TSTP Solution File: RNG039-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG039-1 : 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 : n014.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 13:48:39 EDT 2023
% Result : Unsatisfiable 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 25
% Syntax : Number of formulae : 65 ( 43 unt; 10 typ; 0 def)
% Number of atoms : 71 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 20 ~; 16 |; 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 : 11 ( 5 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 12 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,
multiply: ( $i * $i ) > $i ).
tff(decl_25,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
add: ( $i * $i ) > $i ).
tff(decl_27,type,
additive_inverse: $i > $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(clause44,axiom,
product(a,multiply(b,X1),multiply(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
cnf(clause35,axiom,
multiply(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(b_times_a,negated_conjecture,
product(b,a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a) ).
cnf(clause57,axiom,
product(multiply(X1,b),a,multiply(X1,d)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(clause37,axiom,
multiply(b,a) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
cnf(a_times_b,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(clause32,axiom,
sum(X1,X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
cnf(clause68,axiom,
product(add(b,a),b,add(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause68) ).
cnf(clause34,axiom,
add(X1,X1) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).
cnf(clause70,axiom,
product(add(a,b),a,add(a,d)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause70) ).
cnf(prove_c_equals_d,negated_conjecture,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(c_0_15,axiom,
product(a,multiply(b,X1),multiply(X2,X1)),
clause44 ).
cnf(c_0_16,axiom,
multiply(X1,X1) = X1,
clause35 ).
cnf(c_0_17,plain,
product(a,b,multiply(X1,b)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_19,plain,
product(a,b,b),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_20,plain,
( X1 = b
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,negated_conjecture,
product(b,a,d),
b_times_a ).
cnf(c_0_22,axiom,
product(multiply(X1,b),a,multiply(X1,d)),
clause57 ).
cnf(c_0_23,plain,
multiply(X1,b) = b,
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( X1 = d
| ~ product(b,a,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_25,plain,
product(b,a,multiply(X1,d)),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_27,negated_conjecture,
multiply(X1,d) = d,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,axiom,
multiply(b,a) = d,
clause37 ).
cnf(c_0_29,negated_conjecture,
product(X1,d,d),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
product(a,d,multiply(X1,a)),
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
product(a,b,c),
a_times_b ).
cnf(c_0_32,negated_conjecture,
( X1 = d
| ~ product(X2,d,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_33,plain,
product(a,d,a),
inference(spm,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_34,plain,
product(X1,b,b),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_35,negated_conjecture,
( X1 = c
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
d = a,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_38,axiom,
sum(X1,X1,additive_identity),
clause32 ).
cnf(c_0_39,plain,
( X1 = b
| ~ product(X2,b,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_34]) ).
cnf(c_0_40,axiom,
product(add(b,a),b,add(b,c)),
clause68 ).
cnf(c_0_41,negated_conjecture,
c = b,
inference(spm,[status(thm)],[c_0_35,c_0_19]) ).
cnf(c_0_42,axiom,
add(X1,X1) = additive_identity,
clause34 ).
cnf(c_0_43,negated_conjecture,
( X1 = a
| ~ product(X2,a,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_36]),c_0_36]) ).
cnf(c_0_44,axiom,
product(add(a,b),a,add(a,d)),
clause70 ).
cnf(c_0_45,negated_conjecture,
c != d,
prove_c_equals_d ).
cnf(c_0_46,plain,
( X1 = additive_identity
| ~ sum(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,plain,
additive_identity = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42]) ).
cnf(c_0_48,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_49,negated_conjecture,
add(a,a) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_36]) ).
cnf(c_0_50,negated_conjecture,
d != b,
inference(rw,[status(thm)],[c_0_45,c_0_41]) ).
cnf(c_0_51,plain,
( X1 = b
| ~ sum(X2,X2,X1) ),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
sum(a,a,a),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
b != a,
inference(rw,[status(thm)],[c_0_50,c_0_36]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG039-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 02:00:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 start to proof: theBenchmark
% 0.20/0.64 % Version : CSE_E---1.5
% 0.20/0.64 % Problem : theBenchmark.p
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark.p
% 0.20/0.64 % SZS output start Proof
% See solution above
% 0.20/0.65 % Total time : 0.016000 s
% 0.20/0.65 % SZS output end Proof
% 0.20/0.65 % Total time : 0.020000 s
%------------------------------------------------------------------------------