TSTP Solution File: RNG001-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG001-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 13:48:20 EDT 2023
% Result : Unsatisfiable 89.08s 89.29s
% Output : CNFRefutation 89.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 65 ( 19 unt; 6 typ; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 154 ( 78 ~; 76 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 172 ( 8 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
additive_identity: $i ).
tff(decl_23,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
additive_inverse: $i > $i ).
tff(decl_25,type,
multiply: ( $i * $i ) > $i ).
tff(decl_26,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
a: $i ).
cnf(associativity_of_addition2,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
cnf(additive_inverse1,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
cnf(associativity_of_addition1,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
cnf(distributivity1,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(distributivity2,axiom,
( product(X1,X6,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ sum(X3,X5,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
cnf(prove_a_times_additive_id_is_additive_id,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).
cnf(c_0_8,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_9,axiom,
sum(additive_inverse(X1),X1,additive_identity),
additive_inverse1 ).
cnf(c_0_10,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1 ).
cnf(c_0_11,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_12,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( sum(additive_identity,X1,X2)
| ~ sum(additive_inverse(additive_inverse(X1)),additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_15,plain,
( sum(additive_inverse(X1),X2,X3)
| ~ sum(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_16,plain,
( sum(additive_identity,X1,X2)
| ~ sum(additive_inverse(X1),X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
( sum(additive_identity,X1,X2)
| ~ sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_18,plain,
( sum(additive_identity,additive_inverse(X1),X2)
| ~ sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_19,plain,
sum(additive_identity,additive_inverse(additive_inverse(X1)),X1),
inference(spm,[status(thm)],[c_0_18,c_0_9]) ).
cnf(c_0_20,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
distributivity1 ).
cnf(c_0_21,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_22,plain,
( sum(additive_identity,X1,X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_23,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_17,c_0_9]) ).
cnf(c_0_24,plain,
( sum(X1,additive_inverse(X1),X2)
| ~ sum(additive_identity,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_25,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X1,X3,additive_inverse(X4))
| ~ sum(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_26,plain,
( sum(X1,X2,multiply(X3,X4))
| ~ product(X3,X5,X2)
| ~ product(X3,X6,X1)
| ~ sum(X6,X5,X4) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
sum(X1,additive_inverse(X1),additive_identity),
inference(spm,[status(thm)],[c_0_24,c_0_11]) ).
cnf(c_0_29,plain,
( sum(additive_identity,X1,additive_identity)
| ~ sum(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_11]) ).
cnf(c_0_30,plain,
( sum(X1,multiply(X2,X3),multiply(X2,X4))
| ~ product(X2,X5,X1)
| ~ sum(X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_31,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(additive_inverse(X3)),X2)
| ~ sum(X1,X4,additive_identity) ),
inference(spm,[status(thm)],[c_0_10,c_0_19]) ).
cnf(c_0_32,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_identity,X1)
| ~ sum(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_33,plain,
sum(X1,additive_inverse(X1),additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_34,plain,
( sum(X1,X2,X3)
| ~ sum(additive_inverse(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_35,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X5),X1)
| ~ sum(X4,X6,X3)
| ~ sum(X5,X6,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_15]) ).
cnf(c_0_36,plain,
( sum(additive_identity,X1,additive_identity)
| ~ sum(X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_15]) ).
cnf(c_0_37,plain,
( sum(multiply(X1,X2),multiply(X1,X3),multiply(X1,X4))
| ~ sum(X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_38,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X1,additive_inverse(X2),additive_identity) ),
inference(spm,[status(thm)],[c_0_31,c_0_28]) ).
cnf(c_0_39,plain,
( sum(additive_inverse(additive_identity),X1,X2)
| ~ sum(additive_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_40,plain,
( sum(additive_inverse(additive_identity),X1,X2)
| ~ sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_33]) ).
cnf(c_0_41,plain,
sum(X1,additive_identity,X1),
inference(spm,[status(thm)],[c_0_34,c_0_9]) ).
cnf(c_0_42,plain,
( sum(X1,X2,X3)
| ~ sum(additive_inverse(X1),X4,X2)
| ~ sum(additive_identity,X4,X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_19]) ).
cnf(c_0_43,plain,
( sum(additive_identity,multiply(X1,X2),additive_identity)
| ~ sum(X3,X2,X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
( sum(additive_inverse(additive_identity),additive_identity,X1)
| ~ sum(additive_identity,additive_inverse(X1),additive_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
( sum(X1,X2,X3)
| ~ sum(additive_inverse(X4),X2,X3)
| ~ sum(X4,X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_32,c_0_15]) ).
cnf(c_0_46,plain,
sum(additive_inverse(additive_identity),X1,X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
( sum(X1,X2,X3)
| ~ sum(additive_identity,X4,X3)
| ~ sum(X1,X2,X4) ),
inference(spm,[status(thm)],[c_0_42,c_0_15]) ).
cnf(c_0_48,plain,
sum(additive_identity,multiply(X1,additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_19])]) ).
cnf(c_0_49,plain,
( sum(X1,X2,X2)
| ~ sum(additive_identity,X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,axiom,
( product(X1,X6,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ sum(X3,X5,X7) ),
distributivity2 ).
cnf(c_0_51,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X1,X2,multiply(X3,additive_identity)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
sum(multiply(X1,additive_identity),X2,X2),
inference(spm,[status(thm)],[c_0_49,c_0_48]) ).
cnf(c_0_53,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X5,multiply(X1,X6),X3)
| ~ sum(X4,X6,X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_21]) ).
cnf(c_0_54,plain,
sum(multiply(X1,additive_identity),multiply(X2,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,plain,
( product(X1,X2,additive_identity)
| ~ product(X1,X3,multiply(X4,additive_identity))
| ~ sum(X3,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_56,negated_conjecture,
~ product(a,additive_identity,additive_identity),
prove_a_times_additive_id_is_additive_id ).
cnf(c_0_57,plain,
( product(X1,X2,additive_identity)
| ~ sum(additive_identity,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_21]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG001-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n006.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 : Sun Aug 27 01:55:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.52 start to proof: theBenchmark
% 89.08/89.29 % Version : CSE_E---1.5
% 89.08/89.29 % Problem : theBenchmark.p
% 89.08/89.29 % Proof found
% 89.08/89.29 % SZS status Theorem for theBenchmark.p
% 89.08/89.29 % SZS output start Proof
% See solution above
% 89.08/89.29 % Total time : 88.753000 s
% 89.08/89.29 % SZS output end Proof
% 89.08/89.29 % Total time : 88.759000 s
%------------------------------------------------------------------------------