TSTP Solution File: GRP212-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP212-1 : 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 : n031.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 0.79s 0.86s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 25
% Syntax : Number of formulae : 79 ( 17 unt; 11 typ; 0 def)
% Number of atoms : 146 ( 145 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 111 ( 33 ~; 78 |; 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 : 35 ( 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_c1: $i ).
tff(decl_26,type,
sk_c2: $i ).
tff(decl_27,type,
sk_c8: $i ).
tff(decl_28,type,
sk_c7: $i ).
tff(decl_29,type,
sk_c4: $i ).
tff(decl_30,type,
sk_c6: $i ).
tff(decl_31,type,
sk_c5: $i ).
tff(decl_32,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_27,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
cnf(prove_this_26,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
cnf(prove_this_21,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_10,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_12,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_31,negated_conjecture,
( multiply(X1,X2) != sk_c8
| inverse(X1) != X2
| multiply(X2,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c7) != sk_c8
| multiply(sk_c8,X5) != sk_c7
| multiply(X6,sk_c8) != X5
| inverse(X6) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
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_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
prove_this_27 ).
cnf(c_0_19,negated_conjecture,
( multiply(inverse(sk_c4),sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_26 ).
cnf(c_0_21,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
( multiply(inverse(sk_c3),sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_23,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
prove_this_21 ).
cnf(c_0_24,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
prove_this_4 ).
cnf(c_0_26,negated_conjecture,
( multiply(inverse(sk_c4),sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c4) = sk_c8 ),
prove_this_20 ).
cnf(c_0_28,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c2
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c8,sk_c6) = sk_c7 ),
prove_this_10 ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c8,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
cnf(c_0_32,negated_conjecture,
( multiply(sk_c1,multiply(sk_c2,X1)) = multiply(sk_c8,X1)
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_14,c_0_25]) ).
cnf(c_0_33,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c2 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
multiply(sk_c8,sk_c8) = sk_c7,
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_35,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c6 ),
prove_this_11 ).
cnf(c_0_37,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_38,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_35]),c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c8 ),
prove_this_12 ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_15,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_25,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
multiply(inverse(sk_c8),sk_c7) = sk_c8,
inference(spm,[status(thm)],[c_0_17,c_0_34]) ).
cnf(c_0_43,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
prove_this_5 ).
cnf(c_0_45,negated_conjecture,
( multiply(inverse(sk_c5),sk_c6) = sk_c8
| multiply(sk_c2,sk_c1) = identity ),
inference(spm,[status(thm)],[c_0_17,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
( sk_c7 = sk_c8
| sk_c6 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_41]),c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| inverse(sk_c8) = sk_c5 ),
inference(spm,[status(thm)],[c_0_15,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
( multiply(inverse(sk_c5),sk_c6) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(spm,[status(thm)],[c_0_17,c_0_44]) ).
cnf(c_0_49,negated_conjecture,
( multiply(inverse(sk_c5),sk_c8) = sk_c8
| multiply(sk_c2,sk_c1) = identity
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| inverse(sk_c5) = sk_c8 ),
inference(spm,[status(thm)],[c_0_38,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
( multiply(inverse(sk_c5),sk_c8) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_48,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c5) = sk_c8 ),
prove_this_6 ).
cnf(c_0_53,negated_conjecture,
( multiply(sk_c2,sk_c1) = identity
| sk_c7 = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_34])]) ).
cnf(c_0_54,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| sk_c7 = sk_c8 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_34])]) ).
cnf(c_0_55,negated_conjecture,
( inverse(sk_c2) = sk_c1
| sk_c7 = sk_c8 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_53]),c_0_35]) ).
cnf(c_0_56,negated_conjecture,
( multiply(inverse(sk_c1),sk_c8) = sk_c2
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_17,c_0_54]) ).
cnf(c_0_57,negated_conjecture,
( inverse(sk_c1) = sk_c2
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_38,c_0_55]) ).
cnf(c_0_58,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c2
| sk_c7 = sk_c8 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_59,negated_conjecture,
( sk_c7 = sk_c8
| sk_c8 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_58]),c_0_15]) ).
cnf(c_0_60,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_61,negated_conjecture,
( multiply(X1,X2) != sk_c8
| inverse(X1) != X2
| multiply(X2,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c7) != sk_c8
| multiply(sk_c8,X5) != sk_c7
| multiply(X6,sk_c8) != X5
| inverse(X6) != sk_c8 ),
prove_this_31 ).
cnf(c_0_62,negated_conjecture,
sk_c8 = identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_59]),c_0_15])]) ).
cnf(c_0_63,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_60,c_0_35]) ).
cnf(c_0_64,negated_conjecture,
( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
| multiply(inverse(X2),sk_c7) != sk_c8
| multiply(X2,inverse(X2)) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| multiply(X4,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X3) != sk_c8
| inverse(X4) != sk_c8 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_61])]) ).
cnf(c_0_65,negated_conjecture,
sk_c7 = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_62]),c_0_63]),c_0_16]),c_0_62]) ).
cnf(c_0_66,negated_conjecture,
( multiply(X1,inverse(X1)) != identity
| inverse(X1) != identity ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[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(er,[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_64,c_0_62]),c_0_62]),c_0_35]),c_0_16]),c_0_62]),c_0_62]),c_0_62]),c_0_62]),c_0_62]),c_0_63]),c_0_62]),c_0_62]),c_0_62])]),c_0_65]),c_0_35]),c_0_65]),c_0_35]),c_0_65]),c_0_35]),c_0_65]),c_0_65]),c_0_63])])])]),c_0_63])]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_63]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP212-1 : TPTP v8.1.2. Released v2.5.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n031.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 23:51:10 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.52 start to proof: theBenchmark
% 0.79/0.86 % Version : CSE_E---1.5
% 0.79/0.86 % Problem : theBenchmark.p
% 0.79/0.86 % Proof found
% 0.79/0.86 % SZS status Theorem for theBenchmark.p
% 0.79/0.86 % SZS output start Proof
% See solution above
% 0.79/0.86 % Total time : 0.330000 s
% 0.79/0.86 % SZS output end Proof
% 0.79/0.86 % Total time : 0.333000 s
%------------------------------------------------------------------------------