TSTP Solution File: GRP060-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP060-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n019.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 00:15:25 EDT 2023
% Result : Unsatisfiable 0.85s 0.94s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 11
% Syntax : Number of formulae : 74 ( 62 unt; 9 typ; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 180 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
inverse: $i > $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
a1: $i ).
tff(decl_25,type,
b1: $i ).
tff(decl_26,type,
b2: $i ).
tff(decl_27,type,
a2: $i ).
tff(decl_28,type,
a3: $i ).
tff(decl_29,type,
b3: $i ).
tff(decl_30,type,
c3: $i ).
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X1))))) = X4,
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(c_0_2,axiom,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X1))))) = X4,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X4))),inverse(X5))),multiply(X5,multiply(X3,X1))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(X3,inverse(X4))),multiply(X4,multiply(X5,X1))))) = multiply(X6,multiply(multiply(inverse(X6),inverse(multiply(X3,X5))),inverse(X2))),
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(X2,multiply(inverse(X3),inverse(multiply(X4,multiply(X5,multiply(X2,inverse(X3))))))))),inverse(X5))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_6,plain,
multiply(inverse(X1),inverse(multiply(multiply(inverse(X2),inverse(multiply(X3,multiply(X1,multiply(X4,inverse(X2)))))),X3))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_5]) ).
cnf(c_0_7,plain,
multiply(inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(multiply(X3,X1))),multiply(inverse(X4),inverse(multiply(X5,X6))))))),inverse(multiply(X6,multiply(X4,X3)))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_8,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(X4,X1))))) = multiply(inverse(X5),inverse(multiply(X2,multiply(X3,multiply(X4,inverse(X5)))))),
inference(spm,[status(thm)],[c_0_2,c_0_6]) ).
cnf(c_0_9,plain,
multiply(a1,multiply(multiply(inverse(a1),inverse(X1)),inverse(X2))) = multiply(X3,multiply(multiply(inverse(X3),inverse(X1)),inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_7]),c_0_4]),c_0_7]) ).
cnf(c_0_10,plain,
multiply(a1,multiply(multiply(inverse(a1),inverse(multiply(multiply(inverse(X1),inverse(multiply(X2,X3))),X2))),inverse(X1))) = X3,
inference(rw,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_11,plain,
multiply(inverse(X1),inverse(multiply(multiply(X2,inverse(multiply(X3,multiply(X1,multiply(X4,X2))))),X3))) = X4,
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_12,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(X2)),inverse(X3))) = multiply(X4,multiply(multiply(inverse(X4),inverse(X2)),inverse(X3))),
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_13,plain,
multiply(X1,inverse(multiply(inverse(multiply(X2,multiply(X3,X4))),multiply(X5,multiply(multiply(inverse(X5),inverse(X6)),X1))))) = inverse(multiply(X7,multiply(X8,multiply(multiply(inverse(X8),inverse(multiply(X4,X7))),multiply(inverse(X3),inverse(multiply(X6,X2))))))),
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_14,plain,
multiply(X1,multiply(multiply(inverse(X1),inverse(multiply(multiply(inverse(X2),inverse(multiply(X3,X4))),X3))),inverse(X2))) = X4,
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_15,plain,
multiply(inverse(X1),inverse(multiply(multiply(a1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),a1))))),X2))) = multiply(inverse(X1),inverse(X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_8]) ).
cnf(c_0_16,plain,
multiply(multiply(a1,inverse(multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(a1,multiply(multiply(inverse(a1),inverse(X4)),a1))))),inverse(multiply(X1,multiply(X2,X3)))) = X4,
inference(rw,[status(thm)],[c_0_7,c_0_13]) ).
cnf(c_0_17,plain,
inverse(multiply(multiply(a1,inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),a1))))),X1)) = inverse(X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]) ).
cnf(c_0_18,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,multiply(X4,X1))))) = multiply(X5,inverse(multiply(X2,multiply(X3,multiply(X4,X5))))),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_19,plain,
multiply(multiply(a1,inverse(multiply(inverse(X1),multiply(a1,multiply(multiply(inverse(a1),inverse(X2)),a1))))),inverse(X1)) = X2,
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_20,plain,
inverse(multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),X1))))),X2)) = inverse(X4),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(X4)),X1))))),X2) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_19]) ).
cnf(c_0_22,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(multiply(inverse(X2),inverse(X3)),inverse(X4))),multiply(X4,X3)))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_21]) ).
cnf(c_0_23,plain,
multiply(X1,multiply(inverse(X1),inverse(X2))) = multiply(X3,multiply(inverse(X3),inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_22]),c_0_22]) ).
cnf(c_0_24,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_22]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(X2,inverse(X2))) = multiply(X3,multiply(inverse(X3),inverse(inverse(X1)))),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(a1,inverse(a1))),multiply(multiply(inverse(X2),inverse(X3)),X3)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_25]),c_0_25]) ).
cnf(c_0_27,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(a1,inverse(a1))),multiply(multiply(X3,inverse(X3)),inverse(X2))))) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_28,plain,
multiply(X1,inverse(multiply(multiply(multiply(X2,inverse(X2)),multiply(a1,inverse(a1))),multiply(a1,inverse(a1))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_25]) ).
cnf(c_0_29,plain,
multiply(X1,inverse(multiply(inverse(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),inverse(multiply(X4,X2))),X5)))),multiply(X6,multiply(multiply(inverse(X6),inverse(X4)),X1))))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_30,plain,
multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),multiply(a1,inverse(a1))),multiply(a1,inverse(a1)))) = multiply(X1,multiply(a1,inverse(a1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_28]),c_0_25]) ).
cnf(c_0_31,plain,
multiply(multiply(multiply(X1,inverse(X1)),multiply(a1,inverse(a1))),multiply(a1,inverse(a1))) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_29]) ).
cnf(c_0_32,plain,
multiply(multiply(X1,inverse(multiply(X2,multiply(X3,multiply(multiply(X4,inverse(X4)),X1))))),X2) = inverse(X3),
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_33,plain,
multiply(X1,inverse(multiply(a1,inverse(a1)))) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_34,plain,
inverse(multiply(inverse(X1),inverse(multiply(multiply(X2,inverse(X2)),X3)))) = multiply(X3,multiply(X1,multiply(a1,inverse(a1)))),
inference(spm,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_35,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_33,c_0_24]) ).
cnf(c_0_36,plain,
multiply(inverse(multiply(X1,inverse(X1))),multiply(X2,multiply(a1,inverse(a1)))) = inverse(inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_35]) ).
cnf(c_0_37,plain,
multiply(inverse(X1),inverse(multiply(inverse(a1),inverse(inverse(inverse(X1)))))) = a1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_36]),c_0_35]) ).
cnf(c_0_38,plain,
multiply(X1,multiply(inverse(X1),inverse(X2))) = inverse(inverse(inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_37]),c_0_33]) ).
cnf(c_0_39,plain,
inverse(inverse(inverse(multiply(inverse(a1),inverse(inverse(inverse(X1))))))) = multiply(X1,a1),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_40,plain,
multiply(X1,multiply(inverse(X1),multiply(X2,a1))) = inverse(inverse(multiply(X2,a1))),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,plain,
multiply(X1,multiply(inverse(X1),X2)) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_40,c_0_21]) ).
cnf(c_0_42,plain,
multiply(X1,inverse(X1)) = inverse(inverse(inverse(multiply(X2,inverse(X2))))),
inference(spm,[status(thm)],[c_0_38,c_0_35]) ).
cnf(c_0_43,plain,
multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),inverse(multiply(X3,X4))),inverse(X5)),multiply(X6,multiply(multiply(inverse(X6),inverse(multiply(a1,multiply(multiply(inverse(a1),inverse(multiply(X3,X4))),inverse(X5))))),X1))))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_4]),c_0_4]) ).
cnf(c_0_44,plain,
inverse(inverse(multiply(a1,inverse(a1)))) = inverse(multiply(a1,inverse(a1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_41]),c_0_42]) ).
cnf(c_0_45,plain,
inverse(multiply(a1,inverse(a1))) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_43]) ).
cnf(c_0_46,plain,
multiply(X1,multiply(a1,inverse(a1))) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_45]) ).
cnf(c_0_47,plain,
inverse(multiply(X1,inverse(X1))) = multiply(X1,inverse(X1)),
inference(spm,[status(thm)],[c_0_45,c_0_24]) ).
cnf(c_0_48,plain,
multiply(multiply(X1,inverse(X1)),X2) = inverse(inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_46]),c_0_47]) ).
cnf(c_0_49,plain,
multiply(X1,multiply(X2,inverse(X2))) = inverse(inverse(inverse(inverse(X1)))),
inference(rw,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_50,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_48]),c_0_47]),c_0_48]),c_0_49]),c_0_46]) ).
cnf(c_0_51,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_48,c_0_50]) ).
cnf(c_0_52,plain,
inverse(multiply(inverse(X1),inverse(X2))) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_46]),c_0_51]) ).
cnf(c_0_53,plain,
multiply(inverse(X1),X1) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_52]),c_0_24]) ).
cnf(c_0_54,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_53]),c_0_46]),c_0_51]),c_0_50]) ).
cnf(c_0_55,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_46,c_0_24]) ).
cnf(c_0_56,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_57,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_51,c_0_50]) ).
cnf(c_0_58,plain,
multiply(multiply(multiply(inverse(multiply(inverse(X1),inverse(multiply(X2,X3)))),inverse(multiply(X4,X5))),inverse(X6)),inverse(multiply(X3,multiply(X1,multiply(a1,multiply(multiply(inverse(a1),inverse(multiply(X4,X5))),inverse(X6))))))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_4]),c_0_4]) ).
cnf(c_0_59,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_54]),c_0_55]) ).
cnf(c_0_60,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_56,c_0_57])]) ).
cnf(c_0_61,plain,
multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X2,X3))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_52]),c_0_50]),c_0_54]),c_0_55]) ).
cnf(c_0_62,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_60,c_0_53]),c_0_53])]) ).
cnf(c_0_63,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_61]),c_0_50]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP060-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.30 % Computer : n019.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Aug 28 21:29:43 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.14/0.53 start to proof: theBenchmark
% 0.85/0.94 % Version : CSE_E---1.5
% 0.85/0.94 % Problem : theBenchmark.p
% 0.85/0.94 % Proof found
% 0.85/0.94 % SZS status Theorem for theBenchmark.p
% 0.85/0.94 % SZS output start Proof
% See solution above
% 0.85/0.94 % Total time : 0.401000 s
% 0.85/0.94 % SZS output end Proof
% 0.85/0.94 % Total time : 0.403000 s
%------------------------------------------------------------------------------