TSTP Solution File: GRP001-5 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP001-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 10:32:08 EDT 2022
% Result : Unsatisfiable 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 32 ( 15 unt; 0 nHn; 25 RR)
% Number of literals : 65 ( 0 equ; 34 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 55 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X) ).
cnf(right_identity,axiom,
product(X,identity,X) ).
cnf(associativity1,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ) ).
cnf(associativity2,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ) ).
cnf(square_element,hypothesis,
product(X,X,identity) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c) ).
cnf(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c) ).
cnf(refute_0_0,plain,
product(X_63,X_63,identity),
inference(subst,[],[square_element:[bind(X,$fot(X_63))]]) ).
cnf(refute_0_1,plain,
product(identity,X_43,X_43),
inference(subst,[],[left_identity:[bind(X,$fot(X_43))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_44,X_45,identity)
| ~ product(X_45,X_43,X_42)
| ~ product(identity,X_43,X_43)
| product(X_44,X_42,X_43) ),
inference(subst,[],[associativity1:[bind(U,$fot(identity)),bind(V,$fot(X_42)),bind(W,$fot(X_43)),bind(X,$fot(X_44)),bind(Y,$fot(X_45)),bind(Z,$fot(X_43))]]) ).
cnf(refute_0_3,plain,
( ~ product(X_44,X_45,identity)
| ~ product(X_45,X_43,X_42)
| product(X_44,X_42,X_43) ),
inference(resolve,[$cnf( product(identity,X_43,X_43) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ product(X_63,X_61,X_60)
| ~ product(X_63,X_63,identity)
| product(X_63,X_60,X_61) ),
inference(subst,[],[refute_0_3:[bind(X_42,$fot(X_60)),bind(X_43,$fot(X_61)),bind(X_44,$fot(X_63)),bind(X_45,$fot(X_63))]]) ).
cnf(refute_0_5,plain,
( ~ product(X_63,X_61,X_60)
| product(X_63,X_60,X_61) ),
inference(resolve,[$cnf( product(X_63,X_63,identity) )],[refute_0_0,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ product(b,c,a)
| product(b,a,c) ),
inference(subst,[],[refute_0_5:[bind(X_60,$fot(a)),bind(X_61,$fot(c)),bind(X_63,$fot(b))]]) ).
cnf(refute_0_7,plain,
product(a,a,identity),
inference(subst,[],[square_element:[bind(X,$fot(a))]]) ).
cnf(refute_0_8,plain,
product(identity,b,b),
inference(subst,[],[left_identity:[bind(X,$fot(b))]]) ).
cnf(refute_0_9,plain,
( ~ product(X_41,b,X_43)
| ~ product(X_44,a,X_41)
| ~ product(a,b,c)
| product(X_44,c,X_43) ),
inference(subst,[],[associativity1:[bind(U,$fot(X_41)),bind(V,$fot(c)),bind(W,$fot(X_43)),bind(X,$fot(X_44)),bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_10,plain,
( ~ product(X_41,b,X_43)
| ~ product(X_44,a,X_41)
| product(X_44,c,X_43) ),
inference(resolve,[$cnf( product(a,b,c) )],[a_times_b_is_c,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ product(X_55,a,identity)
| ~ product(identity,b,b)
| product(X_55,c,b) ),
inference(subst,[],[refute_0_10:[bind(X_41,$fot(identity)),bind(X_43,$fot(b)),bind(X_44,$fot(X_55))]]) ).
cnf(refute_0_12,plain,
( ~ product(X_55,a,identity)
| product(X_55,c,b) ),
inference(resolve,[$cnf( product(identity,b,b) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ product(a,a,identity)
| product(a,c,b) ),
inference(subst,[],[refute_0_12:[bind(X_55,$fot(a))]]) ).
cnf(refute_0_14,plain,
product(a,c,b),
inference(resolve,[$cnf( product(a,a,identity) )],[refute_0_7,refute_0_13]) ).
cnf(refute_0_15,plain,
product(X_164,X_164,identity),
inference(subst,[],[square_element:[bind(X,$fot(X_164))]]) ).
cnf(refute_0_16,plain,
product(X_125,identity,X_125),
inference(subst,[],[right_identity:[bind(X,$fot(X_125))]]) ).
cnf(refute_0_17,plain,
( ~ product(X_125,X_127,X_123)
| ~ product(X_125,identity,X_125)
| ~ product(X_127,X_128,identity)
| product(X_123,X_128,X_125) ),
inference(subst,[],[associativity2:[bind(U,$fot(X_123)),bind(V,$fot(identity)),bind(W,$fot(X_125)),bind(X,$fot(X_125)),bind(Y,$fot(X_127)),bind(Z,$fot(X_128))]]) ).
cnf(refute_0_18,plain,
( ~ product(X_125,X_127,X_123)
| ~ product(X_127,X_128,identity)
| product(X_123,X_128,X_125) ),
inference(resolve,[$cnf( product(X_125,identity,X_125) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ product(X_162,X_164,X_161)
| ~ product(X_164,X_164,identity)
| product(X_161,X_164,X_162) ),
inference(subst,[],[refute_0_18:[bind(X_123,$fot(X_161)),bind(X_125,$fot(X_162)),bind(X_127,$fot(X_164)),bind(X_128,$fot(X_164))]]) ).
cnf(refute_0_20,plain,
( ~ product(X_162,X_164,X_161)
| product(X_161,X_164,X_162) ),
inference(resolve,[$cnf( product(X_164,X_164,identity) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ product(a,c,b)
| product(b,c,a) ),
inference(subst,[],[refute_0_20:[bind(X_161,$fot(b)),bind(X_162,$fot(a)),bind(X_164,$fot(c))]]) ).
cnf(refute_0_22,plain,
product(b,c,a),
inference(resolve,[$cnf( product(a,c,b) )],[refute_0_14,refute_0_21]) ).
cnf(refute_0_23,plain,
product(b,a,c),
inference(resolve,[$cnf( product(b,c,a) )],[refute_0_22,refute_0_6]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( product(b,a,c) )],[refute_0_23,prove_b_times_a_is_c]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP001-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 12:28:22 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.39
%------------------------------------------------------------------------------