TSTP Solution File: GRP004-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP004-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 00:13:33 EDT 2023
% Result : Unsatisfiable 0.14s 0.49s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 21 ( 8 unt; 4 typ; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 48 ( 2 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
inverse: $i > $i ).
tff(decl_23,type,
identity: $i ).
tff(decl_24,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
a: $i ).
cnf(associativity1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(prove_there_is_a_right_inverse,negated_conjecture,
~ product(a,X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_right_inverse) ).
cnf(c_0_5,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1 ).
cnf(c_0_6,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_7,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_8,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,identity)
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_10,plain,
( product(X1,X2,X3)
| ~ product(X4,identity,X1)
| ~ product(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_11,plain,
( product(inverse(X1),X2,X3)
| ~ product(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( product(X1,X2,X3)
| ~ product(inverse(X4),X2,X3)
| ~ product(X4,X1,identity) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,plain,
( product(X1,X2,identity)
| ~ product(X2,X1,identity) ),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
~ product(a,X1,identity),
prove_there_is_a_right_inverse ).
cnf(c_0_15,plain,
product(X1,inverse(X1),identity),
inference(spm,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_14,c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : GRP004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Aug 28 20:45:16 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.47 start to proof: theBenchmark
% 0.14/0.49 % Version : CSE_E---1.5
% 0.14/0.49 % Problem : theBenchmark.p
% 0.14/0.49 % Proof found
% 0.14/0.49 % SZS status Theorem for theBenchmark.p
% 0.14/0.49 % SZS output start Proof
% See solution above
% 0.14/0.49 % Total time : 0.005000 s
% 0.14/0.49 % SZS output end Proof
% 0.14/0.49 % Total time : 0.007000 s
%------------------------------------------------------------------------------