TSTP Solution File: GRP568-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP568-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 00:21:37 EDT 2023
% Result : Unsatisfiable 0.11s 0.49s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 31 unt; 6 typ; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
double_divide: ( $i * $i ) > $i ).
tff(decl_23,type,
identity: $i ).
tff(decl_24,type,
multiply: ( $i * $i ) > $i ).
tff(decl_25,type,
inverse: $i > $i ).
tff(decl_26,type,
a: $i ).
tff(decl_27,type,
b: $i ).
cnf(identity,axiom,
identity = double_divide(X1,inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(inverse,axiom,
inverse(X1) = double_divide(X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(single_axiom,axiom,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3))),double_divide(identity,identity)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_4,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
cnf(multiply,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_5,axiom,
identity = double_divide(X1,inverse(X1)),
identity ).
cnf(c_0_6,axiom,
inverse(X1) = double_divide(X1,identity),
inverse ).
cnf(c_0_7,axiom,
double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3))),double_divide(identity,identity)) = X2,
single_axiom ).
cnf(c_0_8,plain,
identity = double_divide(X1,double_divide(X1,identity)),
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
double_divide(double_divide(X1,identity),double_divide(identity,identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_10,plain,
double_divide(double_divide(identity,double_divide(X1,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(X1,identity),
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
cnf(c_0_11,plain,
double_divide(identity,identity) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_8]),c_0_9]) ).
cnf(c_0_12,plain,
double_divide(double_divide(X1,identity),identity) = X1,
inference(rw,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_13,plain,
double_divide(double_divide(identity,double_divide(X1,identity)),identity) = double_divide(X1,identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
cnf(c_0_14,plain,
double_divide(identity,double_divide(X1,identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_12]) ).
cnf(c_0_15,plain,
double_divide(double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3))),double_divide(double_divide(X4,X2),identity)),double_divide(identity,identity)) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_7]),c_0_8]) ).
cnf(c_0_16,plain,
double_divide(identity,X1) = double_divide(X1,identity),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_17,plain,
double_divide(identity,double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3))),double_divide(identity,double_divide(X4,X2)))) = X4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_11]),c_0_16]),c_0_16]) ).
cnf(c_0_18,plain,
double_divide(identity,double_divide(double_divide(identity,X1),double_divide(identity,double_divide(X2,X1)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_11]),c_0_11]),c_0_16]),c_0_14]) ).
cnf(c_0_19,plain,
double_divide(identity,double_divide(identity,X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_20,plain,
double_divide(identity,double_divide(double_divide(X1,X2),X1)) = double_divide(identity,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_18]),c_0_19]) ).
cnf(c_0_21,negated_conjecture,
multiply(a,b) != multiply(b,a),
prove_these_axioms_4 ).
cnf(c_0_22,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_23,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_19]) ).
cnf(c_0_24,plain,
double_divide(identity,double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_11]),c_0_16]) ).
cnf(c_0_25,negated_conjecture,
double_divide(double_divide(b,a),identity) != double_divide(double_divide(a,b),identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22]) ).
cnf(c_0_26,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_23]) ).
cnf(c_0_27,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_24]),c_0_24]),c_0_19]) ).
cnf(c_0_28,negated_conjecture,
double_divide(identity,double_divide(a,b)) != double_divide(identity,double_divide(b,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_16]),c_0_16]) ).
cnf(c_0_29,plain,
double_divide(X1,X2) = double_divide(X2,X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GRP568-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.08 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.06/0.26 % Computer : n018.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Mon Aug 28 23:12:17 EDT 2023
% 0.06/0.26 % CPUTime :
% 0.11/0.47 start to proof: theBenchmark
% 0.11/0.49 % Version : CSE_E---1.5
% 0.11/0.49 % Problem : theBenchmark.p
% 0.11/0.49 % Proof found
% 0.11/0.49 % SZS status Theorem for theBenchmark.p
% 0.11/0.49 % SZS output start Proof
% See solution above
% 0.11/0.49 % Total time : 0.009000 s
% 0.11/0.49 % SZS output end Proof
% 0.11/0.49 % Total time : 0.012000 s
%------------------------------------------------------------------------------