TSTP Solution File: GRP302-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP302-1 : 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 : n006.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 00:18:18 EDT 2023
% Result : Unsatisfiable 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 25
% Syntax : Number of formulae : 90 ( 36 unt; 11 typ; 0 def)
% Number of atoms : 175 ( 174 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 168 ( 72 ~; 96 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 59 ( 0 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_c8: $i ).
tff(decl_26,type,
sk_c7: $i ).
tff(decl_27,type,
sk_c6: $i ).
tff(decl_28,type,
sk_c1: $i ).
tff(decl_29,type,
sk_c3: $i ).
tff(decl_30,type,
sk_c5: $i ).
tff(decl_31,type,
sk_c4: $i ).
tff(decl_32,type,
sk_c2: $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_14,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_1,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c8,sk_c7) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c8) != sk_c6
| inverse(X2) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X4) != X5
| inverse(X5) != sk_c8
| multiply(X4,sk_c8) != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_3,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_5,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_6,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
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_c2,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
prove_this_14 ).
cnf(c_0_19,negated_conjecture,
multiply(sk_c8,sk_c7) = sk_c6,
prove_this_1 ).
cnf(c_0_20,negated_conjecture,
( multiply(inverse(sk_c2),sk_c6) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c7 ),
prove_this_20 ).
cnf(c_0_22,negated_conjecture,
multiply(inverse(sk_c8),sk_c6) = sk_c7,
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
multiply(inverse(inverse(sk_c8)),sk_c7) = sk_c6,
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( inverse(sk_c8) = sk_c7
| sk_c6 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_23]),c_0_15]) ).
cnf(c_0_26,negated_conjecture,
sk_c6 = identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_15])]) ).
cnf(c_0_27,negated_conjecture,
multiply(inverse(sk_c8),identity) = sk_c7,
inference(rw,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c8,sk_c7) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c8) != sk_c6
| inverse(X2) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X4) != X5
| inverse(X5) != sk_c8
| multiply(X4,sk_c8) != X5 ),
prove_this_26 ).
cnf(c_0_29,negated_conjecture,
multiply(inverse(sk_c8),X1) = multiply(sk_c7,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_27]),c_0_16]) ).
cnf(c_0_30,negated_conjecture,
( inverse(multiply(X1,sk_c8)) != sk_c8
| multiply(X1,sk_c8) != inverse(X1)
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c8) != sk_c6
| multiply(X4,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X2) != sk_c8
| inverse(X3) != sk_c8
| inverse(X4) != sk_c8 ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_19])])]) ).
cnf(c_0_31,negated_conjecture,
multiply(inverse(inverse(sk_c8)),sk_c7) = identity,
inference(rw,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_32,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
prove_this_4 ).
cnf(c_0_34,negated_conjecture,
multiply(sk_c7,sk_c8) = identity,
inference(spm,[status(thm)],[c_0_15,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( inverse(multiply(X1,sk_c8)) != sk_c8
| multiply(X1,sk_c8) != inverse(X1)
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c8) != identity
| multiply(X4,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X2) != sk_c8
| inverse(X3) != sk_c8
| inverse(X4) != sk_c8 ),
inference(rw,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_36,negated_conjecture,
inverse(sk_c8) = sk_c7,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_31]),c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( multiply(inverse(sk_c3),sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(spm,[status(thm)],[c_0_17,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
prove_this_3 ).
cnf(c_0_39,negated_conjecture,
multiply(inverse(sk_c7),identity) = sk_c8,
inference(spm,[status(thm)],[c_0_17,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( inverse(multiply(X1,sk_c8)) != sk_c8
| multiply(X1,sk_c8) != inverse(X1)
| multiply(X2,sk_c7) != sk_c8
| multiply(X3,sk_c8) != identity
| multiply(X4,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c8
| inverse(X4) != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_41,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c4 ),
prove_this_7 ).
cnf(c_0_42,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c4 ),
prove_this_5 ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_6 ).
cnf(c_0_44,negated_conjecture,
multiply(sk_c7,multiply(sk_c8,X1)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_45,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,negated_conjecture,
multiply(inverse(inverse(sk_c7)),sk_c8) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c8) != identity
| multiply(X3,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c8 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]) ).
cnf(c_0_48,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
inverse(sk_c7) = sk_c8,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_46]),c_0_32]) ).
cnf(c_0_50,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
cnf(c_0_51,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(X1,sk_c8) != identity
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_52,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_32,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_34]),c_0_49])]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
prove_this_10 ).
cnf(c_0_55,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_52]),c_0_52]) ).
cnf(c_0_56,negated_conjecture,
inverse(sk_c1) = sk_c8,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_48]),c_0_49])]) ).
cnf(c_0_57,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
prove_this_9 ).
cnf(c_0_58,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_59,negated_conjecture,
multiply(sk_c8,sk_c7) = identity,
inference(rw,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_60,negated_conjecture,
( multiply(inverse(sk_c3),sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_17,c_0_54]) ).
cnf(c_0_61,negated_conjecture,
sk_c1 = sk_c7,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_36]) ).
cnf(c_0_62,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_17,c_0_57]) ).
cnf(c_0_63,negated_conjecture,
multiply(inverse(multiply(X1,sk_c8)),X1) = sk_c7,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_52]) ).
cnf(c_0_64,negated_conjecture,
( multiply(inverse(sk_c3),sk_c8) = sk_c7
| multiply(sk_c7,sk_c7) = sk_c8 ),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
( multiply(inverse(sk_c1),multiply(sk_c8,X1)) = multiply(sk_c7,X1)
| inverse(sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_14,c_0_62]) ).
cnf(c_0_66,negated_conjecture,
multiply(inverse(multiply(X1,sk_c7)),X1) = sk_c8,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_34]),c_0_52]) ).
cnf(c_0_67,negated_conjecture,
( multiply(sk_c8,inverse(sk_c3)) = sk_c7
| multiply(sk_c7,sk_c7) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_49]) ).
cnf(c_0_68,negated_conjecture,
( multiply(sk_c7,sk_c7) = inverse(sk_c1)
| inverse(sk_c3) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_59]),c_0_52]) ).
cnf(c_0_69,negated_conjecture,
multiply(sk_c7,inverse(multiply(sk_c7,sk_c7))) = sk_c8,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_66]),c_0_36]) ).
cnf(c_0_70,negated_conjecture,
( multiply(sk_c7,sk_c7) = inverse(sk_c3)
| multiply(sk_c7,sk_c7) = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_67]),c_0_36]) ).
cnf(c_0_71,negated_conjecture,
( multiply(sk_c7,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(rw,[status(thm)],[c_0_68,c_0_56]) ).
cnf(c_0_72,negated_conjecture,
inverse(multiply(sk_c7,sk_c7)) = multiply(sk_c8,sk_c8),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_69]),c_0_49]) ).
cnf(c_0_73,negated_conjecture,
multiply(sk_c7,sk_c7) = sk_c8,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_70]),c_0_71]) ).
cnf(c_0_74,negated_conjecture,
multiply(sk_c8,sk_c8) = sk_c7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73]),c_0_36]) ).
cnf(c_0_75,negated_conjecture,
( multiply(X1,sk_c7) != sk_c8
| multiply(X2,sk_c8) != identity
| multiply(X3,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8
| inverse(X3) != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_74]),c_0_49]),c_0_36])]) ).
cnf(c_0_76,negated_conjecture,
( multiply(X1,sk_c8) != identity
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| inverse(X2) != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_73]),c_0_49])]) ).
cnf(c_0_77,negated_conjecture,
( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_34]),c_0_49])]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_73]),c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP302-1 : TPTP v8.1.2. Released v2.5.0.
% 0.08/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n006.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 : Mon Aug 28 21:01:51 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 0.20/0.63 % Version : CSE_E---1.5
% 0.20/0.63 % Problem : theBenchmark.p
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark.p
% 0.20/0.63 % SZS output start Proof
% See solution above
% 0.20/0.63 % Total time : 0.069000 s
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63 % Total time : 0.072000 s
%------------------------------------------------------------------------------