TSTP Solution File: GRP354-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP354-1 : 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 : 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 00:18:37 EDT 2023
% Result : Unsatisfiable 0.54s 0.62s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 67 ( 20 unt; 12 typ; 0 def)
% Number of atoms : 166 ( 165 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 207 ( 96 ~; 111 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 58 ( 2 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_c9: $i ).
tff(decl_28,type,
sk_c3: $i ).
tff(decl_29,type,
sk_c4: $i ).
tff(decl_30,type,
sk_c5: $i ).
tff(decl_31,type,
sk_c6: $i ).
tff(decl_32,type,
sk_c1: $i ).
tff(decl_33,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_9,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_49,negated_conjecture,
( multiply(sk_c8,sk_c7) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(sk_c9) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c7
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X4) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| multiply(X5,X6) != sk_c8
| inverse(X5) != X6
| multiply(X6,sk_c7) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_27,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(c_0_11,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_12,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_13,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_14,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_15,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
prove_this_9 ).
cnf(c_0_16,negated_conjecture,
( multiply(inverse(sk_c3),sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c9 ),
prove_this_10 ).
cnf(c_0_18,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_20,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
prove_this_17 ).
cnf(c_0_21,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
( multiply(inverse(sk_c3),sk_c8) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_23,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c3) = sk_c9 ),
prove_this_18 ).
cnf(c_0_24,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_26,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_14]) ).
cnf(c_0_27,negated_conjecture,
multiply(sk_c9,sk_c8) = sk_c9,
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_28,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c8,sk_c7) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(sk_c9) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c7
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X4) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| multiply(X5,X6) != sk_c8
| inverse(X5) != X6
| multiply(X6,sk_c7) != sk_c8 ),
prove_this_49 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
prove_this_5 ).
cnf(c_0_31,negated_conjecture,
sk_c8 = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_27]),c_0_12]) ).
cnf(c_0_32,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_28]),c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c9,sk_c7) = sk_c8 ),
prove_this_27 ).
cnf(c_0_34,negated_conjecture,
( multiply(inverse(X1),sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| multiply(X1,inverse(X1)) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(X4,sk_c7) != sk_c8
| multiply(X5,sk_c9) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9
| inverse(X4) != sk_c7
| inverse(X5) != sk_c9 ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c4) = sk_c9 ),
prove_this_4 ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c4,identity) = sk_c9
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_13]),c_0_31]) ).
cnf(c_0_37,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_12,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( multiply(sk_c9,sk_c7) = identity
| inverse(sk_c9) = sk_c7 ),
inference(rw,[status(thm)],[c_0_33,c_0_31]) ).
cnf(c_0_39,negated_conjecture,
( multiply(inverse(X1),sk_c7) != identity
| multiply(sk_c9,sk_c7) != identity
| multiply(X1,inverse(X1)) != identity
| multiply(X2,identity) != sk_c9
| multiply(X3,sk_c9) != identity
| multiply(X4,sk_c7) != identity
| multiply(X5,sk_c9) != identity
| inverse(sk_c9) != sk_c7
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9
| inverse(X4) != sk_c7
| inverse(X5) != sk_c9
| sk_c7 != sk_c9 ),
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_34,c_0_31]),c_0_31]),c_0_13]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]) ).
cnf(c_0_40,negated_conjecture,
( inverse(sk_c4) = sk_c9
| sk_c7 = sk_c9 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_31]),c_0_13]) ).
cnf(c_0_41,negated_conjecture,
( sk_c7 = sk_c9
| sk_c4 = sk_c9 ),
inference(rw,[status(thm)],[c_0_36,c_0_28]) ).
cnf(c_0_42,negated_conjecture,
multiply(sk_c9,sk_c7) = identity,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( multiply(inverse(X1),sk_c7) != identity
| multiply(sk_c9,sk_c7) != identity
| multiply(X1,inverse(X1)) != identity
| multiply(X2,sk_c9) != identity
| multiply(X3,sk_c7) != identity
| multiply(X4,sk_c9) != identity
| inverse(sk_c9) != sk_c7
| inverse(sk_c9) != sk_c9
| inverse(X2) != sk_c9
| inverse(X3) != sk_c7
| inverse(X4) != sk_c9
| sk_c7 != sk_c9 ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_28])]) ).
cnf(c_0_44,negated_conjecture,
( inverse(sk_c9) = sk_c9
| sk_c7 = sk_c9 ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
inverse(sk_c9) = sk_c7,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_42]),c_0_28]) ).
cnf(c_0_46,negated_conjecture,
( multiply(inverse(X1),sk_c7) != identity
| multiply(sk_c9,sk_c7) != identity
| multiply(X2,sk_c9) != identity
| multiply(X3,sk_c7) != identity
| multiply(X4,sk_c9) != identity
| inverse(sk_c9) != sk_c7
| inverse(sk_c9) != sk_c9
| inverse(X2) != sk_c9
| inverse(X3) != sk_c7
| inverse(X4) != sk_c9
| sk_c7 != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_37])]) ).
cnf(c_0_47,negated_conjecture,
sk_c7 = sk_c9,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
( multiply(inverse(X1),sk_c9) != identity
| multiply(X2,sk_c9) != identity
| multiply(X3,sk_c9) != identity
| multiply(X4,sk_c9) != identity
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9
| inverse(X4) != sk_c9 ),
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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_42])]),c_0_47]),c_0_47]),c_0_45]),c_0_47]),c_0_47]),c_0_45]),c_0_47]),c_0_47]),c_0_47])]) ).
cnf(c_0_49,negated_conjecture,
inverse(sk_c9) = sk_c9,
inference(rw,[status(thm)],[c_0_45,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
multiply(sk_c9,sk_c9) = identity,
inference(rw,[status(thm)],[c_0_42,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
( multiply(X1,sk_c9) != identity
| multiply(X2,sk_c9) != identity
| multiply(X3,sk_c9) != identity
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| inverse(X3) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).
cnf(c_0_52,negated_conjecture,
( multiply(X1,sk_c9) != identity
| multiply(X2,sk_c9) != identity
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_50]),c_0_45]),c_0_47])]) ).
cnf(c_0_53,negated_conjecture,
( multiply(X1,sk_c9) != identity
| inverse(X1) != sk_c9 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_50]),c_0_45]),c_0_47])]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_49]),c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP354-1 : TPTP v8.1.2. Released v2.5.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 01:18:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.54/0.62 % Version : CSE_E---1.5
% 0.54/0.62 % Problem : theBenchmark.p
% 0.54/0.62 % Proof found
% 0.54/0.62 % SZS status Theorem for theBenchmark.p
% 0.54/0.62 % SZS output start Proof
% See solution above
% 0.54/0.63 % Total time : 0.045000 s
% 0.54/0.63 % SZS output end Proof
% 0.54/0.63 % Total time : 0.048000 s
%------------------------------------------------------------------------------