TSTP Solution File: GRP029-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP029-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 : 300s
% DateTime : Thu Aug 31 00:13:43 EDT 2023
% Result : Unsatisfiable 0.54s 0.60s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 31 ( 12 unt; 6 typ; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
equalish: ( $i * $i ) > $o ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
inverse: $i > $i ).
tff(decl_26,type,
identity: $i ).
tff(decl_27,type,
not_right_identity: $i > $i ).
cnf(associativity1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
cnf(total_function2,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(product_substitution3,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
cnf(prove_there_is_a_right_identity,negated_conjecture,
~ product(not_right_identity(X1),X1,not_right_identity(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_right_identity) ).
cnf(c_0_7,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1 ).
cnf(c_0_8,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_9,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2 ).
cnf(c_0_10,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_11,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,identity)
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( equalish(X1,identity)
| ~ product(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( product(inverse(X1),X2,X3)
| ~ product(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_14,plain,
( equalish(X1,identity)
| ~ product(X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3 ).
cnf(c_0_16,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_17,plain,
( equalish(X1,identity)
| ~ product(X2,inverse(X2),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_18,plain,
( product(X1,X2,X3)
| ~ equalish(multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
equalish(multiply(X1,inverse(X1)),identity),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_20,plain,
product(X1,inverse(X1),identity),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
( product(X1,X2,X3)
| ~ product(inverse(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
~ product(not_right_identity(X1),X1,not_right_identity(X1)),
prove_there_is_a_right_identity ).
cnf(c_0_23,plain,
product(X1,identity,X1),
inference(spm,[status(thm)],[c_0_21,c_0_10]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_22,c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP029-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 00:35:56 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.54/0.60 % Version : CSE_E---1.5
% 0.54/0.60 % Problem : theBenchmark.p
% 0.54/0.60 % Proof found
% 0.54/0.60 % SZS status Theorem for theBenchmark.p
% 0.54/0.60 % SZS output start Proof
% See solution above
% 0.54/0.60 % Total time : 0.023000 s
% 0.54/0.60 % SZS output end Proof
% 0.54/0.60 % Total time : 0.026000 s
%------------------------------------------------------------------------------