TSTP Solution File: GRP093-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP093-1 : 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 : n022.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 00:15:57 EDT 2023
% Result : Unsatisfiable 0.54s 0.60s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of formulae : 57 ( 36 unt; 13 typ; 0 def)
% Number of atoms : 60 ( 59 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 26 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 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 : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
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,
b1: $i ).
tff(decl_28,type,
b2: $i ).
tff(decl_29,type,
a2: $i ).
tff(decl_30,type,
a3: $i ).
tff(decl_31,type,
b3: $i ).
tff(decl_32,type,
c3: $i ).
tff(decl_33,type,
a4: $i ).
tff(decl_34,type,
b4: $i ).
cnf(single_axiom,axiom,
divide(divide(identity,divide(divide(divide(X1,X2),X3),X1)),X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(identity,axiom,
identity = divide(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
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(inverse,axiom,
inverse(X1) = divide(identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_5,axiom,
divide(divide(identity,divide(divide(divide(X1,X2),X3),X1)),X3) = X2,
single_axiom ).
cnf(c_0_6,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_7,plain,
divide(divide(identity,divide(divide(identity,X1),X2)),X1) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
divide(divide(identity,divide(identity,X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
divide(divide(identity,divide(X1,identity)),identity) = divide(identity,X1),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_10,plain,
divide(identity,divide(identity,X1)) = divide(X1,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_9]) ).
cnf(c_0_11,plain,
divide(divide(identity,divide(X1,identity)),X2) = divide(divide(identity,X2),X1),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_12,plain,
divide(divide(identity,X1),identity) = divide(identity,divide(X1,identity)),
inference(spm,[status(thm)],[c_0_10,c_0_10]) ).
cnf(c_0_13,plain,
divide(identity,divide(X1,identity)) = divide(identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_6]),c_0_6]),c_0_12]) ).
cnf(c_0_14,plain,
divide(divide(X1,identity),identity) = X1,
inference(rw,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_15,plain,
divide(X1,identity) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_13]),c_0_10]),c_0_14]) ).
cnf(c_0_16,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_17,axiom,
inverse(X1) = divide(identity,X1),
inverse ).
cnf(c_0_18,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
multiply ).
cnf(c_0_19,plain,
divide(identity,divide(identity,X1)) = X1,
inference(rw,[status(thm)],[c_0_10,c_0_15]) ).
cnf(c_0_20,plain,
divide(identity,divide(divide(X1,X2),X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_15]),c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(divide(divide(identity,b2),divide(identity,b2)),divide(identity,a2)) != a2
| divide(divide(identity,b1),divide(identity,b1)) != divide(divide(identity,a1),divide(identity,a1))
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]),c_0_17]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_22,plain,
divide(divide(identity,divide(X1,X2)),X2) = divide(identity,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_19]),c_0_15]) ).
cnf(c_0_23,plain,
divide(divide(X1,X2),X1) = divide(identity,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_20]),c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4))
| divide(identity,divide(identity,a2)) != a2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_6]),c_0_6]),c_0_6])]) ).
cnf(c_0_25,plain,
divide(identity,divide(X1,X2)) = divide(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4))
| divide(a2,identity) != a2 ),
inference(rw,[status(thm)],[c_0_24,c_0_10]) ).
cnf(c_0_27,plain,
divide(divide(X1,divide(divide(X1,X2),X3)),X3) = X2,
inference(rw,[status(thm)],[c_0_5,c_0_25]) ).
cnf(c_0_28,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_19]) ).
cnf(c_0_29,negated_conjecture,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_15])]) ).
cnf(c_0_30,plain,
divide(divide(X1,divide(X2,X3)),X3) = divide(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(divide(identity,c3),b3))
| divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4)) ),
inference(rw,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_32,plain,
divide(divide(identity,X1),X2) = divide(divide(identity,X2),X1),
inference(rw,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_33,plain,
divide(X1,divide(X2,divide(X3,X1))) = divide(X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_30]),c_0_25]) ).
cnf(c_0_34,negated_conjecture,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(divide(identity,b3),c3))
| divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4)) ),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
divide(X1,divide(identity,X2)) = divide(X2,divide(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_32]),c_0_25]) ).
cnf(c_0_36,plain,
divide(divide(identity,X1),divide(X2,X3)) = divide(divide(X3,X2),X1),
inference(spm,[status(thm)],[c_0_32,c_0_25]) ).
cnf(c_0_37,plain,
divide(X1,divide(X2,divide(identity,X3))) = divide(divide(X1,X3),X2),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_38,negated_conjecture,
divide(c3,divide(divide(identity,a3),b3)) != divide(a3,divide(divide(identity,b3),c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_25]),c_0_32]),c_0_35])]) ).
cnf(c_0_39,plain,
divide(X1,divide(X2,X3)) = divide(X3,divide(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_33]) ).
cnf(c_0_40,plain,
divide(divide(divide(identity,X1),X2),X3) = divide(divide(divide(identity,X2),X3),X1),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
divide(b3,divide(divide(identity,a3),c3)) != divide(a3,divide(divide(identity,b3),c3)),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
divide(X1,divide(divide(identity,X2),X3)) = divide(X2,divide(divide(identity,X3),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_40]),c_0_25]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP093-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 01:18:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.54/0.60 % Version : CSE_E---1.5
% 0.54/0.60 % Problem : theBenchmark.p
% 0.54/0.60 % Proof found
% 0.54/0.60 % SZS status Theorem for theBenchmark.p
% 0.54/0.60 % SZS output start Proof
% See solution above
% 0.54/0.61 % Total time : 0.024000 s
% 0.54/0.61 % SZS output end Proof
% 0.54/0.61 % Total time : 0.026000 s
%------------------------------------------------------------------------------