TSTP Solution File: GRP088-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP088-1 : 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 : 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 00:15:56 EDT 2023
% Result : Unsatisfiable 0.19s 0.58s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 68 ( 49 unt; 12 typ; 0 def)
% Number of atoms : 73 ( 72 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 25 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 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 : 12 ( 12 usr; 9 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 ).
tff(decl_32,type,
a4: $i ).
tff(decl_33,type,
b4: $i ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(inverse,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(single_axiom,axiom,
divide(X1,divide(X2,divide(X3,divide(X1,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(c_0_4,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
multiply ).
cnf(c_0_5,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
inverse ).
cnf(c_0_6,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,axiom,
divide(X1,divide(X2,divide(X3,divide(X1,X2)))) = X3,
single_axiom ).
cnf(c_0_8,plain,
divide(multiply(inverse(X1),X1),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
inverse(divide(X1,multiply(X2,X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_7]),c_0_5]),c_0_6]) ).
cnf(c_0_10,plain,
multiply(divide(X1,X1),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_11,plain,
divide(inverse(divide(X1,X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_12,plain,
multiply(multiply(inverse(X1),X1),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_13,plain,
multiply(divide(a1,a1),multiply(X1,divide(X2,X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_5]),c_0_10]) ).
cnf(c_0_14,plain,
multiply(inverse(divide(X1,X1)),X2) = multiply(divide(a1,a1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_11]),c_0_10]) ).
cnf(c_0_15,plain,
inverse(multiply(X1,inverse(X1))) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_12]),c_0_6]) ).
cnf(c_0_16,plain,
inverse(divide(X1,X1)) = divide(a1,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_13]) ).
cnf(c_0_17,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_15,c_0_15]) ).
cnf(c_0_18,plain,
inverse(multiply(inverse(X1),X1)) = divide(a1,a1),
inference(spm,[status(thm)],[c_0_16,c_0_6]) ).
cnf(c_0_19,plain,
multiply(inverse(X1),X1) = divide(a1,a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_12]),c_0_15]),c_0_18]) ).
cnf(c_0_20,plain,
divide(a1,a1) = divide(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_6]),c_0_15]),c_0_19]) ).
cnf(c_0_21,plain,
divide(X1,divide(divide(X2,divide(X3,X1)),X2)) = X3,
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_22,plain,
divide(X1,X1) = divide(X2,X2),
inference(spm,[status(thm)],[c_0_20,c_0_20]) ).
cnf(c_0_23,plain,
inverse(divide(X1,divide(a1,a1))) = inverse(X1),
inference(spm,[status(thm)],[c_0_9,c_0_19]) ).
cnf(c_0_24,plain,
multiply(X1,divide(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_5]),c_0_6]) ).
cnf(c_0_25,plain,
inverse(divide(X1,divide(X2,X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_26,plain,
multiply(divide(a1,a1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_24]),c_0_25]),c_0_10]) ).
cnf(c_0_27,plain,
multiply(divide(X1,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_28,plain,
divide(X1,divide(divide(X2,divide(X3,divide(X1,X2))),divide(X4,X3))) = X4,
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_29,plain,
divide(X1,divide(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_30,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_5]),c_0_6]),c_0_24]) ).
cnf(c_0_31,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_32,plain,
multiply(divide(X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(a4,b4) != multiply(b4,a4)
| inverse(inverse(a2)) != a2 ),
inference(rw,[status(thm)],[c_0_31,c_0_12]) ).
cnf(c_0_34,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_9,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(a4,b4) != multiply(b4,a4)
| multiply(divide(a1,a1),a2) != a2 ),
inference(rw,[status(thm)],[c_0_33,c_0_10]) ).
cnf(c_0_36,plain,
divide(multiply(X1,X2),X2) = X1,
inference(rw,[status(thm)],[c_0_9,c_0_34]) ).
cnf(c_0_37,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_6]) ).
cnf(c_0_38,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4)
| multiply(divide(a1,a1),a2) != a2 ),
inference(sr,[status(thm)],[c_0_35,c_0_17]) ).
cnf(c_0_39,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_36]) ).
cnf(c_0_40,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(spm,[status(thm)],[c_0_37,c_0_37]) ).
cnf(c_0_41,plain,
divide(X1,divide(inverse(X2),divide(X3,multiply(X1,X2)))) = X3,
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_42,plain,
divide(inverse(X1),X2) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_6]) ).
cnf(c_0_43,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_24,c_0_36]) ).
cnf(c_0_44,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4)
| multiply(divide(X1,X1),a2) != a2 ),
inference(spm,[status(thm)],[c_0_38,c_0_20]) ).
cnf(c_0_45,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_47,plain,
multiply(X1,multiply(X2,divide(X3,multiply(X1,X2)))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_6]) ).
cnf(c_0_48,plain,
divide(multiply(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_49,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
inference(spm,[status(thm)],[c_0_44,c_0_26]) ).
cnf(c_0_50,plain,
multiply(inverse(X1),X2) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_37,c_0_32]) ).
cnf(c_0_51,plain,
inverse(inverse(multiply(X1,X2))) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_10]),c_0_26]) ).
cnf(c_0_52,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_43]),c_0_43])]) ).
cnf(c_0_54,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_6]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(ar,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54]),c_0_43,c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP088-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.08/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 00:43:26 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.58 % Version : CSE_E---1.5
% 0.19/0.58 % Problem : theBenchmark.p
% 0.19/0.58 % Proof found
% 0.19/0.58 % SZS status Theorem for theBenchmark.p
% 0.19/0.58 % SZS output start Proof
% See solution above
% 0.19/0.59 % Total time : 0.015000 s
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time : 0.017000 s
%------------------------------------------------------------------------------