TSTP Solution File: GRP047-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP047-2 : 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 : n019.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 00:13:50 EDT 2023
% Result : Unsatisfiable 0.19s 0.73s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 52 ( 21 unt; 8 typ; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 39 ~; 35 |; 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 : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 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 ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
c: $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(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(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_inverse) ).
cnf(a_equals_b,hypothesis,
equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function1) ).
cnf(prove_multiply_substitution2,negated_conjecture,
~ equalish(multiply(c,a),multiply(c,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_multiply_substitution2) ).
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,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity1 ).
cnf(c_0_12,plain,
( product(identity,X1,X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( equalish(X1,X2)
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_14,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_15,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,identity)
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_16,plain,
( equalish(X1,X2)
| ~ equalish(X3,X2)
| ~ product(identity,X3,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
cnf(c_0_17,plain,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_18,hypothesis,
equalish(a,b),
a_equals_b ).
cnf(c_0_19,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_20,plain,
( equalish(X1,identity)
| ~ product(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_21,plain,
( product(inverse(X1),X2,X3)
| ~ product(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_22,plain,
( equalish(X1,X2)
| ~ equalish(X3,X2)
| ~ equalish(X3,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_23,hypothesis,
equalish(b,a),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
equalish(multiply(identity,X1),X1),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_25,plain,
( equalish(X1,identity)
| ~ product(X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,hypothesis,
( equalish(X1,a)
| ~ equalish(b,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
equalish(X1,multiply(identity,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_28,plain,
( equalish(X1,identity)
| ~ product(X2,inverse(X2),X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_21]) ).
cnf(c_0_29,plain,
( equalish(X1,multiply(X2,X3))
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_19]) ).
cnf(c_0_30,plain,
( product(X1,X2,X3)
| ~ equalish(multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_19]) ).
cnf(c_0_31,hypothesis,
equalish(multiply(identity,b),a),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
equalish(multiply(X1,inverse(X1)),identity),
inference(spm,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_33,negated_conjecture,
~ equalish(multiply(c,a),multiply(c,b)),
prove_multiply_substitution2 ).
cnf(c_0_34,plain,
( equalish(multiply(X1,X2),X3)
| ~ product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_35,plain,
( product(X1,X2,multiply(X3,X4))
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_19]) ).
cnf(c_0_36,hypothesis,
product(identity,b,a),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
product(X1,inverse(X1),identity),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
~ product(c,a,multiply(c,b)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,hypothesis,
( product(X1,a,multiply(X2,b))
| ~ product(X1,identity,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( product(X1,X2,X3)
| ~ product(inverse(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
~ product(c,identity,c),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
product(X1,identity,X1),
inference(spm,[status(thm)],[c_0_40,c_0_14]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP047-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 21:14:58 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.73 % Version : CSE_E---1.5
% 0.19/0.73 % Problem : theBenchmark.p
% 0.19/0.73 % Proof found
% 0.19/0.73 % SZS status Theorem for theBenchmark.p
% 0.19/0.73 % SZS output start Proof
% See solution above
% 0.19/0.74 % Total time : 0.171000 s
% 0.19/0.74 % SZS output end Proof
% 0.19/0.74 % Total time : 0.174000 s
%------------------------------------------------------------------------------