TSTP Solution File: GRP003-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP003-2 : 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 : n031.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 0.68s 0.78s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 58 ( 17 unt; 6 typ; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 114 ( 58 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 130 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
multiply: ( $i * $i ) > $i ).
tff(decl_26,type,
equalish: ( $i * $i ) > $o ).
tff(decl_27,type,
a: $i ).
cnf(product_substitution3,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_identity) ).
cnf(total_function2,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function2) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function1) ).
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',associativity2) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_inverse) ).
cnf(associativity1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',associativity1) ).
cnf(prove_right_identity,negated_conjecture,
~ product(a,identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_identity) ).
cnf(c_0_8,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3 ).
cnf(c_0_9,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_10,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2 ).
cnf(c_0_11,plain,
( product(identity,X1,X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( equalish(X1,X2)
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_13,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_14,plain,
( product(identity,X1,X2)
| ~ equalish(X3,X2)
| ~ equalish(X1,X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_15,plain,
equalish(multiply(identity,X1),X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( product(identity,X1,X2)
| ~ equalish(X1,multiply(identity,X2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
( equalish(X1,multiply(X2,X3))
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_13]) ).
cnf(c_0_18,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_19,plain,
equalish(X1,X1),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_20,plain,
( product(identity,X1,X2)
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_22,plain,
product(identity,multiply(identity,X1),X1),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_23,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_24,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1 ).
cnf(c_0_25,plain,
( product(identity,X1,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_11]) ).
cnf(c_0_26,plain,
( product(X1,X2,X2)
| ~ product(identity,identity,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( product(X1,X2,X3)
| ~ product(X4,inverse(X2),X1)
| ~ product(X4,identity,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_28,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,identity)
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_9]) ).
cnf(c_0_29,plain,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_30,plain,
( equalish(X1,X2)
| ~ equalish(X2,X3)
| ~ product(identity,X3,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_25]) ).
cnf(c_0_31,plain,
( product(X1,X2,X2)
| ~ equalish(identity,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_11]) ).
cnf(c_0_32,plain,
( product(identity,X1,X2)
| ~ product(inverse(inverse(X1)),identity,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_23]) ).
cnf(c_0_33,plain,
( product(inverse(X1),X2,X3)
| ~ product(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_34,plain,
( product(X1,X2,X3)
| ~ equalish(multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_35,plain,
equalish(X1,multiply(identity,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_15]) ).
cnf(c_0_36,plain,
( equalish(X1,X2)
| ~ equalish(X2,X3)
| ~ equalish(X3,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_11]) ).
cnf(c_0_37,plain,
( equalish(X1,X2)
| ~ equalish(identity,X3)
| ~ product(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_31]) ).
cnf(c_0_38,plain,
( product(identity,X1,X2)
| ~ product(inverse(X1),X2,identity) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
product(X1,X2,multiply(identity,multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( equalish(X1,X2)
| ~ equalish(multiply(X3,X4),X1)
| ~ product(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_17]) ).
cnf(c_0_41,plain,
( equalish(multiply(X1,X2),X2)
| ~ equalish(identity,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_13]) ).
cnf(c_0_42,plain,
( product(identity,X1,X2)
| ~ product(X1,identity,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_33]) ).
cnf(c_0_43,plain,
( product(X1,X2,X3)
| ~ equalish(multiply(identity,multiply(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_39]) ).
cnf(c_0_44,plain,
( equalish(multiply(identity,X1),X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_13]) ).
cnf(c_0_45,plain,
( equalish(X1,X2)
| ~ equalish(identity,X3)
| ~ product(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
product(identity,X1,multiply(X1,identity)),
inference(spm,[status(thm)],[c_0_42,c_0_13]) ).
cnf(c_0_47,plain,
( product(X1,X2,X3)
| ~ equalish(X3,multiply(X1,X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
equalish(X1,multiply(X1,identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_19])]) ).
cnf(c_0_49,negated_conjecture,
~ product(a,identity,a),
prove_right_identity ).
cnf(c_0_50,plain,
product(X1,identity,X1),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP003-2 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.34 % Computer : n031.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Tue Aug 29 01:55:25 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.17/0.50 start to proof: theBenchmark
% 0.68/0.78 % Version : CSE_E---1.5
% 0.68/0.78 % Problem : theBenchmark.p
% 0.68/0.78 % Proof found
% 0.68/0.78 % SZS status Theorem for theBenchmark.p
% 0.68/0.78 % SZS output start Proof
% See solution above
% 0.68/0.79 % Total time : 0.278000 s
% 0.68/0.79 % SZS output end Proof
% 0.68/0.79 % Total time : 0.281000 s
%------------------------------------------------------------------------------