TSTP Solution File: GRP539-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP539-1 : TPTP v8.1.2. Released v2.6.0.
% 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 00:21:30 EDT 2023
% Result : Unsatisfiable 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 37 unt; 7 typ; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 5 ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 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,
identity: $i ).
tff(decl_26,type,
a3: $i ).
tff(decl_27,type,
b3: $i ).
tff(decl_28,type,
c3: $i ).
cnf(inverse,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(identity,axiom,
identity = divide(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(single_axiom,axiom,
divide(divide(X1,X2),divide(divide(X1,X3),X2)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c_0_5,axiom,
inverse(X1) = divide(divide(X2,X2),X1),
inverse ).
cnf(c_0_6,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_7,axiom,
multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
multiply ).
cnf(c_0_8,plain,
divide(identity,X1) = inverse(X1),
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,axiom,
divide(divide(X1,X2),divide(divide(X1,X3),X2)) = X3,
single_axiom ).
cnf(c_0_10,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_6]),c_0_8]) ).
cnf(c_0_11,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_12,plain,
divide(X1,divide(divide(divide(X2,X3),X4),divide(divide(X2,X1),X3))) = X4,
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_13,plain,
divide(X1,identity) = multiply(X1,identity),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_6]),c_0_13]) ).
cnf(c_0_15,plain,
divide(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_15]),c_0_13]),c_0_14]) ).
cnf(c_0_17,plain,
multiply(divide(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_6]),c_0_8]),c_0_10]) ).
cnf(c_0_18,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_19,plain,
divide(X1,multiply(X1,X2)) = inverse(X2),
inference(spm,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_20,plain,
multiply(X1,divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,plain,
divide(X1,multiply(identity,X2)) = multiply(X1,inverse(X2)),
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_22,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_6]) ).
cnf(c_0_23,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
divide(X1,divide(X2,X3)) = multiply(X1,divide(X3,X2)),
inference(spm,[status(thm)],[c_0_10,c_0_23]) ).
cnf(c_0_26,plain,
divide(multiply(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_24]),c_0_10]) ).
cnf(c_0_27,plain,
multiply(divide(X1,X2),multiply(X2,divide(X3,X1))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_25]),c_0_25]) ).
cnf(c_0_28,plain,
divide(X1,multiply(X2,divide(X1,X3))) = divide(X3,X2),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_30,plain,
multiply(X1,divide(X2,X3)) = divide(multiply(X1,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_19]),c_0_24]),c_0_25]) ).
cnf(c_0_31,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
prove_these_axioms_3 ).
cnf(c_0_32,plain,
multiply(divide(X1,X2),X3) = divide(multiply(X3,X1),X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_10]),c_0_10]) ).
cnf(c_0_34,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_35,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_10]),c_0_10]),c_0_33]),c_0_33]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP539-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 22:57:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.57 % Version : CSE_E---1.5
% 0.19/0.57 % Problem : theBenchmark.p
% 0.19/0.57 % Proof found
% 0.19/0.57 % SZS status Theorem for theBenchmark.p
% 0.19/0.57 % SZS output start Proof
% See solution above
% 0.19/0.58 % Total time : 0.012000 s
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58 % Total time : 0.014000 s
%------------------------------------------------------------------------------