TSTP Solution File: RNG001-4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG001-4 : 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 : n018.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 0.71s 0.84s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of formulae : 84 ( 37 unt; 7 typ; 0 def)
% Number of atoms : 158 ( 32 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 164 ( 83 ~; 81 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 230 ( 7 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 ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
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/Axioms/RNG001-0.ax',associativity_of_addition2) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
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/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(cancellation2,axiom,
( X1 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation2) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(associativity_of_multiplication2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication2) ).
cnf(cancellation1,axiom,
( X2 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation1) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
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/Axioms/RNG001-0.ax',distributivity2) ).
cnf(associativity_of_multiplication1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication1) ).
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_16,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_17,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_18,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_19,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_20,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_21,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_22,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,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_25,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_26,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,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_24,c_0_25]) ).
cnf(c_0_29,axiom,
( X1 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X3) ),
cancellation2 ).
cnf(c_0_30,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_19]),c_0_27]) ).
cnf(c_0_31,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_32,plain,
( product(X1,X2,X3)
| ~ sum(multiply(X4,X2),multiply(X5,X2),X3)
| ~ sum(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_33,plain,
( X1 = X2
| ~ sum(X1,X3,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_34,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_35,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_36,plain,
( X1 = X2
| ~ sum(X1,X3,add(X3,X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_37,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_38,plain,
( product(X1,X2,X3)
| ~ sum(multiply(additive_identity,X2),multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_39,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity_of_multiplication2 ).
cnf(c_0_40,axiom,
( X2 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X3) ),
cancellation1 ).
cnf(c_0_41,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_42,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_43,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_34]),c_0_35]) ).
cnf(c_0_44,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_25]) ).
cnf(c_0_45,plain,
product(X1,X2,add(multiply(additive_identity,X2),multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_38,c_0_19]) ).
cnf(c_0_46,plain,
( X1 = additive_identity
| ~ sum(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_47,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_25]) ).
cnf(c_0_48,plain,
( X1 = additive_inverse(X2)
| ~ sum(X2,X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_35]) ).
cnf(c_0_50,plain,
add(multiply(additive_identity,X1),multiply(X2,X1)) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_46,c_0_23]) ).
cnf(c_0_52,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_53,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity_of_multiplication1 ).
cnf(c_0_54,plain,
( product(multiply(X1,X2),X3,X4)
| ~ product(X1,multiply(X2,X3),X4) ),
inference(spm,[status(thm)],[c_0_47,c_0_25]) ).
cnf(c_0_55,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_21]) ).
cnf(c_0_56,plain,
additive_inverse(multiply(additive_identity,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_57,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_22,c_0_41]) ).
cnf(c_0_58,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_52,c_0_25]) ).
cnf(c_0_59,plain,
( product(X1,X2,multiply(X3,X4))
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_25]) ).
cnf(c_0_60,plain,
product(multiply(X1,X2),X3,multiply(X1,multiply(X2,X3))),
inference(spm,[status(thm)],[c_0_54,c_0_25]) ).
cnf(c_0_61,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
cnf(c_0_62,plain,
( product(X1,X2,X3)
| ~ sum(multiply(X1,X4),multiply(X1,X5),X3)
| ~ sum(X4,X5,X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_25]) ).
cnf(c_0_63,plain,
( product(X1,multiply(X2,X3),multiply(X4,X3))
| ~ product(X1,X2,X4) ),
inference(spm,[status(thm)],[c_0_59,c_0_25]) ).
cnf(c_0_64,plain,
product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,plain,
( product(X1,X2,X3)
| ~ sum(multiply(X1,additive_identity),multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_62,c_0_17]) ).
cnf(c_0_66,plain,
product(X1,multiply(X2,X3),multiply(multiply(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_63,c_0_25]) ).
cnf(c_0_67,plain,
( X1 = multiply(X2,additive_identity)
| ~ product(multiply(X2,additive_identity),X3,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_64]) ).
cnf(c_0_68,plain,
product(X1,X2,add(multiply(X1,additive_identity),multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_65,c_0_19]) ).
cnf(c_0_69,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_44,c_0_66]) ).
cnf(c_0_70,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_42]),c_0_35]) ).
cnf(c_0_71,plain,
add(multiply(X1,additive_identity),multiply(X1,additive_identity)) = multiply(X1,additive_identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_61]),c_0_69]),c_0_61]) ).
cnf(c_0_72,plain,
additive_inverse(multiply(X1,additive_identity)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_51]) ).
cnf(c_0_73,plain,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_72]),c_0_57]) ).
cnf(c_0_74,negated_conjecture,
~ product(a,additive_identity,additive_identity),
prove_a_times_additive_id_is_additive_id ).
cnf(c_0_75,plain,
product(X1,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_25,c_0_73]) ).
cnf(c_0_76,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG001-4 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 03:01:45 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.71/0.84 % Version : CSE_E---1.5
% 0.71/0.84 % Problem : theBenchmark.p
% 0.71/0.84 % Proof found
% 0.71/0.84 % SZS status Theorem for theBenchmark.p
% 0.71/0.84 % SZS output start Proof
% See solution above
% 0.71/0.85 % Total time : 0.264000 s
% 0.71/0.85 % SZS output end Proof
% 0.71/0.85 % Total time : 0.267000 s
%------------------------------------------------------------------------------