TSTP Solution File: GRP012-2 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP012-2 : 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 : n020.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 00:13:36 EDT 2023
% Result : Unsatisfiable 0.48s 0.64s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 45 ( 24 unt; 8 typ; 0 def)
% Number of atoms : 59 ( 10 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 : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 55 ( 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,
a: $i ).
tff(decl_27,type,
b: $i ).
tff(decl_28,type,
c: $i ).
tff(decl_29,type,
d: $i ).
cnf(associativity2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(inverse_b_multiply_inverse_a_is_d,hypothesis,
product(inverse(b),inverse(a),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_b_multiply_inverse_a_is_d) ).
cnf(total_function2,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(a_multiply_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_multiply_b_is_c) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(prove_c_inverse_equals_d,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_inverse_equals_d) ).
cnf(c_0_10,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity2 ).
cnf(c_0_11,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_12,plain,
( product(identity,X1,X2)
| ~ product(inverse(X3),X1,X4)
| ~ product(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,hypothesis,
product(inverse(b),inverse(a),d),
inverse_b_multiply_inverse_a_is_d ).
cnf(c_0_14,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2 ).
cnf(c_0_15,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_16,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_17,hypothesis,
( product(identity,inverse(a),X1)
| ~ product(b,d,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( X1 = X2
| ~ product(identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( multiply(X1,X2) = X3
| ~ product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_20,hypothesis,
product(identity,inverse(a),multiply(b,d)),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_22,hypothesis,
multiply(b,d) = inverse(a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_23,hypothesis,
product(a,b,c),
a_multiply_b_is_c ).
cnf(c_0_24,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_25,plain,
( product(X1,X2,identity)
| ~ product(X3,X2,inverse(X4))
| ~ product(X4,X3,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_26,hypothesis,
product(b,d,inverse(a)),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_27,hypothesis,
( c = X1
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_28,plain,
( product(identity,X1,X2)
| ~ product(inverse(X3),X4,X2)
| ~ product(X3,X1,X4) ),
inference(spm,[status(thm)],[c_0_10,c_0_24]) ).
cnf(c_0_29,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_30,hypothesis,
( product(X1,d,identity)
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,hypothesis,
multiply(a,b) = c,
inference(spm,[status(thm)],[c_0_27,c_0_16]) ).
cnf(c_0_32,plain,
( product(identity,X1,inverse(X2))
| ~ product(X2,X1,identity) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,hypothesis,
product(c,d,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_16]),c_0_31]) ).
cnf(c_0_34,hypothesis,
product(identity,d,inverse(c)),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,negated_conjecture,
inverse(c) != d,
prove_c_inverse_equals_d ).
cnf(c_0_36,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_34]),c_0_21]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP012-2 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 01:47:43 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.48/0.62 start to proof: theBenchmark
% 0.48/0.64 % Version : CSE_E---1.5
% 0.48/0.64 % Problem : theBenchmark.p
% 0.48/0.64 % Proof found
% 0.48/0.64 % SZS status Theorem for theBenchmark.p
% 0.48/0.64 % SZS output start Proof
% See solution above
% 0.48/0.64 % Total time : 0.008000 s
% 0.48/0.64 % SZS output end Proof
% 0.48/0.64 % Total time : 0.010000 s
%------------------------------------------------------------------------------