TSTP Solution File: RNG039-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG039-2 : 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 : n024.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 13:48:40 EDT 2023
% Result : Unsatisfiable 0.19s 0.70s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 28
% Syntax : Number of formulae : 74 ( 36 unt; 10 typ; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 80 ( 42 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 5 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 82 ( 11 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
equalish: ( $i * $i ) > $o ).
tff(decl_23,type,
add: ( $i * $i ) > $i ).
tff(decl_24,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
multiply: ( $i * $i ) > $i ).
tff(decl_26,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
additive_identity: $i ).
tff(decl_28,type,
a: $i ).
tff(decl_29,type,
b: $i ).
tff(decl_30,type,
c: $i ).
tff(decl_31,type,
d: $i ).
cnf(multiplication_is_well_defined,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(clause46,axiom,
product(a,multiply(b,c),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).
cnf(clause44,axiom,
product(a,multiply(b,X1),multiply(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
cnf(transitivity,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(product_substitution1,axiom,
( product(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ product(X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution1) ).
cnf(multiplicative_identity1,axiom,
product(additive_identity,X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
cnf(product_substitution2,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution2) ).
cnf(clause39,axiom,
product(a,c,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).
cnf(clause60,axiom,
product(c,a,multiply(a,d)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).
cnf(product_substitution3,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
cnf(clause41,axiom,
product(c,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).
cnf(clause43,axiom,
product(X1,multiply(X1,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).
cnf(clause56,axiom,
product(d,b,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
cnf(clause42,axiom,
product(d,a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).
cnf(clause49,axiom,
product(b,multiply(a,d),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).
cnf(clause50,axiom,
product(b,c,multiply(d,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
cnf(prove_c_equals_d,negated_conjecture,
~ equalish(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(c_0_18,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_19,axiom,
product(a,multiply(b,c),c),
clause46 ).
cnf(c_0_20,plain,
( equalish(X1,c)
| ~ product(a,multiply(b,c),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
product(a,multiply(b,X1),multiply(X2,X1)),
clause44 ).
cnf(c_0_22,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
transitivity ).
cnf(c_0_23,plain,
equalish(multiply(X1,c),c),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_25,plain,
( equalish(X1,c)
| ~ equalish(X1,multiply(X2,c)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( equalish(X1,multiply(X2,X3))
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_27,axiom,
( product(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ product(X1,X3,X4) ),
product_substitution1 ).
cnf(c_0_28,axiom,
product(additive_identity,X1,additive_identity),
multiplicative_identity1 ).
cnf(c_0_29,plain,
( equalish(X1,c)
| ~ product(X2,c,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( product(X1,X2,additive_identity)
| ~ equalish(additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
equalish(additive_identity,c),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_32,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
product_substitution2 ).
cnf(c_0_33,axiom,
product(a,c,c),
clause39 ).
cnf(c_0_34,axiom,
product(c,a,multiply(a,d)),
clause60 ).
cnf(c_0_35,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3 ).
cnf(c_0_36,plain,
product(c,X1,additive_identity),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,axiom,
product(c,b,c),
clause41 ).
cnf(c_0_38,plain,
( product(a,X1,c)
| ~ equalish(c,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
( equalish(X1,multiply(a,d))
| ~ product(c,a,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_34]) ).
cnf(c_0_40,plain,
( product(c,X1,X2)
| ~ equalish(additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
( equalish(X1,c)
| ~ product(c,b,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_37]) ).
cnf(c_0_42,axiom,
product(X1,multiply(X1,X2),multiply(X1,X2)),
clause43 ).
cnf(c_0_43,plain,
( product(a,multiply(a,d),c)
| ~ product(c,a,c) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
product(c,X1,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_36])]) ).
cnf(c_0_45,axiom,
product(d,b,multiply(b,c)),
clause56 ).
cnf(c_0_46,axiom,
product(d,a,d),
clause42 ).
cnf(c_0_47,axiom,
product(b,multiply(a,d),d),
clause49 ).
cnf(c_0_48,axiom,
product(b,c,multiply(d,b)),
clause50 ).
cnf(c_0_49,plain,
( equalish(X1,multiply(X2,X3))
| ~ product(X2,multiply(X2,X3),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_42]) ).
cnf(c_0_50,plain,
product(a,multiply(a,d),c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_51,plain,
( equalish(X1,multiply(b,c))
| ~ product(d,b,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_45]) ).
cnf(c_0_52,negated_conjecture,
~ equalish(c,d),
prove_c_equals_d ).
cnf(c_0_53,plain,
( equalish(X1,d)
| ~ product(d,a,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_46]) ).
cnf(c_0_54,plain,
( equalish(X1,d)
| ~ product(b,multiply(a,d),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_47]) ).
cnf(c_0_55,plain,
( product(b,X1,multiply(d,b))
| ~ equalish(c,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_48]) ).
cnf(c_0_56,plain,
equalish(c,multiply(a,d)),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,plain,
( product(d,a,X1)
| ~ equalish(d,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_58,plain,
( equalish(X1,c)
| ~ product(d,b,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_51]) ).
cnf(c_0_59,negated_conjecture,
~ product(d,a,c),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,plain,
( product(X1,X2,X3)
| ~ equalish(multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_24]) ).
cnf(c_0_61,plain,
equalish(multiply(d,b),d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).
cnf(c_0_62,plain,
~ product(d,b,d),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_63,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : RNG039-2 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n024.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 02:38:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 0.19/0.70 % Version : CSE_E---1.5
% 0.19/0.70 % Problem : theBenchmark.p
% 0.19/0.70 % Proof found
% 0.19/0.70 % SZS status Theorem for theBenchmark.p
% 0.19/0.70 % SZS output start Proof
% See solution above
% 0.19/0.71 % Total time : 0.119000 s
% 0.19/0.71 % SZS output end Proof
% 0.19/0.71 % Total time : 0.122000 s
%------------------------------------------------------------------------------