TSTP Solution File: GRP072-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP072-1 : 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 : n009.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 00:15:29 EDT 2023
% Result : Unsatisfiable 0.51s 0.95s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 13
% Syntax : Number of formulae : 82 ( 65 unt; 10 typ; 0 def)
% Number of atoms : 82 ( 81 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 18 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 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 : 200 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
divide: ( $i * $i ) > $i ).
tff(decl_23,type,
inverse: $i > $i ).
tff(decl_24,type,
multiply: ( $i * $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(divide(inverse(divide(X1,X2)),divide(divide(X3,X4),X1)),divide(X4,X3)) = X2,
file('/export/starexec/sandbox2/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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,inverse(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_3,axiom,
divide(divide(inverse(divide(X1,X2)),divide(divide(X3,X4),X1)),divide(X4,X3)) = X2,
single_axiom ).
cnf(c_0_4,plain,
divide(divide(inverse(X1),divide(divide(X2,X3),divide(inverse(divide(X4,X1)),divide(divide(X5,X6),X4)))),divide(X3,X2)) = divide(X6,X5),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
divide(divide(X1,X2),divide(inverse(X3),divide(divide(X2,X1),divide(inverse(divide(X4,X3)),divide(divide(X5,X6),X4))))) = divide(X5,X6),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_4]),c_0_4]) ).
cnf(c_0_6,plain,
divide(divide(X1,X2),divide(inverse(X3),divide(divide(X2,X1),divide(inverse(divide(X4,X3)),divide(X5,X4))))) = X5,
inference(spm,[status(thm)],[c_0_5,c_0_3]) ).
cnf(c_0_7,plain,
divide(divide(divide(divide(divide(X1,X2),inverse(divide(X2,X3))),X4),inverse(divide(X4,X5))),divide(inverse(X3),X5)) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_3]) ).
cnf(c_0_8,plain,
divide(divide(X1,inverse(divide(divide(inverse(X2),X3),X4))),divide(inverse(X3),X4)) = divide(divide(X1,X5),inverse(divide(X5,X2))),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_9,plain,
divide(divide(divide(divide(divide(X1,X2),inverse(divide(X2,X3))),divide(inverse(X4),X3)),X5),inverse(divide(X5,X4))) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
divide(divide(inverse(divide(divide(X1,X2),X3)),X4),divide(divide(divide(X2,X1),X5),inverse(divide(X5,X4)))) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_11,plain,
divide(divide(X1,X2),inverse(divide(X2,X3))) = divide(divide(X1,X4),inverse(divide(X4,X3))),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_12,plain,
divide(divide(divide(divide(divide(X1,divide(inverse(X2),X3)),X4),inverse(divide(X4,X2))),X5),inverse(divide(X5,X3))) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_13,plain,
divide(divide(inverse(X1),divide(divide(X2,X3),divide(inverse(divide(divide(X4,X5),X1)),X6))),divide(X3,X2)) = divide(divide(divide(X5,X4),X7),inverse(divide(X7,X6))),
inference(spm,[status(thm)],[c_0_3,c_0_10]) ).
cnf(c_0_14,plain,
divide(divide(inverse(divide(inverse(divide(X1,X2)),X3)),divide(divide(X4,X5),inverse(divide(X5,X2)))),divide(X1,X4)) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_11]) ).
cnf(c_0_15,plain,
divide(X1,inverse(divide(inverse(divide(divide(inverse(X2),X3),X4)),X2))) = divide(X1,divide(inverse(X3),X4)),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_16,plain,
divide(divide(divide(X1,X2),X3),inverse(divide(X3,divide(divide(X4,X5),divide(X2,X1))))) = divide(X5,X4),
inference(spm,[status(thm)],[c_0_4,c_0_13]) ).
cnf(c_0_17,plain,
inverse(divide(inverse(divide(divide(inverse(X1),X2),X3)),X1)) = divide(inverse(X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]) ).
cnf(c_0_18,plain,
divide(inverse(divide(X1,divide(divide(X2,X3),divide(X4,X5)))),divide(divide(X5,X4),X1)) = divide(X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_16]),c_0_4]) ).
cnf(c_0_19,plain,
inverse(divide(inverse(X1),divide(X2,X1))) = divide(inverse(divide(divide(X3,X4),X2)),divide(X4,X3)),
inference(spm,[status(thm)],[c_0_17,c_0_3]) ).
cnf(c_0_20,plain,
divide(inverse(divide(X1,divide(X2,divide(X3,X4)))),divide(divide(X4,X3),X1)) = X2,
inference(spm,[status(thm)],[c_0_18,c_0_9]) ).
cnf(c_0_21,plain,
inverse(divide(inverse(X1),divide(X2,X1))) = inverse(divide(inverse(X3),divide(X2,X3))),
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_22,plain,
divide(inverse(divide(inverse(X1),divide(X2,X1))),divide(divide(X3,X4),inverse(divide(X4,X3)))) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
divide(inverse(divide(X1,X2)),divide(divide(X3,divide(X4,X5)),X1)) = inverse(divide(X3,divide(X2,divide(X5,X4)))),
inference(spm,[status(thm)],[c_0_20,c_0_20]) ).
cnf(c_0_24,plain,
inverse(divide(X1,divide(divide(X2,divide(divide(X3,X4),X1)),divide(X4,X3)))) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
divide(inverse(divide(X1,X2)),divide(X3,X1)) = divide(inverse(divide(X4,X2)),divide(X3,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_11]),c_0_4]) ).
cnf(c_0_26,plain,
inverse(inverse(divide(X1,divide(X2,inverse(divide(inverse(a1),divide(X2,a1))))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_23]),c_0_19]) ).
cnf(c_0_27,plain,
inverse(inverse(divide(X1,divide(X2,inverse(divide(inverse(X3),divide(X2,X3))))))) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_28,plain,
inverse(inverse(divide(X1,divide(inverse(divide(X2,X3)),divide(X3,X2))))) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_16]) ).
cnf(c_0_29,plain,
inverse(inverse(divide(inverse(X1),divide(inverse(divide(X2,X3)),X1)))) = inverse(divide(X3,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_30,plain,
inverse(divide(divide(X1,X2),inverse(X2))) = inverse(divide(divide(X1,X3),inverse(X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_21]),c_0_29]) ).
cnf(c_0_31,plain,
divide(inverse(X1),inverse(X1)) = divide(inverse(X2),inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_30]),c_0_17]) ).
cnf(c_0_32,plain,
divide(inverse(X1),inverse(X1)) = divide(X2,X2),
inference(spm,[status(thm)],[c_0_31,c_0_27]) ).
cnf(c_0_33,plain,
divide(a1,a1) = divide(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_32]),c_0_32]) ).
cnf(c_0_34,plain,
divide(X1,X1) = divide(X2,X2),
inference(spm,[status(thm)],[c_0_33,c_0_33]) ).
cnf(c_0_35,plain,
divide(inverse(X1),inverse(divide(X1,X2))) = divide(inverse(X3),inverse(divide(X3,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_11]),c_0_17]) ).
cnf(c_0_36,plain,
inverse(divide(X1,divide(divide(X2,X2),divide(X3,X4)))) = divide(divide(X4,X3),X1),
inference(spm,[status(thm)],[c_0_24,c_0_34]) ).
cnf(c_0_37,plain,
inverse(inverse(divide(X1,divide(inverse(X2),inverse(divide(X2,divide(inverse(inverse(a1)),a1))))))) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_38,plain,
inverse(divide(X1,divide(X2,X2))) = divide(divide(X3,X3),X1),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_39,plain,
inverse(inverse(divide(divide(X1,X2),divide(inverse(inverse(a1)),a1)))) = inverse(divide(X2,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_40,plain,
divide(X1,X1) = divide(divide(a1,a1),divide(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_38]),c_0_38]) ).
cnf(c_0_41,plain,
inverse(divide(divide(divide(a1,inverse(inverse(a1))),X1),inverse(divide(X1,X2)))) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_39,c_0_3]) ).
cnf(c_0_42,plain,
divide(X1,X1) = divide(divide(X2,X2),divide(X3,X3)),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
cnf(c_0_43,plain,
divide(divide(a1,a1),divide(divide(a1,inverse(inverse(a1))),X1)) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_38]),c_0_42]),c_0_38]) ).
cnf(c_0_44,plain,
inverse(divide(a1,inverse(inverse(a1)))) = inverse(inverse(divide(a1,a1))),
inference(spm,[status(thm)],[c_0_39,c_0_33]) ).
cnf(c_0_45,plain,
divide(X1,X1) = divide(divide(X2,X2),divide(a1,a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_40]),c_0_4]) ).
cnf(c_0_46,plain,
inverse(inverse(inverse(divide(a1,a1)))) = divide(a1,a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_34]),c_0_40]),c_0_44]) ).
cnf(c_0_47,plain,
inverse(divide(a1,a1)) = divide(a1,a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_43]),c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_48,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_49,axiom,
multiply(X1,X2) = divide(X1,inverse(X2)),
multiply ).
cnf(c_0_50,plain,
inverse(divide(inverse(divide(divide(X1,X1),X2)),X3)) = divide(inverse(inverse(X3)),X2),
inference(spm,[status(thm)],[c_0_17,c_0_34]) ).
cnf(c_0_51,plain,
inverse(divide(X1,X1)) = divide(X1,X1),
inference(spm,[status(thm)],[c_0_47,c_0_34]) ).
cnf(c_0_52,plain,
inverse(divide(divide(X1,X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_42]),c_0_38]),c_0_42]),c_0_36]) ).
cnf(c_0_53,negated_conjecture,
( divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(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)],[c_0_48,c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]),c_0_49]) ).
cnf(c_0_54,plain,
divide(inverse(inverse(X1)),X1) = divide(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_52]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2 ),
inference(sr,[status(thm)],[c_0_53,c_0_31]) ).
cnf(c_0_56,plain,
divide(inverse(divide(X1,X2)),inverse(X1)) = divide(inverse(divide(X3,X2)),inverse(X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_35]),c_0_4]) ).
cnf(c_0_57,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_54]),c_0_7]) ).
cnf(c_0_58,negated_conjecture,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(divide(inverse(X1),inverse(X1)),inverse(a2)) != a2 ),
inference(spm,[status(thm)],[c_0_55,c_0_31]) ).
cnf(c_0_59,plain,
inverse(divide(inverse(divide(divide(inverse(divide(X1,X2)),inverse(X1)),X3)),divide(X4,X2))) = divide(inverse(inverse(X4)),X3),
inference(spm,[status(thm)],[c_0_17,c_0_56]) ).
cnf(c_0_60,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_52]),c_0_57]) ).
cnf(c_0_61,negated_conjecture,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(divide(X1,X1),inverse(a2)) != a2 ),
inference(spm,[status(thm)],[c_0_58,c_0_27]) ).
cnf(c_0_62,plain,
divide(X1,divide(X2,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_38]),c_0_52]) ).
cnf(c_0_63,plain,
divide(divide(X1,X2),divide(X3,divide(divide(X2,X4),inverse(X4)))) = divide(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_57]),c_0_60]),c_0_60]),c_0_60]) ).
cnf(c_0_64,plain,
inverse(divide(inverse(X1),divide(divide(X2,divide(divide(X3,X4),inverse(divide(X4,X3)))),X1))) = X2,
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_65,negated_conjecture,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3))
| divide(divide(X1,X1),inverse(a2)) != a2 ),
inference(rw,[status(thm)],[c_0_61,c_0_60]) ).
cnf(c_0_66,plain,
divide(divide(X1,X1),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_60,c_0_62]) ).
cnf(c_0_67,plain,
divide(divide(X1,X2),divide(X3,X2)) = divide(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_62]),c_0_51]),c_0_62]) ).
cnf(c_0_68,plain,
divide(divide(X1,X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_60]),c_0_60]),c_0_34]),c_0_62]) ).
cnf(c_0_69,negated_conjecture,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_57])]) ).
cnf(c_0_70,plain,
divide(divide(X1,inverse(X2)),X3) = divide(X1,divide(X3,X2)),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP072-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.06/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 21:11:05 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.48/0.56 start to proof: theBenchmark
% 0.51/0.95 % Version : CSE_E---1.5
% 0.51/0.95 % Problem : theBenchmark.p
% 0.51/0.95 % Proof found
% 0.51/0.95 % SZS status Theorem for theBenchmark.p
% 0.51/0.95 % SZS output start Proof
% See solution above
% 0.51/0.95 % Total time : 0.381000 s
% 0.51/0.95 % SZS output end Proof
% 0.51/0.95 % Total time : 0.384000 s
%------------------------------------------------------------------------------