TSTP Solution File: GRP103-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP103-1 : 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 : n007.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 00:16:03 EDT 2023
% Result : Unsatisfiable 1.33s 1.43s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 16
% Syntax : Number of formulae : 82 ( 64 unt; 11 typ; 0 def)
% Number of atoms : 87 ( 86 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 25 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 9 ( 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 128 ( 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 ).
tff(decl_31,type,
a4: $i ).
tff(decl_32,type,
b4: $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(identity,X2),double_divide(X3,double_divide(X2,X1)))),double_divide(identity,identity)) = 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))
| multiply(a4,b4) != multiply(b4,a4) ),
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(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),double_divide(identity,identity)) = 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(identity,double_divide(double_divide(identity,X1),identity)),double_divide(identity,identity)) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
double_divide(identity,identity) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_8]),c_0_8]),c_0_8]) ).
cnf(c_0_11,plain,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),identity) = X3,
inference(rw,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_12,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X1),identity)),identity) = X1,
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_10]),c_0_10]) ).
cnf(c_0_14,plain,
double_divide(double_divide(identity,X1),identity) = double_divide(identity,double_divide(X1,identity)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
double_divide(double_divide(identity,X1),double_divide(identity,double_divide(X1,identity))) = identity,
inference(spm,[status(thm)],[c_0_8,c_0_14]) ).
cnf(c_0_16,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(X1,identity),identity))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_17,plain,
double_divide(double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))),X3) = identity,
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_18,plain,
double_divide(double_divide(double_divide(X1,identity),identity),identity) = double_divide(identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_15]),c_0_10]),c_0_10]) ).
cnf(c_0_19,plain,
double_divide(X1,double_divide(double_divide(identity,X2),double_divide(identity,double_divide(X2,X1)))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_8]),c_0_10]) ).
cnf(c_0_20,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,X1),identity)),X1) = identity,
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_21,plain,
double_divide(identity,double_divide(identity,double_divide(identity,X1))) = double_divide(X1,identity),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_22,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1))))),double_divide(X4,X3)),identity)) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_11]),c_0_14]) ).
cnf(c_0_23,plain,
double_divide(X1,double_divide(identity,X1)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_14]),c_0_21]),c_0_10]),c_0_18]) ).
cnf(c_0_24,plain,
double_divide(double_divide(X1,identity),identity) = X1,
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_22,c_0_23]),c_0_14]),c_0_11]),c_0_14]),c_0_14]),c_0_21]) ).
cnf(c_0_25,plain,
double_divide(X1,identity) = double_divide(identity,X1),
inference(rw,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_26,plain,
double_divide(double_divide(X1,double_divide(identity,double_divide(X2,double_divide(identity,X1)))),identity) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_8]),c_0_10]) ).
cnf(c_0_27,plain,
double_divide(double_divide(X1,identity),X1) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_23]),c_0_10]),c_0_10]) ).
cnf(c_0_28,plain,
double_divide(identity,double_divide(X1,identity)) = X1,
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
double_divide(identity,double_divide(X1,double_divide(identity,double_divide(X2,double_divide(identity,X1))))) = X2,
inference(rw,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_30,plain,
double_divide(double_divide(X1,X2),double_divide(identity,double_divide(X2,X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_27]),c_0_14]),c_0_28]),c_0_25]) ).
cnf(c_0_31,plain,
double_divide(X1,X2) = double_divide(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_10]),c_0_28]) ).
cnf(c_0_32,plain,
double_divide(identity,double_divide(identity,X1)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_33,plain,
double_divide(identity,double_divide(X1,double_divide(X1,double_divide(identity,X2)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_29]),c_0_31]) ).
cnf(c_0_34,plain,
double_divide(X1,double_divide(X1,double_divide(identity,X2))) = double_divide(identity,X2),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,plain,
double_divide(identity,double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1))))) = X3,
inference(rw,[status(thm)],[c_0_11,c_0_25]) ).
cnf(c_0_36,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_37,plain,
double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,identity))) = X2,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(X1,identity),X2)) = X2,
inference(spm,[status(thm)],[c_0_37,c_0_31]) ).
cnf(c_0_39,plain,
double_divide(X1,double_divide(identity,double_divide(X2,double_divide(identity,X1)))) = double_divide(identity,X2),
inference(spm,[status(thm)],[c_0_36,c_0_29]) ).
cnf(c_0_40,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_41,plain,
double_divide(double_divide(identity,X1),double_divide(identity,X2)) = double_divide(identity,double_divide(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_42,plain,
double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1)))) = double_divide(identity,X3),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_43,plain,
double_divide(identity,double_divide(double_divide(identity,X1),X2)) = double_divide(double_divide(identity,X2),X1),
inference(spm,[status(thm)],[c_0_41,c_0_36]) ).
cnf(c_0_44,plain,
double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X3))) = double_divide(X3,double_divide(identity,X2)),
inference(spm,[status(thm)],[c_0_36,c_0_42]) ).
cnf(c_0_45,plain,
double_divide(identity,double_divide(X1,double_divide(identity,X2))) = double_divide(X2,double_divide(identity,X1)),
inference(spm,[status(thm)],[c_0_36,c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
prove_these_axioms ).
cnf(c_0_47,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_48,plain,
double_divide(X1,double_divide(identity,double_divide(X2,double_divide(X1,X3)))) = double_divide(X2,double_divide(identity,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_31]) ).
cnf(c_0_49,plain,
double_divide(double_divide(identity,X1),double_divide(X2,double_divide(identity,X3))) = double_divide(identity,double_divide(double_divide(X3,double_divide(identity,X2)),X1)),
inference(spm,[status(thm)],[c_0_41,c_0_45]) ).
cnf(c_0_50,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(b4,a4),identity) != double_divide(double_divide(a4,b4),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_6]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]) ).
cnf(c_0_51,plain,
double_divide(double_divide(identity,X1),double_divide(X2,identity)) = double_divide(identity,double_divide(X2,X1)),
inference(spm,[status(thm)],[c_0_41,c_0_31]) ).
cnf(c_0_52,plain,
double_divide(X1,double_divide(double_divide(X2,double_divide(identity,X1)),X3)) = double_divide(double_divide(identity,X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_36]),c_0_32]) ).
cnf(c_0_53,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(a4,b4),identity) != double_divide(double_divide(b4,a4),identity)
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(rw,[status(thm)],[c_0_50,c_0_8]) ).
cnf(c_0_54,plain,
double_divide(double_divide(X1,double_divide(identity,X2)),double_divide(X3,identity)) = double_divide(identity,double_divide(X3,double_divide(X2,double_divide(identity,X1)))),
inference(spm,[status(thm)],[c_0_51,c_0_45]) ).
cnf(c_0_55,plain,
double_divide(double_divide(X1,double_divide(identity,X2)),X3) = double_divide(X2,double_divide(double_divide(identity,X3),X1)),
inference(spm,[status(thm)],[c_0_36,c_0_52]) ).
cnf(c_0_56,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(a4,b4),identity) != double_divide(double_divide(b4,a4),identity)
| double_divide(double_divide(a2,identity),identity) != a2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_10])]) ).
cnf(c_0_57,plain,
double_divide(double_divide(identity,double_divide(X1,X2)),X3) = double_divide(X2,double_divide(identity,double_divide(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_52]),c_0_36]) ).
cnf(c_0_58,plain,
double_divide(identity,double_divide(X1,double_divide(X2,double_divide(identity,X3)))) = double_divide(X2,double_divide(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_40]) ).
cnf(c_0_59,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(a4,b4),identity) != double_divide(double_divide(b4,a4),identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_24])]) ).
cnf(c_0_60,plain,
double_divide(double_divide(X1,X2),double_divide(X3,double_divide(X2,X1))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_51]),c_0_41]),c_0_31]),c_0_36]) ).
cnf(c_0_61,plain,
double_divide(double_divide(X1,double_divide(X2,X3)),X4) = double_divide(X3,double_divide(double_divide(X4,X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_55]),c_0_36]) ).
cnf(c_0_62,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))))
| double_divide(identity,double_divide(a4,b4)) != double_divide(identity,double_divide(b4,a4)) ),
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_59,c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_25]) ).
cnf(c_0_63,plain,
double_divide(double_divide(X1,X2),X3) = double_divide(X3,double_divide(X2,X1)),
inference(spm,[status(thm)],[c_0_36,c_0_60]) ).
cnf(c_0_64,plain,
double_divide(double_divide(double_divide(X1,X2),X3),X4) = double_divide(X2,double_divide(double_divide(X4,X1),X3)),
inference(spm,[status(thm)],[c_0_61,c_0_31]) ).
cnf(c_0_65,negated_conjecture,
double_divide(identity,double_divide(a3,double_divide(identity,double_divide(c3,b3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_31]),c_0_31])]) ).
cnf(c_0_66,plain,
double_divide(X1,double_divide(X2,double_divide(X3,double_divide(X1,X4)))) = double_divide(X3,double_divide(X2,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_48]),c_0_58]) ).
cnf(c_0_67,plain,
double_divide(X1,double_divide(double_divide(X2,X3),X4)) = double_divide(X3,double_divide(double_divide(X2,X1),X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_63]),c_0_64]) ).
cnf(c_0_68,negated_conjecture,
double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(identity,c3),double_divide(b3,a3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_45]),c_0_31]),c_0_45]),c_0_31]) ).
cnf(c_0_69,plain,
double_divide(double_divide(X1,X2),double_divide(X3,X4)) = double_divide(double_divide(X1,X3),double_divide(X2,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_66]) ).
cnf(c_0_70,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP103-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n007.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 : Tue Aug 29 02:06:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.59 start to proof: theBenchmark
% 1.33/1.43 % Version : CSE_E---1.5
% 1.33/1.43 % Problem : theBenchmark.p
% 1.33/1.43 % Proof found
% 1.33/1.43 % SZS status Theorem for theBenchmark.p
% 1.33/1.43 % SZS output start Proof
% See solution above
% 1.33/1.44 % Total time : 0.837000 s
% 1.33/1.44 % SZS output end Proof
% 1.33/1.44 % Total time : 0.839000 s
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