TSTP Solution File: RNG001-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG001-2 : TPTP v8.1.2. Released v1.0.0.
% 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 13:48:20 EDT 2023
% Result : Unsatisfiable 4.23s 4.37s
% Output : CNFRefutation 4.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 76 ( 30 unt; 8 typ; 0 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 152 ( 77 ~; 75 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 6 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 195 ( 13 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
equalish: ( $i * $i ) > $o ).
tff(decl_23,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
additive_identity: $i ).
tff(decl_25,type,
multiply: ( $i * $i ) > $i ).
tff(decl_26,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
add: ( $i * $i ) > $i ).
tff(decl_28,type,
additive_inverse: $i > $i ).
tff(decl_29,type,
a: $i ).
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/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(addition_is_well_defined,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
cnf(sum_substitution3,axiom,
( sum(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ sum(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution3) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(associativity_of_addition1,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition1) ).
cnf(additive_inverse2,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
cnf(associativity_of_addition2,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(distributivity4,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
cnf(theorem,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem) ).
cnf(c_0_13,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_14,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_15,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_16,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_17,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_13,c_0_14]) ).
cnf(c_0_18,axiom,
( sum(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ sum(X3,X4,X1) ),
sum_substitution3 ).
cnf(c_0_19,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_20,plain,
( equalish(X1,X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_22,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1 ).
cnf(c_0_23,axiom,
sum(X1,additive_inverse(X1),additive_identity),
additive_inverse2 ).
cnf(c_0_24,plain,
( sum(X1,multiply(X2,X3),multiply(X2,X4))
| ~ product(X2,X5,X1)
| ~ sum(X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_25,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_26,plain,
( sum(X1,additive_identity,X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
equalish(add(additive_identity,X1),X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(X4),X2)
| ~ sum(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( sum(multiply(X1,X2),multiply(X1,X3),multiply(X1,X4))
| ~ sum(X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_30,plain,
( sum(X1,additive_inverse(X2),X3)
| ~ sum(X4,additive_identity,X3)
| ~ sum(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_31,plain,
sum(add(additive_identity,X1),additive_identity,X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_33,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X3,X4,X2)
| ~ sum(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_34,plain,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_35,plain,
sum(multiply(X1,additive_identity),multiply(X1,X2),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_16]) ).
cnf(c_0_36,plain,
( sum(X1,additive_inverse(X2),X3)
| ~ sum(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_37,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,add(additive_identity,X3))
| ~ sum(X4,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_31]) ).
cnf(c_0_38,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_39,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_40,plain,
sum(multiply(X1,additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
sum(additive_identity,additive_inverse(additive_inverse(X1)),X1),
inference(spm,[status(thm)],[c_0_36,c_0_23]) ).
cnf(c_0_42,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
distributivity4 ).
cnf(c_0_43,plain,
( sum(X1,X2,X1)
| ~ sum(additive_identity,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
sum(additive_identity,additive_identity,multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
equalish(X1,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_20,c_0_41]) ).
cnf(c_0_46,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_47,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X5,multiply(X6,X2),X3)
| ~ sum(X4,X6,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_14]) ).
cnf(c_0_48,plain,
sum(X1,multiply(X2,additive_identity),X1),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_identity,X2)
| ~ sum(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_50,plain,
sum(X1,additive_identity,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_26,c_0_45]) ).
cnf(c_0_51,plain,
( sum(X1,X2,X3)
| ~ sum(additive_inverse(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_23]) ).
cnf(c_0_52,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_identity,X1)
| ~ sum(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_53,plain,
( product(X1,additive_identity,X2)
| ~ product(X3,additive_identity,X2)
| ~ sum(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
( sum(X1,additive_inverse(additive_inverse(X2)),X3)
| ~ sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,plain,
sum(X1,add(additive_inverse(X1),X2),X2),
inference(spm,[status(thm)],[c_0_51,c_0_21]) ).
cnf(c_0_56,plain,
( sum(multiply(X1,additive_identity),X2,X3)
| ~ sum(additive_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_52,c_0_44]) ).
cnf(c_0_57,plain,
( product(X1,additive_identity,multiply(X2,additive_identity))
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_14]) ).
cnf(c_0_58,plain,
sum(X1,additive_inverse(additive_inverse(add(additive_inverse(X1),X2))),X2),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,plain,
( sum(X1,additive_inverse(X1),X2)
| ~ equalish(additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_60,plain,
sum(multiply(X1,additive_identity),multiply(X2,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_56,c_0_48]) ).
cnf(c_0_61,plain,
product(X1,additive_identity,multiply(X2,additive_identity)),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,plain,
sum(X1,additive_inverse(X1),additive_inverse(additive_inverse(additive_identity))),
inference(spm,[status(thm)],[c_0_59,c_0_45]) ).
cnf(c_0_63,plain,
( product(X1,additive_identity,additive_identity)
| ~ sum(X2,X3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_60]),c_0_61])]) ).
cnf(c_0_64,plain,
sum(additive_inverse(additive_inverse(additive_identity)),additive_inverse(additive_inverse(X1)),X1),
inference(spm,[status(thm)],[c_0_36,c_0_62]) ).
cnf(c_0_65,negated_conjecture,
~ product(a,additive_identity,additive_identity),
theorem ).
cnf(c_0_66,plain,
product(X1,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG001-2 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % 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 : Sun Aug 27 01:59:50 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 4.23/4.37 % Version : CSE_E---1.5
% 4.23/4.37 % Problem : theBenchmark.p
% 4.23/4.37 % Proof found
% 4.23/4.37 % SZS status Theorem for theBenchmark.p
% 4.23/4.37 % SZS output start Proof
% See solution above
% 4.23/4.38 % Total time : 3.802000 s
% 4.23/4.38 % SZS output end Proof
% 4.23/4.38 % Total time : 3.805000 s
%------------------------------------------------------------------------------