TSTP Solution File: GRP210-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP210-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 00:17:45 EDT 2023
% Result : Unsatisfiable 0.65s 0.71s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 27
% Syntax : Number of formulae : 82 ( 17 unt; 13 typ; 0 def)
% Number of atoms : 190 ( 189 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 206 ( 85 ~; 121 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 67 ( 9 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
sk_c1: $i ).
tff(decl_26,type,
sk_c2: $i ).
tff(decl_27,type,
sk_c10: $i ).
tff(decl_28,type,
sk_c4: $i ).
tff(decl_29,type,
sk_c9: $i ).
tff(decl_30,type,
sk_c5: $i ).
tff(decl_31,type,
sk_c6: $i ).
tff(decl_32,type,
sk_c8: $i ).
tff(decl_33,type,
sk_c7: $i ).
tff(decl_34,type,
sk_c3: $i ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_this_34,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
cnf(prove_this_33,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
cnf(prove_this_26,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_25,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(prove_this_14,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_7,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c7,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_41,negated_conjecture,
( multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| multiply(X2,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X5,X6) != sk_c9
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c9
| multiply(sk_c10,X7) != sk_c9
| multiply(X8,sk_c10) != X7
| inverse(X8) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
cnf(c_0_14,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_15,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_16,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_17,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_18,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
prove_this_34 ).
cnf(c_0_19,negated_conjecture,
( multiply(inverse(sk_c4),sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_33 ).
cnf(c_0_21,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c10
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
( multiply(inverse(sk_c3),sk_c10) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_23,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c4,sk_c9) = sk_c10 ),
prove_this_26 ).
cnf(c_0_24,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
prove_this_6 ).
cnf(c_0_26,negated_conjecture,
( multiply(inverse(sk_c4),sk_c10) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c4) = sk_c10 ),
prove_this_25 ).
cnf(c_0_28,negated_conjecture,
( multiply(inverse(sk_c1),sk_c10) = sk_c2
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c10,sk_c8) = sk_c9 ),
prove_this_14 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c10,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c1,multiply(sk_c2,X1)) = multiply(sk_c10,X1)
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_14,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c2 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
multiply(sk_c10,sk_c10) = sk_c9,
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c9 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c7,sk_c10) = sk_c8 ),
prove_this_7 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_25,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
multiply(inverse(sk_c10),sk_c9) = sk_c10,
inference(spm,[status(thm)],[c_0_17,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( multiply(inverse(sk_c7),sk_c8) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(spm,[status(thm)],[c_0_17,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( sk_c9 = sk_c10
| sk_c8 = sk_c10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_36]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( multiply(inverse(sk_c7),sk_c10) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c7) = sk_c10 ),
prove_this_8 ).
cnf(c_0_42,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c9 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_33])]) ).
cnf(c_0_43,negated_conjecture,
( multiply(inverse(sk_c1),sk_c10) = sk_c2
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_17,c_0_42]) ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c7,sk_c10) = sk_c8 ),
prove_this_15 ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c2
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,negated_conjecture,
( multiply(inverse(sk_c7),sk_c8) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c2
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_17,c_0_45]) ).
cnf(c_0_47,negated_conjecture,
( multiply(inverse(sk_c7),sk_c10) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c2
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_46,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c7) = sk_c10 ),
prove_this_16 ).
cnf(c_0_49,negated_conjecture,
( multiply(X1,X2) != sk_c10
| inverse(X1) != X2
| multiply(X2,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X5,X6) != sk_c9
| inverse(X5) != X6
| multiply(X6,sk_c10) != sk_c9
| multiply(sk_c10,X7) != sk_c9
| multiply(X8,sk_c10) != X7
| inverse(X8) != sk_c10 ),
prove_this_41 ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c2
| inverse(sk_c1) = sk_c2
| sk_c9 = sk_c10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_33])]) ).
cnf(c_0_51,negated_conjecture,
( multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(inverse(X3),sk_c9) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c10 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_49])])]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c2
| sk_c9 = sk_c10 ),
inference(spm,[status(thm)],[c_0_43,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c10,multiply(X1,multiply(X2,sk_c10))) != sk_c9
| multiply(inverse(X3),sk_c10) != sk_c9
| multiply(inverse(X4),sk_c9) != sk_c10
| multiply(X3,inverse(X3)) != sk_c9
| multiply(X4,inverse(X4)) != sk_c10
| inverse(multiply(X1,X2)) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| multiply(X6,sk_c9) != sk_c10
| inverse(X5) != sk_c10
| inverse(X6) != sk_c10 ),
inference(spm,[status(thm)],[c_0_51,c_0_14]) ).
cnf(c_0_54,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
cnf(c_0_55,negated_conjecture,
( sk_c9 = sk_c10
| sk_c10 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_52]),c_0_15]) ).
cnf(c_0_56,negated_conjecture,
( multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9
| multiply(inverse(X2),sk_c10) != sk_c9
| multiply(inverse(X3),sk_c9) != sk_c10
| inverse(multiply(X1,identity)) != sk_c10
| multiply(X2,inverse(X2)) != sk_c9
| multiply(X3,inverse(X3)) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| inverse(X5) != sk_c10 ),
inference(spm,[status(thm)],[c_0_53,c_0_16]) ).
cnf(c_0_57,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_15,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
sk_c10 = identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_55]),c_0_15])]) ).
cnf(c_0_59,negated_conjecture,
( inverse(multiply(inverse(sk_c10),identity)) != sk_c10
| multiply(inverse(X1),sk_c10) != sk_c9
| multiply(inverse(X2),sk_c9) != sk_c10
| multiply(sk_c10,identity) != sk_c9
| multiply(X1,inverse(X1)) != sk_c9
| multiply(X2,inverse(X2)) != sk_c10
| multiply(X3,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| inverse(X4) != sk_c10 ),
inference(spm,[status(thm)],[c_0_56,c_0_15]) ).
cnf(c_0_60,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_16,c_0_57]) ).
cnf(c_0_61,negated_conjecture,
sk_c9 = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_58]),c_0_58]),c_0_16]) ).
cnf(c_0_62,negated_conjecture,
( multiply(inverse(X1),identity) != identity
| multiply(inverse(X2),identity) != identity
| multiply(X3,identity) != identity
| multiply(X4,identity) != identity
| inverse(X3) != identity
| inverse(X4) != identity ),
inference(cn,[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)],[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)],[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_59,c_0_58]),c_0_15]),c_0_58]),c_0_58]),c_0_58]),c_0_58]),c_0_16]),c_0_58]),c_0_58]),c_0_58]),c_0_58]),c_0_58]),c_0_60]),c_0_61]),c_0_61]),c_0_61]),c_0_57]),c_0_61]),c_0_57]),c_0_61]),c_0_61])]) ).
cnf(c_0_63,plain,
multiply(inverse(X1),identity) = inverse(X1),
inference(spm,[status(thm)],[c_0_17,c_0_57]) ).
cnf(c_0_64,negated_conjecture,
( multiply(X1,identity) != identity
| multiply(X2,identity) != identity
| inverse(X3) != identity
| inverse(X4) != identity
| inverse(X1) != identity
| inverse(X2) != identity ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63]),c_0_63]) ).
cnf(c_0_65,negated_conjecture,
( multiply(X1,identity) != identity
| inverse(X2) != identity
| inverse(X3) != identity
| inverse(X1) != identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_15]),c_0_60]),c_0_60])]) ).
cnf(c_0_66,negated_conjecture,
( inverse(X1) != identity
| inverse(X2) != identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_15]),c_0_60]),c_0_60])]) ).
cnf(c_0_67,negated_conjecture,
inverse(X1) != identity,
inference(spm,[status(thm)],[c_0_66,c_0_60]) ).
cnf(c_0_68,plain,
$false,
inference(sr,[status(thm)],[c_0_60,c_0_67]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP210-1 : TPTP v8.1.2. Released v2.5.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 00:48:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.65/0.71 % Version : CSE_E---1.5
% 0.65/0.71 % Problem : theBenchmark.p
% 0.65/0.71 % Proof found
% 0.65/0.71 % SZS status Theorem for theBenchmark.p
% 0.65/0.71 % SZS output start Proof
% See solution above
% 0.65/0.71 % Total time : 0.141000 s
% 0.65/0.71 % SZS output end Proof
% 0.65/0.71 % Total time : 0.145000 s
%------------------------------------------------------------------------------