TSTP Solution File: SWC256-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWC256-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 21:27:22 EDT 2022
% Result : Unsatisfiable 1.03s 1.20s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of clauses : 49 ( 15 unt; 10 nHn; 46 RR)
% Number of literals : 101 ( 49 equ; 48 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause86,axiom,
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ).
cnf(clause115,axiom,
( U != V
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ) ).
cnf(clause116,axiom,
( cons(U,nil) != V
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) ) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4 ).
cnf(co1_6,negated_conjecture,
sk1 = sk3 ).
cnf(co1_7,negated_conjecture,
neq(sk2,nil) ).
cnf(co1_8,negated_conjecture,
~ singletonP(sk1) ).
cnf(co1_9,negated_conjecture,
( ssItem(sk5)
| nil = sk4 ) ).
cnf(co1_11,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk4 ) ).
cnf(refute_0_0,plain,
( V != V
| ~ neq(V,V)
| ~ ssList(V) ),
inference(subst,[],[clause115:[bind(U,$fot(V))]]) ).
cnf(refute_0_1,plain,
V = V,
introduced(tautology,[refl,[$fot(V)]]) ).
cnf(refute_0_2,plain,
( ~ neq(V,V)
| ~ ssList(V) ),
inference(resolve,[$cnf( $equal(V,V) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( ~ neq(nil,nil)
| ~ ssList(nil) ),
inference(subst,[],[refute_0_2:[bind(V,$fot(nil))]]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_5,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_6,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( sk2 != sk4
| sk4 = sk2 ),
inference(subst,[],[refute_0_6:[bind(X,$fot(sk2)),bind(Y,$fot(sk4))]]) ).
cnf(refute_0_8,plain,
sk4 = sk2,
inference(resolve,[$cnf( $equal(sk2,sk4) )],[co1_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( nil != sk4
| sk4 != sk2
| nil = sk2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(nil,sk2) ),[0],$fot(sk4)]]) ).
cnf(refute_0_10,plain,
( nil != sk4
| nil = sk2 ),
inference(resolve,[$cnf( $equal(sk4,sk2) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( nil = sk2
| ssItem(sk5) ),
inference(resolve,[$cnf( $equal(nil,sk4) )],[co1_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ ssItem(X_754)
| ~ ssList(nil)
| ssList(cons(X_754,nil)) ),
inference(subst,[],[clause86:[bind(U,$fot(X_754)),bind(V,$fot(nil))]]) ).
cnf(refute_0_13,plain,
( ~ ssItem(X_754)
| ssList(cons(X_754,nil)) ),
inference(resolve,[$cnf( ssList(nil) )],[clause8,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ ssItem(sk5)
| ssList(cons(sk5,nil)) ),
inference(subst,[],[refute_0_13:[bind(X_754,$fot(sk5))]]) ).
cnf(refute_0_15,plain,
( nil = sk2
| ssList(cons(sk5,nil)) ),
inference(resolve,[$cnf( ssItem(sk5) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( cons(U,nil) != cons(U,nil)
| ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) ),
inference(subst,[],[clause116:[bind(V,$fot(cons(U,nil)))]]) ).
cnf(refute_0_17,plain,
cons(U,nil) = cons(U,nil),
introduced(tautology,[refl,[$fot(cons(U,nil))]]) ).
cnf(refute_0_18,plain,
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) ),
inference(resolve,[$cnf( $equal(cons(U,nil),cons(U,nil)) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
( ~ ssItem(sk5)
| ~ ssList(cons(sk5,nil))
| singletonP(cons(sk5,nil)) ),
inference(subst,[],[refute_0_18:[bind(U,$fot(sk5))]]) ).
cnf(refute_0_20,plain,
( ~ ssItem(sk5)
| nil = sk2
| singletonP(cons(sk5,nil)) ),
inference(resolve,[$cnf( ssList(cons(sk5,nil)) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
( nil = sk2
| singletonP(cons(sk5,nil)) ),
inference(resolve,[$cnf( ssItem(sk5) )],[refute_0_11,refute_0_20]) ).
cnf(refute_0_22,plain,
( sk1 != sk3
| sk3 = sk1 ),
inference(subst,[],[refute_0_6:[bind(X,$fot(sk1)),bind(Y,$fot(sk3))]]) ).
cnf(refute_0_23,plain,
sk3 = sk1,
inference(resolve,[$cnf( $equal(sk1,sk3) )],[co1_6,refute_0_22]) ).
cnf(refute_0_24,plain,
( cons(sk5,nil) != sk3
| sk3 != sk1
| cons(sk5,nil) = sk1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(cons(sk5,nil),sk1) ),[0],$fot(sk3)]]) ).
cnf(refute_0_25,plain,
( cons(sk5,nil) != sk3
| cons(sk5,nil) = sk1 ),
inference(resolve,[$cnf( $equal(sk3,sk1) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( cons(sk5,nil) = sk1
| nil = sk4 ),
inference(resolve,[$cnf( $equal(cons(sk5,nil),sk3) )],[co1_11,refute_0_25]) ).
cnf(refute_0_27,plain,
( cons(sk5,nil) = sk1
| nil = sk2 ),
inference(resolve,[$cnf( $equal(nil,sk4) )],[refute_0_26,refute_0_10]) ).
cnf(refute_0_28,plain,
( cons(sk5,nil) != sk1
| ~ singletonP(cons(sk5,nil))
| singletonP(sk1) ),
introduced(tautology,[equality,[$cnf( singletonP(cons(sk5,nil)) ),[0],$fot(sk1)]]) ).
cnf(refute_0_29,plain,
( ~ singletonP(cons(sk5,nil))
| nil = sk2
| singletonP(sk1) ),
inference(resolve,[$cnf( $equal(cons(sk5,nil),sk1) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( nil = sk2
| singletonP(sk1) ),
inference(resolve,[$cnf( singletonP(cons(sk5,nil)) )],[refute_0_21,refute_0_29]) ).
cnf(refute_0_31,plain,
nil = sk2,
inference(resolve,[$cnf( singletonP(sk1) )],[refute_0_30,co1_8]) ).
cnf(refute_0_32,plain,
( nil != sk2
| sk2 = nil ),
inference(subst,[],[refute_0_6:[bind(X,$fot(nil)),bind(Y,$fot(sk2))]]) ).
cnf(refute_0_33,plain,
sk2 = nil,
inference(resolve,[$cnf( $equal(nil,sk2) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( sk2 != nil
| ~ neq(sk2,nil)
| neq(nil,nil) ),
introduced(tautology,[equality,[$cnf( neq(sk2,nil) ),[0],$fot(nil)]]) ).
cnf(refute_0_35,plain,
( ~ neq(sk2,nil)
| neq(nil,nil) ),
inference(resolve,[$cnf( $equal(sk2,nil) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
neq(nil,nil),
inference(resolve,[$cnf( neq(sk2,nil) )],[co1_7,refute_0_35]) ).
cnf(refute_0_37,plain,
~ ssList(nil),
inference(resolve,[$cnf( neq(nil,nil) )],[refute_0_36,refute_0_3]) ).
cnf(refute_0_38,plain,
$false,
inference(resolve,[$cnf( ssList(nil) )],[clause8,refute_0_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC256-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 12 15:31:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.03/1.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.03/1.20
% 1.03/1.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.03/1.20
%------------------------------------------------------------------------------