_3,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ big_p(a)
| a = d
| e = d ),
inference(subst,[],[refute_0_14:[bind(X,$fot(a))]]) ).
cnf(refute_0_45,plain,
( a = d
| e = d ),
inference(resolve,[$cnf( big_p(a) )],[clause_2,refute_0_44]) ).
cnf(refute_0_46,plain,
( a != d
| d != b
| a = b ),
introduced(tautology,[equality,[$cnf( ~ $equal(a,b) ),[0],$fot(d)]]) ).
cnf(refute_0_47,plain,
( a != d
| a = b ),
inference(resolve,[$cnf( $equal(d,b) )],[refute_0_39,refute_0_46]) ).
cnf(refute_0_48,plain,
( a = b
| e = d ),
inference(resolve,[$cnf( $equal(a,d) )],[refute_0_45,refute_0_47]) ).
cnf(refute_0_49,plain,
( e != c
| e != d
| c = d ),
introduced(tautology,[equality,[$cnf( $equal(e,d) ),[0],$fot(c)]]) ).
cnf(refute_0_50,plain,
( e != d
| c = d ),
inference(resolve,[$cnf( $equal(e,c) )],[refute_0_43,refute_0_49]) ).
cnf(refute_0_51,plain,
( c != d
| d != b
| c = b ),
introduced(tautology,[equality,[$cnf( ~ $equal(c,b) ),[0],$fot(d)]]) ).
cnf(refute_0_52,plain,
( c != d
| c = b ),
inference(resolve,[$cnf( $equal(d,b) )],[refute_0_39,refute_0_51]) ).
cnf(refute_0_53,plain,
( e != d
| c = b ),
inference(resolve,[$cnf( $equal(c,d) )],[refute_0_50,refute_0_52]) ).
cnf(refute_0_54,plain,
( a = b
| c = b ),
inference(resolve,[$cnf( $equal(e,d) )],[refute_0_48,refute_0_53]) ).
cnf(refute_0_55,plain,
c = b,
inference(resolve,[$cnf( $equal(a,b) )],[refute_0_54,clause_4]) ).
cnf(refute_0_56,plain,
( c != b
| e != c
| e = b ),
introduced(tautology,[equality,[$cnf( $equal(e,c) ),[1],$fot(b)]]) ).
cnf(refute_0_57,plain,
( e != c
| e = b ),
inference(resolve,[$cnf( $equal(c,b) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
e = b,
inference(resolve,[$cnf( $equal(e,c) )],[refute_0_43,refute_0_57]) ).
cnf(refute_0_59,plain,
( e != b
| ~ big_p(b)
| big_p(e) ),
introduced(tautology,[equality,[$cnf( ~ big_p(e) ),[0],$fot(b)]]) ).
cnf(refute_0_60,plain,
( ~ big_p(b)
| big_p(e) ),
inference(resolve,[$cnf( $equal(e,b) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
~ big_p(b),
inference(resolve,[$cnf( big_p(e) )],[refute_0_60,prove_this]) ).
cnf(refute_0_62,plain,
$false,
inference(resolve,[$cnf( big_p(b) )],[clause_3,refute_0_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN072-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n012.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 : Tue Jul 12 04:08:12 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.39
% 0.20/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.39
%------------------------------------------------------------------------------