TSTP Solution File: GRP075-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP075-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 00:15:31 EDT 2023
% Result : Unsatisfiable 0.58s 0.70s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 14
% Syntax : Number of formulae : 59 ( 45 unt; 9 typ; 0 def)
% Number of atoms : 59 ( 58 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 18 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
double_divide: ( $i * $i ) > $i ).
tff(decl_24,type,
multiply: ( $i * $i ) > $i ).
tff(decl_25,type,
inverse: $i > $i ).
tff(decl_26,type,
a1: $i ).
tff(decl_27,type,
a2: $i ).
tff(decl_28,type,
a3: $i ).
tff(decl_29,type,
b3: $i ).
tff(decl_30,type,
c3: $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(double_divide(X1,double_divide(X2,identity)),double_divide(double_divide(X3,double_divide(X4,double_divide(X4,identity))),double_divide(X1,identity))),X2) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
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(double_divide(X1,double_divide(X2,identity)),double_divide(double_divide(X3,double_divide(X4,double_divide(X4,identity))),double_divide(X1,identity))),X2) = X3,
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(double_divide(X1,double_divide(X2,identity)),double_divide(double_divide(X3,identity),double_divide(X1,identity))),X2) = X3,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
double_divide(double_divide(double_divide(double_divide(X1,identity),double_divide(X2,identity)),identity),X2) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_11,plain,
double_divide(double_divide(identity,identity),double_divide(X1,identity)) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_12,plain,
double_divide(identity,identity) = identity,
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_13,plain,
double_divide(identity,double_divide(X1,identity)) = X1,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
double_divide(double_divide(double_divide(X1,identity),identity),identity) = double_divide(identity,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_10]),c_0_12]) ).
cnf(c_0_15,plain,
double_divide(double_divide(X1,identity),identity) = double_divide(identity,double_divide(identity,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
double_divide(identity,double_divide(identity,double_divide(identity,X1))) = double_divide(X1,identity),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_17,plain,
double_divide(double_divide(identity,X1),identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_16]),c_0_13]) ).
cnf(c_0_18,plain,
double_divide(double_divide(identity,X1),X1) = identity,
inference(spm,[status(thm)],[c_0_8,c_0_17]) ).
cnf(c_0_19,plain,
double_divide(double_divide(X1,identity),X1) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_18]),c_0_13]),c_0_12]) ).
cnf(c_0_20,plain,
double_divide(X1,double_divide(identity,X1)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_10]),c_0_12]),c_0_15]),c_0_17]) ).
cnf(c_0_21,plain,
double_divide(identity,X1) = double_divide(X1,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_19]),c_0_12]) ).
cnf(c_0_22,plain,
double_divide(identity,double_divide(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_20]),c_0_12]),c_0_15]),c_0_16]),c_0_15]) ).
cnf(c_0_23,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_21]),c_0_13]),c_0_12]),c_0_15]),c_0_22]) ).
cnf(c_0_24,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_23]) ).
cnf(c_0_25,plain,
double_divide(double_divide(identity,double_divide(X1,double_divide(X2,identity))),X2) = double_divide(X1,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_23]),c_0_21]) ).
cnf(c_0_26,plain,
double_divide(identity,double_divide(X1,double_divide(X2,identity))) = double_divide(X2,double_divide(X1,identity)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
prove_these_axioms ).
cnf(c_0_28,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_29,plain,
double_divide(double_divide(X1,identity),double_divide(X2,identity)) = double_divide(identity,double_divide(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_9]),c_0_12]),c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( double_divide(double_divide(a2,identity),identity) != a2
| double_divide(double_divide(a1,double_divide(a1,identity)),identity) != identity
| double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) ),
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_6]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_28]) ).
cnf(c_0_31,plain,
double_divide(double_divide(X1,identity),double_divide(identity,X2)) = double_divide(identity,double_divide(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_32,plain,
double_divide(double_divide(double_divide(double_divide(X1,identity),double_divide(X2,identity)),double_divide(double_divide(X3,identity),X1)),X2) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_9]),c_0_12]),c_0_24]) ).
cnf(c_0_33,negated_conjecture,
( double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity)
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(rw,[status(thm)],[c_0_30,c_0_8]) ).
cnf(c_0_34,plain,
double_divide(double_divide(double_divide(X1,double_divide(X2,identity)),double_divide(X3,double_divide(X1,identity))),X2) = double_divide(identity,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_9]),c_0_12]),c_0_29]),c_0_31]),c_0_23]) ).
cnf(c_0_35,plain,
double_divide(identity,double_divide(double_divide(X1,identity),X2)) = double_divide(double_divide(X2,identity),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_12]),c_0_15]),c_0_22]),c_0_24]) ).
cnf(c_0_36,negated_conjecture,
( double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity)
| double_divide(identity,double_divide(identity,a2)) != a2 ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_12])]),c_0_15]) ).
cnf(c_0_37,plain,
double_divide(double_divide(double_divide(X1,double_divide(X2,identity)),X3),X2) = double_divide(double_divide(X3,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_23]),c_0_35]) ).
cnf(c_0_38,negated_conjecture,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_22])]) ).
cnf(c_0_39,plain,
double_divide(double_divide(X1,double_divide(X2,identity)),X3) = double_divide(X2,double_divide(double_divide(X3,identity),X1)),
inference(spm,[status(thm)],[c_0_24,c_0_37]) ).
cnf(c_0_40,plain,
double_divide(double_divide(identity,X1),double_divide(X2,identity)) = double_divide(identity,double_divide(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_41,negated_conjecture,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_21]),c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_42,plain,
double_divide(identity,double_divide(X1,double_divide(identity,X2))) = double_divide(X2,double_divide(X1,identity)),
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_43,plain,
double_divide(double_divide(identity,double_divide(X1,X2)),X3) = double_divide(X1,double_divide(identity,double_divide(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_31]) ).
cnf(c_0_44,negated_conjecture,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_21]) ).
cnf(c_0_45,plain,
double_divide(identity,double_divide(double_divide(identity,X1),X2)) = double_divide(double_divide(X2,identity),X1),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_46,plain,
double_divide(double_divide(X1,X2),double_divide(identity,double_divide(X1,X3))) = double_divide(double_divide(identity,X2),X3),
inference(spm,[status(thm)],[c_0_43,c_0_23]) ).
cnf(c_0_47,negated_conjecture,
double_divide(double_divide(b3,a3),double_divide(identity,c3)) != double_divide(double_divide(identity,a3),double_divide(c3,b3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_21]) ).
cnf(c_0_48,plain,
double_divide(double_divide(X1,X2),double_divide(identity,X3)) = double_divide(double_divide(identity,X2),double_divide(X3,X1)),
inference(spm,[status(thm)],[c_0_46,c_0_24]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP075-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.04/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n029.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 23:59:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.47/0.61 start to proof: theBenchmark
% 0.58/0.70 % Version : CSE_E---1.5
% 0.58/0.70 % Problem : theBenchmark.p
% 0.58/0.70 % Proof found
% 0.58/0.70 % SZS status Theorem for theBenchmark.p
% 0.58/0.70 % SZS output start Proof
% See solution above
% 0.58/0.71 % Total time : 0.082000 s
% 0.58/0.71 % SZS output end Proof
% 0.58/0.71 % Total time : 0.085000 s
%------------------------------------------------------------------------------