TSTP Solution File: HWV023-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HWV023-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 18:29:44 EDT 2022
% Result : Unsatisfiable 219.96s 220.13s
% Output : CNFRefutation 219.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 27
% Syntax : Number of clauses : 68 ( 28 unt; 13 nHn; 56 RR)
% Number of literals : 137 ( 81 equ; 57 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_2,axiom,
gt(plus(X_1,n1),n0) ).
cnf(axiom_5,axiom,
( minus(X_3,Y_4) = Z_5
| plus(Z_5,Y_4) != X_3
| def_10(Y_4,X_3) ) ).
cnf(axiom_7,axiom,
( ~ def_10(Y_4,X_3)
| X_3 != Y_4 ) ).
cnf(axiom_19,axiom,
plus(n0,X_31) = X_31 ).
cnf(axiom_21,axiom,
level(X_t_32) = int_level(X_t_32) ).
cnf(axiom_24,axiom,
( int_level(X_t_35) != n0
| p_Empty(X_t_35) ) ).
cnf(axiom_71,axiom,
( p_Reset(X_t_42)
| p_Wr(X_t_42)
| ~ p_Rd(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ).
cnf(quest_1,negated_conjecture,
level(t_139) = n1 ).
cnf(quest_2,negated_conjecture,
~ p_Wr(t_139) ).
cnf(quest_3,negated_conjecture,
p_Rd(t_139) ).
cnf(quest_4,negated_conjecture,
~ p_Reset(t_139) ).
cnf(quest_5,negated_conjecture,
~ p_Empty(plus(t_139,n1)) ).
cnf(refute_0_0,plain,
( int_level(plus(t_139,n1)) != n0
| p_Empty(plus(t_139,n1)) ),
inference(subst,[],[axiom_24:[bind(X_t_35,$fot(plus(t_139,n1)))]]) ).
cnf(refute_0_1,plain,
( ~ gt(int_level(t_139),n0)
| ~ p_Rd(t_139)
| int_level(plus(t_139,n1)) = minus(int_level(t_139),n1)
| p_Reset(t_139)
| p_Wr(t_139) ),
inference(subst,[],[axiom_71:[bind(X_t_42,$fot(t_139))]]) ).
cnf(refute_0_2,plain,
level(t_139) = int_level(t_139),
inference(subst,[],[axiom_21:[bind(X_t_32,$fot(t_139))]]) ).
cnf(refute_0_3,plain,
( level(t_139) != int_level(t_139)
| level(t_139) != n1
| int_level(t_139) = n1 ),
introduced(tautology,[equality,[$cnf( $equal(level(t_139),n1) ),[0],$fot(int_level(t_139))]]) ).
cnf(refute_0_4,plain,
( level(t_139) != n1
| int_level(t_139) = n1 ),
inference(resolve,[$cnf( $equal(level(t_139),int_level(t_139)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
int_level(t_139) = n1,
inference(resolve,[$cnf( $equal(level(t_139),n1) )],[quest_1,refute_0_4]) ).
cnf(refute_0_6,plain,
( int_level(t_139) != n1
| ~ gt(n1,n0)
| gt(int_level(t_139),n0) ),
introduced(tautology,[equality,[$cnf( ~ gt(int_level(t_139),n0) ),[0],$fot(n1)]]) ).
cnf(refute_0_7,plain,
( ~ gt(n1,n0)
| gt(int_level(t_139),n0) ),
inference(resolve,[$cnf( $equal(int_level(t_139),n1) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ gt(n1,n0)
| ~ p_Rd(t_139)
| int_level(plus(t_139,n1)) = minus(int_level(t_139),n1)
| p_Reset(t_139)
| p_Wr(t_139) ),
inference(resolve,[$cnf( gt(int_level(t_139),n0) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
( plus(Z_5,Y_4) != plus(Z_5,Y_4)
| minus(plus(Z_5,Y_4),Y_4) = Z_5
| def_10(Y_4,plus(Z_5,Y_4)) ),
inference(subst,[],[axiom_5:[bind(X_3,$fot(plus(Z_5,Y_4)))]]) ).
cnf(refute_0_10,plain,
plus(Z_5,Y_4) = plus(Z_5,Y_4),
introduced(tautology,[refl,[$fot(plus(Z_5,Y_4))]]) ).
cnf(refute_0_11,plain,
( minus(plus(Z_5,Y_4),Y_4) = Z_5
| def_10(Y_4,plus(Z_5,Y_4)) ),
inference(resolve,[$cnf( $equal(plus(Z_5,Y_4),plus(Z_5,Y_4)) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
( minus(plus(n0,X_87),X_87) = n0
| def_10(X_87,plus(n0,X_87)) ),
inference(subst,[],[refute_0_11:[bind(Y_4,$fot(X_87)),bind(Z_5,$fot(n0))]]) ).
cnf(refute_0_13,plain,
plus(n0,X_87) = X_87,
inference(subst,[],[axiom_19:[bind(X_31,$fot(X_87))]]) ).
cnf(refute_0_14,plain,
( minus(plus(n0,X_87),X_87) != n0
| plus(n0,X_87) != X_87
| minus(X_87,X_87) = n0 ),
introduced(tautology,[equality,[$cnf( $equal(minus(plus(n0,X_87),X_87),n0) ),[0,0],$fot(X_87)]]) ).
cnf(refute_0_15,plain,
( minus(plus(n0,X_87),X_87) != n0
| minus(X_87,X_87) = n0 ),
inference(resolve,[$cnf( $equal(plus(n0,X_87),X_87) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( minus(X_87,X_87) = n0
| def_10(X_87,plus(n0,X_87)) ),
inference(resolve,[$cnf( $equal(minus(plus(n0,X_87),X_87),n0) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
( plus(n0,X_87) != X_87
| ~ def_10(X_87,plus(n0,X_87))
| def_10(X_87,X_87) ),
introduced(tautology,[equality,[$cnf( def_10(X_87,plus(n0,X_87)) ),[1],$fot(X_87)]]) ).
cnf(refute_0_18,plain,
( ~ def_10(X_87,plus(n0,X_87))
| def_10(X_87,X_87) ),
inference(resolve,[$cnf( $equal(plus(n0,X_87),X_87) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( minus(X_87,X_87) = n0
| def_10(X_87,X_87) ),
inference(resolve,[$cnf( def_10(X_87,plus(n0,X_87)) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
( Y_4 != Y_4
| ~ def_10(Y_4,Y_4) ),
inference(subst,[],[axiom_7:[bind(X_3,$fot(Y_4))]]) ).
cnf(refute_0_21,plain,
Y_4 = Y_4,
introduced(tautology,[refl,[$fot(Y_4)]]) ).
cnf(refute_0_22,plain,
~ def_10(Y_4,Y_4),
inference(resolve,[$cnf( $equal(Y_4,Y_4) )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
~ def_10(X_87,X_87),
inference(subst,[],[refute_0_22:[bind(Y_4,$fot(X_87))]]) ).
cnf(refute_0_24,plain,
minus(X_87,X_87) = n0,
inference(resolve,[$cnf( def_10(X_87,X_87) )],[refute_0_19,refute_0_23]) ).
cnf(refute_0_25,plain,
minus(n1,n1) = n0,
inference(subst,[],[refute_0_24:[bind(X_87,$fot(n1))]]) ).
cnf(refute_0_26,plain,
minus(int_level(t_139),n1) = minus(int_level(t_139),n1),
introduced(tautology,[refl,[$fot(minus(int_level(t_139),n1))]]) ).
cnf(refute_0_27,plain,
( int_level(t_139) != n1
| minus(int_level(t_139),n1) != minus(int_level(t_139),n1)
| minus(int_level(t_139),n1) = minus(n1,n1) ),
introduced(tautology,[equality,[$cnf( $equal(minus(int_level(t_139),n1),minus(int_level(t_139),n1)) ),[1,0],$fot(n1)]]) ).
cnf(refute_0_28,plain,
( int_level(t_139) != n1
| minus(int_level(t_139),n1) = minus(n1,n1) ),
inference(resolve,[$cnf( $equal(minus(int_level(t_139),n1),minus(int_level(t_139),n1)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
minus(int_level(t_139),n1) = minus(n1,n1),
inference(resolve,[$cnf( $equal(int_level(t_139),n1) )],[refute_0_5,refute_0_28]) ).
cnf(refute_0_30,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_31,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_32,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_34,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( minus(int_level(t_139),n1) != minus(n1,n1)
| minus(n1,n1) != n0
| minus(int_level(t_139),n1) = n0 ),
inference(subst,[],[refute_0_34:[bind(X,$fot(minus(int_level(t_139),n1))),bind(Y,$fot(minus(n1,n1))),bind(Z,$fot(n0))]]) ).
cnf(refute_0_36,plain,
( minus(n1,n1) != n0
| minus(int_level(t_139),n1) = n0 ),
inference(resolve,[$cnf( $equal(minus(int_level(t_139),n1),minus(n1,n1)) )],[refute_0_29,refute_0_35]) ).
cnf(refute_0_37,plain,
minus(int_level(t_139),n1) = n0,
inference(resolve,[$cnf( $equal(minus(n1,n1),n0) )],[refute_0_25,refute_0_36]) ).
cnf(refute_0_38,plain,
( int_level(plus(t_139,n1)) != minus(int_level(t_139),n1)
| minus(int_level(t_139),n1) != n0
| int_level(plus(t_139,n1)) = n0 ),
introduced(tautology,[equality,[$cnf( ~ $equal(int_level(plus(t_139,n1)),n0) ),[0],$fot(minus(int_level(t_139),n1))]]) ).
cnf(refute_0_39,plain,
( int_level(plus(t_139,n1)) != minus(int_level(t_139),n1)
| int_level(plus(t_139,n1)) = n0 ),
inference(resolve,[$cnf( $equal(minus(int_level(t_139),n1),n0) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ gt(n1,n0)
| ~ p_Rd(t_139)
| int_level(plus(t_139,n1)) = n0
| p_Reset(t_139)
| p_Wr(t_139) ),
inference(resolve,[$cnf( $equal(int_level(plus(t_139,n1)),minus(int_level(t_139),n1)) )],[refute_0_8,refute_0_39]) ).
cnf(refute_0_41,plain,
gt(plus(n0,n1),n0),
inference(subst,[],[axiom_2:[bind(X_1,$fot(n0))]]) ).
cnf(refute_0_42,plain,
plus(n0,n1) = n1,
inference(subst,[],[axiom_19:[bind(X_31,$fot(n1))]]) ).
cnf(refute_0_43,plain,
( plus(n0,n1) != n1
| ~ gt(plus(n0,n1),n0)
| gt(n1,n0) ),
introduced(tautology,[equality,[$cnf( gt(plus(n0,n1),n0) ),[0],$fot(n1)]]) ).
cnf(refute_0_44,plain,
( ~ gt(plus(n0,n1),n0)
| gt(n1,n0) ),
inference(resolve,[$cnf( $equal(plus(n0,n1),n1) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
gt(n1,n0),
inference(resolve,[$cnf( gt(plus(n0,n1),n0) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ p_Rd(t_139)
| int_level(plus(t_139,n1)) = n0
| p_Reset(t_139)
| p_Wr(t_139) ),
inference(resolve,[$cnf( gt(n1,n0) )],[refute_0_45,refute_0_40]) ).
cnf(refute_0_47,plain,
( int_level(plus(t_139,n1)) = n0
| p_Reset(t_139)
| p_Wr(t_139) ),
inference(resolve,[$cnf( p_Rd(t_139) )],[quest_3,refute_0_46]) ).
cnf(refute_0_48,plain,
( int_level(plus(t_139,n1)) = n0
| p_Wr(t_139) ),
inference(resolve,[$cnf( p_Reset(t_139) )],[refute_0_47,quest_4]) ).
cnf(refute_0_49,plain,
int_level(plus(t_139,n1)) = n0,
inference(resolve,[$cnf( p_Wr(t_139) )],[refute_0_48,quest_2]) ).
cnf(refute_0_50,plain,
( int_level(plus(t_139,n1)) != n0
| n0 != n0
| int_level(plus(t_139,n1)) = n0 ),
introduced(tautology,[equality,[$cnf( ~ $equal(int_level(plus(t_139,n1)),n0) ),[0],$fot(n0)]]) ).
cnf(refute_0_51,plain,
( n0 != n0
| int_level(plus(t_139,n1)) = n0 ),
inference(resolve,[$cnf( $equal(int_level(plus(t_139,n1)),n0) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( n0 != n0
| p_Empty(plus(t_139,n1)) ),
inference(resolve,[$cnf( $equal(int_level(plus(t_139,n1)),n0) )],[refute_0_51,refute_0_0]) ).
cnf(refute_0_53,plain,
n0 = n0,
introduced(tautology,[refl,[$fot(n0)]]) ).
cnf(refute_0_54,plain,
p_Empty(plus(t_139,n1)),
inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_53,refute_0_52]) ).
cnf(refute_0_55,plain,
$false,
inference(resolve,[$cnf( p_Empty(plus(t_139,n1)) )],[refute_0_54,quest_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : HWV023-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jun 16 22:50:41 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 219.96/220.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 219.96/220.13
% 219.96/220.13 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 219.96/220.13
%------------------------------------------------------------------------------