%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 : Mon Jul 18 12:24:02 EDT 2022
% Result : Unsatisfiable 7.27s 7.43s
% Output : CNFRefutation 7.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of clauses : 54 ( 29 unt; 0 nHn; 26 RR)
% Number of literals : 89 ( 0 equ; 36 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 143 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(reflexivity,axiom,
equalish(A,A) ).
cnf(transitivity,axiom,
( ~ equalish(A,B)
| ~ equalish(B,C)
| equalish(A,C) ) ).
cnf(commutativity_of_addition,axiom,
equalish(add(A,B),add(B,A)) ).
cnf(addition_inverts_subtraction1,axiom,
equalish(subtract(add(A,B),B),A) ).
cnf(addition_inverts_subtraction2,axiom,
equalish(A,subtract(add(A,B),B)) ).
cnf(commutativity1,axiom,
equalish(add(subtract(A,B),C),subtract(add(A,C),B)) ).
cnf(commutativity2,axiom,
equalish(subtract(add(A,B),C),add(subtract(A,C),B)) ).
cnf(add_substitution1,axiom,
( ~ equalish(A,B)
| ~ equalish(C,add(A,D))
| equalish(C,add(B,D)) ) ).
cnf(subtract_substitution1,axiom,
( ~ equalish(A,B)
| ~ equalish(C,subtract(A,D))
| equalish(C,subtract(B,D)) ) ).
cnf(prove_equation,negated_conjecture,
~ equalish(add(a,subtract(b,c)),add(subtract(a,c),b)) ).
cnf(refute_0_0,plain,
equalish(subtract(add(X_56,X_55),X_55),add(subtract(X_56,X_55),X_55)),
inference(subst,[],[commutativity2:[bind(A,$fot(X_56)),bind(B,$fot(X_55)),bind(C,$fot(X_55))]]) ).
cnf(refute_0_1,plain,
equalish(X_25,subtract(add(X_25,B),B)),
inference(subst,[],[addition_inverts_subtraction2:[bind(A,$fot(X_25))]]) ).
cnf(refute_0_2,plain,
( ~ equalish(X_25,subtract(add(X_25,B),B))
| ~ equalish(subtract(add(X_25,B),B),X_27)
| equalish(X_25,X_27) ),
inference(subst,[],[transitivity:[bind(A,$fot(X_25)),bind(B,$fot(subtract(add(X_25,B),B))),bind(C,$fot(X_27))]]) ).
cnf(refute_0_3,plain,
( ~ equalish(subtract(add(X_25,B),B),X_27)
| equalish(X_25,X_27) ),
inference(resolve,[$cnf( equalish(X_25,subtract(add(X_25,B),B)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ equalish(subtract(add(X_56,X_55),X_55),add(subtract(X_56,X_55),X_55))
| equalish(X_56,add(subtract(X_56,X_55),X_55)) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(X_55)),bind(X_25,$fot(X_56)),bind(X_27,$fot(add(subtract(X_56,X_55),X_55)))]]) ).
cnf(refute_0_5,plain,
equalish(X_56,add(subtract(X_56,X_55),X_55)),
inference(resolve,[$cnf( equalish(subtract(add(X_56,X_55),X_55),add(subtract(X_56,X_55),X_55)) )],[refute_0_0,refute_0_4]) ).
cnf(refute_0_6,plain,
equalish(X_202,add(subtract(X_202,X_203),X_203)),
inference(subst,[],[refute_0_5:[bind(X_55,$fot(X_203)),bind(X_56,$fot(X_202))]]) ).
cnf(refute_0_7,plain,
( ~ equalish(X_202,add(subtract(X_202,X_203),X_203))
| ~ equalish(subtract(X_202,X_203),X_201)
| equalish(X_202,add(X_201,X_203)) ),
inference(subst,[],[add_substitution1:[bind(A,$fot(subtract(X_202,X_203))),bind(B,$fot(X_201)),bind(C,$fot(X_202)),bind(D,$fot(X_203))]]) ).
cnf(refute_0_8,plain,
( ~ equalish(subtract(X_202,X_203),X_201)
| equalish(X_202,add(X_201,X_203)) ),
inference(resolve,[$cnf( equalish(X_202,add(subtract(X_202,X_203),X_203)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ equalish(subtract(add(X_3573,subtract(X_3574,X_3572)),X_3574),subtract(X_3573,X_3572))
| equalish(add(X_3573,subtract(X_3574,X_3572)),add(subtract(X_3573,X_3572),X_3574)) ),
inference(subst,[],[refute_0_8:[bind(X_201,$fot(subtract(X_3573,X_3572))),bind(X_202,$fot(add(X_3573,subtract(X_3574,X_3572)))),bind(X_203,$fot(X_3574))]]) ).
cnf(refute_0_10,plain,
( ~ equalish(add(A,B),add(B,A))
| ~ equalish(add(B,A),X_27)
| equalish(add(A,B),X_27) ),
inference(subst,[],[transitivity:[bind(A,$fot(add(A,B))),bind(B,$fot(add(B,A))),bind(C,$fot(X_27))]]) ).
cnf(refute_0_11,plain,
( ~ equalish(add(B,A),X_27)
| equalish(add(A,B),X_27) ),
inference(resolve,[$cnf( equalish(add(A,B),add(B,A)) )],[commutativity_of_addition,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ equalish(add(subtract(X_2966,X_2967),subtract(X_2965,X_2966)),subtract(X_2965,X_2967))
| equalish(add(subtract(X_2965,X_2966),subtract(X_2966,X_2967)),subtract(X_2965,X_2967)) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(subtract(X_2965,X_2966))),bind(B,$fot(subtract(X_2966,X_2967))),bind(X_27,$fot(subtract(X_2965,X_2967)))]]) ).
cnf(refute_0_13,plain,
equalish(add(subtract(A,B),X_28),subtract(add(A,X_28),B)),
inference(subst,[],[commutativity1:[bind(C,$fot(X_28))]]) ).
cnf(refute_0_14,plain,
( ~ equalish(add(subtract(A,B),X_28),subtract(add(A,X_28),B))
| equalish(add(X_28,subtract(A,B)),subtract(add(A,X_28),B)) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(X_28)),bind(B,$fot(subtract(A,B))),bind(X_27,$fot(subtract(add(A,X_28),B)))]]) ).
cnf(refute_0_15,plain,
equalish(add(X_28,subtract(A,B)),subtract(add(A,X_28),B)),
inference(resolve,[$cnf( equalish(add(subtract(A,B),X_28),subtract(add(A,X_28),B)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
equalish(add(X_102,subtract(X_104,X_102)),subtract(add(X_104,X_102),X_102)),
inference(subst,[],[refute_0_15:[bind(A,$fot(X_104)),bind(B,$fot(X_102)),bind(X_28,$fot(X_102))]]) ).
cnf(refute_0_17,plain,
equalish(subtract(add(X_27,B),B),X_27),
inference(subst,[],[addition_inverts_subtraction1:[bind(A,$fot(X_27))]]) ).
cnf(refute_0_18,plain,
( ~ equalish(X_25,subtract(add(X_27,B),B))
| ~ equalish(subtract(add(X_27,B),B),X_27)
| equalish(X_25,X_27) ),
inference(subst,[],[transitivity:[bind(A,$fot(X_25)),bind(B,$fot(subtract(add(X_27,B),B))),bind(C,$fot(X_27))]]) ).
cnf(refute_0_19,plain,
( ~ equalish(X_25,subtract(add(X_27,B),B))
| equalish(X_25,X_27) ),
inference(resolve,[$cnf( equalish(subtract(add(X_27,B),B),X_27) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ equalish(add(X_102,subtract(X_104,X_102)),subtract(add(X_104,X_102),X_102))
| equalish(add(X_102,subtract(X_104,X_102)),X_104) ),
inference(subst,[],[refute_0_19:[bind(B,$fot(X_102)),bind(X_25,$fot(add(X_102,subtract(X_104,X_102)))),bind(X_27,$fot(X_104))]]) ).
cnf(refute_0_21,plain,
equalish(add(X_102,subtract(X_104,X_102)),X_104),
inference(resolve,[$cnf( equalish(add(X_102,subtract(X_104,X_102)),subtract(add(X_104,X_102),X_102)) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
equalish(add(X_102,subtract(X_256,X_102)),X_256),
inference(subst,[],[refute_0_21:[bind(X_104,$fot(X_256))]]) ).
cnf(refute_0_23,plain,
equalish(subtract(X_208,X_211),subtract(X_208,X_211)),
inference(subst,[],[reflexivity:[bind(A,$fot(subtract(X_208,X_211)))]]) ).
cnf(refute_0_24,plain,
( ~ equalish(X_208,X_209)
| ~ equalish(subtract(X_208,X_211),subtract(X_208,X_211))
| equalish(subtract(X_208,X_211),subtract(X_209,X_211)) ),
inference(subst,[],[subtract_substitution1:[bind(A,$fot(X_208)),bind(B,$fot(X_209)),bind(C,$fot(subtract(X_208,X_211))),bind(D,$fot(X_211))]]) ).
cnf(refute_0_25,plain,
( ~ equalish(X_208,X_209)
| equalish(subtract(X_208,X_211),subtract(X_209,X_211)) ),
inference(resolve,[$cnf( equalish(subtract(X_208,X_211),subtract(X_208,X_211)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ equalish(add(X_102,subtract(X_256,X_102)),X_256)
| equalish(subtract(add(X_102,subtract(X_256,X_102)),X_257),subtract(X_256,X_257)) ),
inference(subst,[],[refute_0_25:[bind(X_208,$fot(add(X_102,subtract(X_256,X_102)))),bind(X_209,$fot(X_256)),bind(X_211,$fot(X_257))]]) ).
cnf(refute_0_27,plain,
equalish(subtract(add(X_102,subtract(X_256,X_102)),X_257),subtract(X_256,X_257)),
inference(resolve,[$cnf( equalish(add(X_102,subtract(X_256,X_102)),X_256) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
equalish(subtract(add(X_2929,subtract(X_256,X_2929)),X_2930),subtract(X_256,X_2930)),
inference(subst,[],[refute_0_27:[bind(X_102,$fot(X_2929)),bind(X_257,$fot(X_2930))]]) ).
cnf(refute_0_29,plain,
( ~ equalish(add(subtract(A,B),C),subtract(add(A,C),B))
| ~ equalish(subtract(add(A,C),B),X_27)
| equalish(add(subtract(A,B),C),X_27) ),
inference(subst,[],[transitivity:[bind(A,$fot(add(subtract(A,B),C))),bind(B,$fot(subtract(add(A,C),B))),bind(C,$fot(X_27))]]) ).
cnf(refute_0_30,plain,
( ~ equalish(subtract(add(A,C),B),X_27)
| equalish(add(subtract(A,B),C),X_27) ),
inference(resolve,[$cnf( equalish(add(subtract(A,B),C),subtract(add(A,C),B)) )],[commutativity1,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ equalish(subtract(add(X_2929,subtract(X_256,X_2929)),X_2930),subtract(X_256,X_2930))
| equalish(add(subtract(X_2929,X_2930),subtract(X_256,X_2929)),subtract(X_256,X_2930)) ),
inference(subst,[],[refute_0_30:[bind(A,$fot(X_2929)),bind(B,$fot(X_2930)),bind(C,$fot(subtract(X_256,X_2929))),bind(X_27,$fot(subtract(X_256,X_2930)))]]) ).
cnf(refute_0_32,plain,
equalish(add(subtract(X_2929,X_2930),subtract(X_256,X_2929)),subtract(X_256,X_2930)),
inference(resolve,[$cnf( equalish(subtract(add(X_2929,subtract(X_256,X_2929)),X_2930),subtract(X_256,X_2930)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
equalish(add(subtract(X_2966,X_2967),subtract(X_2965,X_2966)),subtract(X_2965,X_2967)),
inference(subst,[],[refute_0_32:[bind(X_256,$fot(X_2965)),bind(X_2929,$fot(X_2966)),bind(X_2930,$fot(X_2967))]]) ).
cnf(refute_0_34,plain,
equalish(add(subtract(X_2965,X_2966),subtract(X_2966,X_2967)),subtract(X_2965,X_2967)),
inference(resolve,[$cnf( equalish(add(subtract(X_2966,X_2967),subtract(X_2965,X_2966)),subtract(X_2965,X_2967)) )],[refute_0_33,refute_0_12]) ).
cnf(refute_0_35,plain,
equalish(add(subtract(X_3498,X_3500),subtract(X_3500,X_2967)),subtract(X_3498,X_2967)),
inference(subst,[],[refute_0_34:[bind(X_2965,$fot(X_3498)),bind(X_2966,$fot(X_3500))]]) ).
cnf(refute_0_36,plain,
( ~ equalish(add(subtract(A,C),B),X_27)
| ~ equalish(subtract(add(A,B),C),add(subtract(A,C),B))
| equalish(subtract(add(A,B),C),X_27) ),
inference(subst,[],[transitivity:[bind(A,$fot(subtract(add(A,B),C))),bind(B,$fot(add(subtract(A,C),B))),bind(C,$fot(X_27))]]) ).
cnf(refute_0_37,plain,
( ~ equalish(add(subtract(A,C),B),X_27)
| equalish(subtract(add(A,B),C),X_27) ),
inference(resolve,[$cnf( equalish(subtract(add(A,B),C),add(subtract(A,C),B)) )],[commutativity2,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ equalish(add(subtract(X_3498,X_3500),subtract(X_3500,X_2967)),subtract(X_3498,X_2967))
| equalish(subtract(add(X_3498,subtract(X_3500,X_2967)),X_3500),subtract(X_3498,X_2967)) ),
inference(subst,[],[refute_0_37:[bind(A,$fot(X_3498)),bind(B,$fot(subtract(X_3500,X_2967))),bind(C,$fot(X_3500)),bind(X_27,$fot(subtract(X_3498,X_2967)))]]) ).
cnf(refute_0_39,plain,
equalish(subtract(add(X_3498,subtract(X_3500,X_2967)),X_3500),subtract(X_3498,X_2967)),
inference(resolve,[$cnf( equalish(add(subtract(X_3498,X_3500),subtract(X_3500,X_2967)),subtract(X_3498,X_2967)) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
equalish(subtract(add(X_3573,subtract(X_3574,X_3572)),X_3574),subtract(X_3573,X_3572)),
inference(subst,[],[refute_0_39:[bind(X_2967,$fot(X_3572)),bind(X_3498,$fot(X_3573)),bind(X_3500,$fot(X_3574))]]) ).
cnf(refute_0_41,plain,
equalish(add(X_3573,subtract(X_3574,X_3572)),add(subtract(X_3573,X_3572),X_3574)),
inference(resolve,[$cnf( equalish(subtract(add(X_3573,subtract(X_3574,X_3572)),X_3574),subtract(X_3573,X_3572)) )],[refute_0_40,refute_0_9]) ).
cnf(refute_0_42,plain,
equalish(add(a,subtract(b,c)),add(subtract(a,c),b)),
inference(subst,[],[refute_0_41:[bind(X_3572,$fot(c)),bind(X_3573,$fot(a)),bind(X_3574,$fot(b))]]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( equalish(add(a,subtract(b,c)),add(subtract(a,c),b)) )],[refute_0_42,prove_equation]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jul 7 22:22:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 7.27/7.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.27/7.43
% 7.27/7.43 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.27/7.44
%------------------------------------------------------------------------------