TSTP Solution File: GRP292-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP292-1 : 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 : n028.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 00:18:15 EDT 2023
% Result : Unsatisfiable 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 19
% Syntax : Number of formulae : 58 ( 18 unt; 10 typ; 0 def)
% Number of atoms : 113 ( 112 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 116 ( 51 ~; 65 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 44 ( 3 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_c7: $i ).
tff(decl_26,type,
sk_c6: $i ).
tff(decl_27,type,
sk_c5: $i ).
tff(decl_28,type,
sk_c3: $i ).
tff(decl_29,type,
sk_c4: $i ).
tff(decl_30,type,
sk_c1: $i ).
tff(decl_31,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_19,negated_conjecture,
( inverse(sk_c2) = sk_c5
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c7,sk_c6) != sk_c5
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(X3,X4) != sk_c6
| inverse(X3) != X4
| multiply(X4,sk_c5) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_1,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(c_0_9,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_10,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_11,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_12,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_13,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_14,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_12]) ).
cnf(c_0_15,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_15]) ).
cnf(c_0_17,negated_conjecture,
( inverse(sk_c2) = sk_c5
| inverse(sk_c3) = sk_c4 ),
prove_this_19 ).
cnf(c_0_18,negated_conjecture,
( inverse(sk_c2) = sk_c5
| multiply(sk_c3,sk_c4) = sk_c6 ),
prove_this_18 ).
cnf(c_0_19,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( multiply(sk_c5,sk_c2) = identity
| inverse(sk_c3) = sk_c4 ),
inference(spm,[status(thm)],[c_0_10,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c5,sk_c2) = identity ),
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( multiply(sk_c5,sk_c2) = identity
| multiply(sk_c3,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( multiply(sk_c5,sk_c2) = identity
| sk_c6 = identity ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c4 ),
prove_this_15 ).
cnf(c_0_25,negated_conjecture,
( inverse(sk_c5) = sk_c2
| sk_c6 = identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_23]),c_0_15]) ).
cnf(c_0_26,negated_conjecture,
( multiply(sk_c7,sk_c6) != sk_c5
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(X3,X4) != sk_c6
| inverse(X3) != X4
| multiply(X4,sk_c5) != sk_c6 ),
prove_this_21 ).
cnf(c_0_27,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
prove_this_14 ).
cnf(c_0_28,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_29,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c3,sk_c4) = identity ),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( multiply(sk_c2,sk_c5) = identity
| sk_c6 = identity ),
inference(spm,[status(thm)],[c_0_10,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c7 ),
prove_this_1 ).
cnf(c_0_32,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_33,negated_conjecture,
( multiply(inverse(X1),sk_c5) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(X1,inverse(X1)) != sk_c6
| multiply(X2,sk_c5) != sk_c6
| multiply(X3,sk_c7) != sk_c6
| inverse(X2) != sk_c5
| inverse(X3) != sk_c7 ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_34,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c6
| sk_c6 = identity ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( multiply(sk_c3,sk_c4) = identity
| sk_c6 = identity ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( multiply(sk_c7,multiply(sk_c6,X1)) = multiply(sk_c5,X1)
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(spm,[status(thm)],[c_0_9,c_0_31]) ).
cnf(c_0_37,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( multiply(inverse(X1),sk_c5) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(X2,sk_c5) != sk_c6
| multiply(X3,sk_c7) != sk_c6
| inverse(X2) != sk_c5
| inverse(X3) != sk_c7
| sk_c6 != identity ),
inference(rw,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_39,negated_conjecture,
sk_c6 = identity,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( multiply(sk_c5,inverse(sk_c6)) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_19]),c_0_15]) ).
cnf(c_0_41,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_10,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( multiply(inverse(X1),sk_c5) != identity
| multiply(X2,sk_c5) != identity
| multiply(X3,sk_c7) != identity
| inverse(X2) != sk_c5
| inverse(X3) != sk_c7
| sk_c7 != sk_c5 ),
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)],[c_0_38,c_0_39]),c_0_39]),c_0_15]),c_0_39]),c_0_15]),c_0_39]),c_0_39]),c_0_39])]) ).
cnf(c_0_43,negated_conjecture,
sk_c7 = sk_c5,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_39]),c_0_41]),c_0_15]),c_0_39]),c_0_15])]) ).
cnf(c_0_44,negated_conjecture,
( multiply(inverse(X1),sk_c5) != identity
| multiply(X2,sk_c5) != identity
| multiply(X3,sk_c5) != identity
| inverse(X2) != sk_c5
| inverse(X3) != sk_c5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_43]),c_0_43])]) ).
cnf(c_0_45,negated_conjecture,
( multiply(X1,sk_c5) != identity
| multiply(X2,sk_c5) != identity
| inverse(X1) != sk_c5
| inverse(X2) != sk_c5 ),
inference(spm,[status(thm)],[c_0_44,c_0_10]) ).
cnf(c_0_46,negated_conjecture,
( multiply(X1,sk_c5) != identity
| inverse(X1) != sk_c5 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_10]),c_0_16])]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_16])]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP292-1 : 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
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 02:13:25 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.57 % Version : CSE_E---1.5
% 0.19/0.57 % Problem : theBenchmark.p
% 0.19/0.57 % Proof found
% 0.19/0.57 % SZS status Theorem for theBenchmark.p
% 0.19/0.57 % SZS output start Proof
% See solution above
% 0.19/0.58 % Total time : 0.020000 s
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58 % Total time : 0.023000 s
%------------------------------------------------------------------------------