TSTP Solution File: GRP105-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP105-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 00:16:04 EDT 2023
% Result : Unsatisfiable 0.19s 0.68s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 39 unt; 12 typ; 0 def)
% Number of atoms : 59 ( 58 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 21 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 11 ( 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
double_divide: ( $i * $i ) > $i ).
tff(decl_23,type,
inverse: $i > $i ).
tff(decl_24,type,
multiply: ( $i * $i ) > $i ).
tff(decl_25,type,
a1: $i ).
tff(decl_26,type,
b1: $i ).
tff(decl_27,type,
b2: $i ).
tff(decl_28,type,
a2: $i ).
tff(decl_29,type,
a3: $i ).
tff(decl_30,type,
b3: $i ).
tff(decl_31,type,
c3: $i ).
tff(decl_32,type,
a4: $i ).
tff(decl_33,type,
b4: $i ).
cnf(single_axiom,axiom,
double_divide(inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(X3))))),X2) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(multiply,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_3,axiom,
double_divide(inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(X3))))),X2) = X3,
single_axiom ).
cnf(c_0_4,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X1,inverse(X2)),inverse(double_divide(X1,inverse(X3))))),X4),inverse(X3))),X4) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
double_divide(inverse(double_divide(X1,inverse(X1))),inverse(X2)) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_6,plain,
double_divide(inverse(double_divide(X1,inverse(X2))),inverse(X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_5]),c_0_5]) ).
cnf(c_0_7,plain,
double_divide(inverse(X1),inverse(inverse(double_divide(X2,inverse(X1))))) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_8,plain,
double_divide(inverse(X1),inverse(inverse(X2))) = inverse(double_divide(X1,inverse(X2))),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
inverse(double_divide(X1,inverse(double_divide(X2,inverse(X1))))) = X2,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
double_divide(inverse(X1),inverse(X2)) = inverse(double_divide(X1,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
inverse(double_divide(double_divide(X1,inverse(X1)),X2)) = X2,
inference(rw,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_12,plain,
inverse(double_divide(X1,inverse(double_divide(X2,inverse(X2))))) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_13,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_12]) ).
cnf(c_0_14,plain,
inverse(double_divide(double_divide(X1,inverse(X2)),X1)) = X2,
inference(rw,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_15,plain,
inverse(double_divide(X1,inverse(X2))) = double_divide(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_16,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_17,plain,
double_divide(inverse(double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X2,X3),inverse(double_divide(X2,inverse(X1))))),inverse(X4))))),X3) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_18,plain,
double_divide(X1,X2) = double_divide(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_10]),c_0_16]),c_0_16]) ).
cnf(c_0_19,plain,
double_divide(double_divide(X1,inverse(X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_20,plain,
inverse(inverse(double_divide(double_divide(X1,X2),X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_10]) ).
cnf(c_0_21,plain,
double_divide(X1,inverse(double_divide(X2,double_divide(double_divide(double_divide(X3,X1),double_divide(X2,inverse(X3))),X4)))) = X4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_15]),c_0_10]),c_0_15]),c_0_10]),c_0_18]),c_0_18]) ).
cnf(c_0_22,plain,
double_divide(X1,double_divide(X2,inverse(X2))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_19]),c_0_16]),c_0_15]) ).
cnf(c_0_23,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(rw,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_24,plain,
inverse(double_divide(double_divide(X1,X2),double_divide(X3,inverse(X1)))) = double_divide(X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_16]) ).
cnf(c_0_25,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_26,plain,
inverse(double_divide(X1,double_divide(X2,inverse(X3)))) = double_divide(double_divide(X3,X1),X2),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
prove_these_axioms ).
cnf(c_0_28,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_29,plain,
inverse(double_divide(inverse(X1),X2)) = double_divide(X1,inverse(X2)),
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
cnf(c_0_30,plain,
double_divide(X1,double_divide(X2,inverse(X3))) = inverse(double_divide(double_divide(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1)))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]) ).
cnf(c_0_32,plain,
double_divide(double_divide(X1,inverse(X2)),X3) = inverse(double_divide(double_divide(X3,X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_16]),c_0_15]),c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1)))
| inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_12])]) ).
cnf(c_0_34,plain,
double_divide(inverse(double_divide(X1,X2)),X3) = double_divide(X1,inverse(double_divide(X3,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_10]),c_0_15]) ).
cnf(c_0_35,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_23]) ).
cnf(c_0_36,negated_conjecture,
( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != double_divide(double_divide(b3,a3),inverse(c3))
| double_divide(a1,inverse(a1)) != double_divide(b1,inverse(b1))
| inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_37,plain,
double_divide(X1,inverse(double_divide(double_divide(X2,X1),X3))) = double_divide(X3,inverse(X2)),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_38,plain,
double_divide(X1,inverse(double_divide(X2,double_divide(X3,X1)))) = double_divide(inverse(X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_21]),c_0_30]),c_0_25]),c_0_34]),c_0_30]),c_0_18]),c_0_35]),c_0_16]) ).
cnf(c_0_39,negated_conjecture,
( double_divide(inverse(a3),double_divide(c3,b3)) != double_divide(inverse(c3),double_divide(b3,a3))
| double_divide(a1,inverse(a1)) != double_divide(b1,inverse(b1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_18]),c_0_15]),c_0_18]),c_0_18]),c_0_18])]) ).
cnf(c_0_40,plain,
double_divide(X1,inverse(X1)) = double_divide(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_35,c_0_19]) ).
cnf(c_0_41,plain,
double_divide(double_divide(X1,X2),inverse(X3)) = double_divide(inverse(X1),double_divide(X3,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
double_divide(inverse(a3),double_divide(c3,b3)) != double_divide(inverse(c3),double_divide(b3,a3)),
inference(sr,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,plain,
double_divide(inverse(X1),double_divide(X2,X3)) = double_divide(inverse(X2),double_divide(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_34]),c_0_15]),c_0_41]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP105-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n014.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 21:05:30 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 0.19/0.68 % Version : CSE_E---1.5
% 0.19/0.68 % Problem : theBenchmark.p
% 0.19/0.68 % Proof found
% 0.19/0.68 % SZS status Theorem for theBenchmark.p
% 0.19/0.68 % SZS output start Proof
% See solution above
% 0.19/0.68 % Total time : 0.085000 s
% 0.19/0.68 % SZS output end Proof
% 0.19/0.68 % Total time : 0.088000 s
%------------------------------------------------------------------------------