TSTP Solution File: GRP063-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP063-1 : 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 : n025.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 00:15:27 EDT 2023
% Result : Unsatisfiable 0.19s 0.62s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 61 ( 46 unt; 10 typ; 0 def)
% Number of atoms : 60 ( 59 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 15 ~; 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
divide: ( $i * $i ) > $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $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 ).
cnf(single_axiom,axiom,
divide(X1,divide(divide(divide(divide(X1,X1),X2),X3),divide(divide(divide(X1,X1),X1),X3))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(inverse,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_0_4,axiom,
divide(X1,divide(divide(divide(divide(X1,X1),X2),X3),divide(divide(divide(X1,X1),X1),X3))) = X2,
single_axiom ).
cnf(c_0_5,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
inverse ).
cnf(c_0_6,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
multiply ).
cnf(c_0_7,plain,
divide(X1,divide(divide(inverse(X2),X3),divide(inverse(X1),X3))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4,c_0_5]),c_0_5]) ).
cnf(c_0_8,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_9,plain,
divide(inverse(divide(X1,X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_10,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_5]),c_0_8]),c_0_8]) ).
cnf(c_0_11,plain,
inverse(multiply(divide(inverse(X1),X2),X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_7]),c_0_9]),c_0_8]) ).
cnf(c_0_12,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_10,c_0_10]) ).
cnf(c_0_13,plain,
inverse(multiply(inverse(X1),X1)) = divide(X2,X2),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_14,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
cnf(c_0_15,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_13]),c_0_8]) ).
cnf(c_0_16,plain,
multiply(divide(X1,X1),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_17,plain,
multiply(divide(a1,a1),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_18,plain,
divide(X1,X1) = divide(X2,X2),
inference(spm,[status(thm)],[c_0_13,c_0_13]) ).
cnf(c_0_19,plain,
inverse(multiply(multiply(inverse(X1),X2),inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_8]) ).
cnf(c_0_20,plain,
multiply(divide(X1,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
inverse(multiply(X1,inverse(multiply(X2,X1)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_10]),c_0_16]),c_0_20]) ).
cnf(c_0_22,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_23,plain,
divide(X1,divide(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_18]) ).
cnf(c_0_24,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_10]),c_0_16]),c_0_20]) ).
cnf(c_0_25,plain,
divide(X1,multiply(inverse(X2),X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_23]),c_0_23]),c_0_8]) ).
cnf(c_0_26,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_27,plain,
inverse(inverse(multiply(X1,X2))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_28,plain,
divide(multiply(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_10]),c_0_16]),c_0_20]) ).
cnf(c_0_29,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_26]),c_0_27]) ).
cnf(c_0_30,plain,
divide(multiply(inverse(X1),X1),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_31,plain,
inverse(multiply(X1,X2)) = divide(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_28,c_0_24]) ).
cnf(c_0_32,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_21,c_0_29]) ).
cnf(c_0_33,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,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)) ),
prove_these_axioms ).
cnf(c_0_35,plain,
multiply(multiply(inverse(X1),X1),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_8,c_0_30]) ).
cnf(c_0_36,plain,
divide(X1,divide(X2,divide(inverse(X1),divide(divide(inverse(X2),X3),divide(X4,X3))))) = X4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_7]),c_0_16]),c_0_17]) ).
cnf(c_0_37,plain,
divide(X1,divide(inverse(X2),X3)) = multiply(X1,multiply(X3,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_31]) ).
cnf(c_0_38,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| inverse(inverse(a2)) != a2 ),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
divide(X1,multiply(X2,multiply(divide(divide(inverse(X2),X3),divide(X4,X3)),X1))) = X4,
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
multiply(X1,divide(X2,X3)) = divide(X1,divide(X3,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(divide(a1,a1),a2) != a2 ),
inference(rw,[status(thm)],[c_0_39,c_0_16]) ).
cnf(c_0_43,plain,
multiply(divide(X1,X2),X2) = X1,
inference(rw,[status(thm)],[c_0_29,c_0_33]) ).
cnf(c_0_44,plain,
divide(multiply(divide(X1,X2),multiply(X2,X3)),X3) = 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_5,c_0_40]),c_0_41]),c_0_23]),c_0_41]),c_0_37]),c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_17])]) ).
cnf(c_0_46,plain,
multiply(inverse(X1),X1) = divide(a1,a1),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_47,plain,
multiply(divide(X1,X2),multiply(X2,X3)) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_46])]) ).
cnf(c_0_49,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_14]),c_0_8]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP063-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n025.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 20:18:10 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.60 start to proof: theBenchmark
% 0.19/0.62 % Version : CSE_E---1.5
% 0.19/0.62 % Problem : theBenchmark.p
% 0.19/0.62 % Proof found
% 0.19/0.62 % SZS status Theorem for theBenchmark.p
% 0.19/0.62 % SZS output start Proof
% See solution above
% 0.19/0.63 % Total time : 0.019000 s
% 0.19/0.63 % SZS output end Proof
% 0.19/0.63 % Total time : 0.022000 s
%------------------------------------------------------------------------------