TSTP Solution File: GRP017-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP017-1 : 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 : n006.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 00:13:38 EDT 2023
% Result : Unsatisfiable 0.21s 0.57s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 16 unt; 7 typ; 0 def)
% Number of atoms : 41 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 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 ).
cnf(total_function2,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_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/Axioms/GRP003-0.ax',associativity2) ).
cnf(a_times_c_is_identity,hypothesis,
product(a,c,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_identity) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(b_times_a_is_identity,hypothesis,
product(b,a,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_is_identity) ).
cnf(prove_b_equals_c,negated_conjecture,
b != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_equals_c) ).
cnf(c_0_8,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
total_function2 ).
cnf(c_0_9,axiom,
product(X1,identity,X1),
right_identity ).
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,hypothesis,
product(a,c,identity),
a_times_c_is_identity ).
cnf(c_0_12,plain,
( X1 = X2
| ~ product(X2,identity,X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_14,hypothesis,
( product(X1,c,X2)
| ~ product(X3,identity,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_17,hypothesis,
( product(X1,c,X2)
| ~ product(X2,a,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_15]) ).
cnf(c_0_18,hypothesis,
product(b,a,identity),
b_times_a_is_identity ).
cnf(c_0_19,plain,
( X1 = X2
| ~ product(identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_16]) ).
cnf(c_0_20,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_21,hypothesis,
product(identity,c,b),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_23,negated_conjecture,
b != c,
prove_b_equals_c ).
cnf(c_0_24,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP017-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 21:15:36 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.55 start to proof: theBenchmark
% 0.21/0.57 % Version : CSE_E---1.5
% 0.21/0.57 % Problem : theBenchmark.p
% 0.21/0.57 % Proof found
% 0.21/0.57 % SZS status Theorem for theBenchmark.p
% 0.21/0.57 % SZS output start Proof
% See solution above
% 0.21/0.57 % Total time : 0.004000 s
% 0.21/0.57 % SZS output end Proof
% 0.21/0.57 % Total time : 0.007000 s
%------------------------------------------------------------------------------