TSTP Solution File: RNG001-10 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG001-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n003.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 13:48:19 EDT 2023
% Result : Unsatisfiable 15.26s 15.38s
% Output : CNFRefutation 15.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 28
% Syntax : Number of formulae : 144 ( 134 unt; 10 typ; 0 def)
% Number of atoms : 134 ( 133 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 19 ( 7 >; 12 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 387 ( 8 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(decl_24,type,
additive_identity: $i ).
tff(decl_25,type,
sum: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
true: $i ).
tff(decl_27,type,
multiply: ( $i * $i ) > $i ).
tff(decl_28,type,
product: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
add: ( $i * $i ) > $i ).
tff(decl_30,type,
additive_inverse: $i > $i ).
tff(decl_31,type,
a: $i ).
cnf(associativity_of_addition2,axiom,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X1,X6),true,sum(X6,X2,X5),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(ifeq_axiom_001,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
cnf(addition_is_well_defined,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(ifeq_axiom,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(commutativity_of_addition,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(cancellation2,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X4,X2,X3),true,X4,X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation2) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(distributivity4,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,X5),true,ifeq(sum(X5,X3,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X2,X6),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(multiplication_is_well_defined,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(associativity_of_multiplication2,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,ifeq(product(X4,X1,X6),true,product(X6,X2,X5),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
cnf(distributivity3,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,X5),true,ifeq(product(X6,X2,X7),true,ifeq(sum(X6,X4,X1),true,sum(X7,X5,X3),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
cnf(distributivity2,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X4,X5),true,ifeq(sum(X5,X3,X6),true,ifeq(sum(X4,X2,X7),true,product(X1,X7,X6),true),true),true),true) = true,
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) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).
cnf(c_0_18,axiom,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X1,X6),true,sum(X6,X2,X5),true),true),true) = true,
associativity_of_addition2 ).
cnf(c_0_19,axiom,
sum(X1,X2,add(X1,X2)) = true,
closure_of_addition ).
cnf(c_0_20,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_21,plain,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,sum(add(X4,X1),X2,X5),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_22,axiom,
sum(X1,additive_identity,X1) = true,
additive_identity2 ).
cnf(c_0_23,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
addition_is_well_defined ).
cnf(c_0_24,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_25,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
commutativity_of_addition ).
cnf(c_0_26,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X4,X2,X3),true,X4,X1),X1) = X1,
cancellation2 ).
cnf(c_0_27,plain,
ifeq(sum(X1,X2,additive_identity),true,sum(add(X3,X1),X2,X3),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_20]) ).
cnf(c_0_28,axiom,
sum(additive_inverse(X1),X1,additive_identity) = true,
left_inverse ).
cnf(c_0_29,plain,
ifeq2(sum(X1,X2,X3),true,add(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_19]),c_0_24]) ).
cnf(c_0_30,plain,
sum(X1,X2,add(X2,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_20]) ).
cnf(c_0_31,plain,
ifeq2(sum(X1,X2,add(X3,X2)),true,X3,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_19]),c_0_24]) ).
cnf(c_0_32,plain,
sum(add(X1,additive_inverse(X2)),X2,X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20]) ).
cnf(c_0_33,plain,
add(X1,X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24]) ).
cnf(c_0_34,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,X5),true,ifeq(sum(X5,X3,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X2,X6),true),true),true),true) = true,
distributivity4 ).
cnf(c_0_35,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_24]),c_0_33]) ).
cnf(c_0_36,axiom,
sum(additive_identity,X1,X1) = true,
additive_identity1 ).
cnf(c_0_37,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(additive_inverse(X1),X2,X4),true,ifeq(sum(X4,X3,X5),true,product(additive_identity,X2,X5),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_20]) ).
cnf(c_0_38,plain,
sum(additive_inverse(X1),add(X2,X1),X2) = true,
inference(spm,[status(thm)],[c_0_19,c_0_35]) ).
cnf(c_0_39,plain,
ifeq2(sum(X1,X2,X2),true,X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_36]),c_0_24]) ).
cnf(c_0_40,plain,
ifeq(product(X1,X2,add(X3,X4)),true,ifeq(product(additive_inverse(X1),X2,additive_inverse(X4)),true,product(additive_identity,X2,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_20]) ).
cnf(c_0_41,plain,
additive_inverse(additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_28]),c_0_24]) ).
cnf(c_0_42,plain,
ifeq2(sum(X1,X2,additive_identity),true,additive_inverse(X2),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_28]),c_0_24]) ).
cnf(c_0_43,axiom,
sum(X1,additive_inverse(X1),additive_identity) = true,
right_inverse ).
cnf(c_0_44,plain,
ifeq2(sum(X1,X2,add(X2,X3)),true,X1,X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_30]),c_0_24]) ).
cnf(c_0_45,plain,
ifeq(product(additive_identity,X1,add(X2,X3)),true,ifeq(product(additive_identity,X1,additive_inverse(X3)),true,product(additive_identity,X1,X2),true),true) = true,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_24]) ).
cnf(c_0_47,plain,
ifeq2(sum(additive_inverse(X1),X1,X2),true,X2,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_28]),c_0_24]) ).
cnf(c_0_48,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_32]),c_0_24]),c_0_33]) ).
cnf(c_0_49,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_35]),c_0_33]) ).
cnf(c_0_50,plain,
ifeq(product(additive_identity,X1,add(X2,additive_inverse(X3))),true,ifeq(product(additive_identity,X1,X3),true,product(additive_identity,X1,X2),true),true) = true,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,axiom,
product(X1,X2,multiply(X1,X2)) = true,
closure_of_multiplication ).
cnf(c_0_52,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_30]),c_0_24]) ).
cnf(c_0_53,plain,
additive_inverse(add(X1,X2)) = add(additive_inverse(X1),additive_inverse(X2)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_24]),c_0_33]) ).
cnf(c_0_55,plain,
ifeq(product(additive_identity,X1,add(X2,additive_inverse(multiply(additive_identity,X1)))),true,product(additive_identity,X1,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_20]) ).
cnf(c_0_56,plain,
add(add(X1,X2),add(additive_inverse(X1),additive_inverse(X2))) = additive_identity,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_54,c_0_33]) ).
cnf(c_0_58,plain,
ifeq(sum(X1,X2,X3),true,sum(add(X4,X1),X2,add(X4,X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_20]) ).
cnf(c_0_59,plain,
ifeq(product(additive_identity,X1,add(additive_inverse(multiply(additive_identity,X1)),X2)),true,product(additive_identity,X1,X2),true) = true,
inference(spm,[status(thm)],[c_0_55,c_0_33]) ).
cnf(c_0_60,plain,
ifeq(sum(additive_identity,X1,X2),true,ifeq(sum(X3,X2,X4),true,sum(X3,X1,X4),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_22]),c_0_20]) ).
cnf(c_0_61,plain,
sum(add(X1,X2),additive_inverse(X2),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_43]),c_0_20]) ).
cnf(c_0_62,plain,
add(add(X1,X2),add(additive_inverse(X2),additive_inverse(X1))) = additive_identity,
inference(spm,[status(thm)],[c_0_56,c_0_33]) ).
cnf(c_0_63,plain,
ifeq2(sum(X1,X2,X3),true,X1,add(additive_inverse(X2),X3)) = add(additive_inverse(X2),X3),
inference(spm,[status(thm)],[c_0_44,c_0_57]) ).
cnf(c_0_64,plain,
sum(add(X1,X2),X3,add(X1,add(X2,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_19]),c_0_20]) ).
cnf(c_0_65,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
multiplication_is_well_defined ).
cnf(c_0_66,plain,
ifeq(product(additive_identity,X1,X2),true,product(additive_identity,X1,add(multiply(additive_identity,X1),X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_57]),c_0_46]) ).
cnf(c_0_67,plain,
ifeq(sum(additive_identity,X1,X2),true,sum(X3,X1,add(X3,X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_19]),c_0_20]) ).
cnf(c_0_68,plain,
sum(additive_identity,add(X1,X2),add(X2,X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_53]),c_0_46]),c_0_46]) ).
cnf(c_0_69,plain,
add(additive_inverse(X1),add(X2,add(X3,X1))) = add(X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_24]) ).
cnf(c_0_70,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_64]),c_0_24]) ).
cnf(c_0_71,plain,
ifeq2(product(X1,X2,X3),true,multiply(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_51]),c_0_24]) ).
cnf(c_0_72,plain,
product(additive_identity,X1,add(multiply(additive_identity,X1),multiply(additive_identity,X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_51]),c_0_20]) ).
cnf(c_0_73,plain,
ifeq2(sum(X1,X2,X3),true,X3,add(X2,X1)) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_30]),c_0_24]) ).
cnf(c_0_74,plain,
sum(X1,add(X2,X3),add(X1,add(X3,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_20]) ).
cnf(c_0_75,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(additive_inverse(X1),X2,X4),true,product(additive_identity,X2,add(X4,X3)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_19]),c_0_20]) ).
cnf(c_0_76,plain,
add(additive_inverse(X1),add(X2,add(X3,add(X4,X1)))) = add(X2,add(X3,X4)),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_77,plain,
add(multiply(additive_identity,X1),multiply(additive_identity,X1)) = multiply(additive_identity,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_24]) ).
cnf(c_0_78,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,ifeq(product(X4,X1,X6),true,product(X6,X2,X5),true),true),true) = true,
associativity_of_multiplication2 ).
cnf(c_0_79,plain,
add(X1,add(X2,X3)) = add(add(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_24]) ).
cnf(c_0_80,plain,
ifeq(product(X1,X2,X3),true,product(additive_identity,X2,add(multiply(additive_inverse(X1),X2),X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_51]),c_0_20]) ).
cnf(c_0_81,plain,
add(X1,add(X2,multiply(additive_identity,X3))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_69]) ).
cnf(c_0_82,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,product(multiply(X4,X1),X2,X5),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_51]),c_0_20]) ).
cnf(c_0_83,plain,
add(X1,add(X2,X3)) = add(X3,add(X2,X1)),
inference(rw,[status(thm)],[c_0_79,c_0_70]) ).
cnf(c_0_84,plain,
product(additive_identity,X1,add(multiply(X2,X1),multiply(additive_inverse(X2),X1))) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_51]),c_0_20]),c_0_33]) ).
cnf(c_0_85,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_81]),c_0_52]) ).
cnf(c_0_86,plain,
ifeq2(sum(X1,additive_identity,X2),true,X2,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_22]),c_0_24]) ).
cnf(c_0_87,plain,
ifeq(product(X1,X2,X3),true,product(multiply(X4,X1),X2,multiply(X4,X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_51]),c_0_20]) ).
cnf(c_0_88,plain,
add(additive_inverse(X1),add(X2,add(X1,X3))) = add(X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_57]),c_0_70]) ).
cnf(c_0_89,plain,
add(multiply(X1,X2),multiply(additive_inverse(X1),X2)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_84]),c_0_85]),c_0_24]) ).
cnf(c_0_90,plain,
add(X1,additive_identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_19]),c_0_24]) ).
cnf(c_0_91,plain,
product(multiply(X1,X2),X3,multiply(X1,multiply(X2,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_51]),c_0_20]) ).
cnf(c_0_92,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,X5),true,ifeq(sum(X5,X3,X6),true,product(add(X4,X1),X2,X6),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_19]),c_0_20]) ).
cnf(c_0_93,plain,
add(additive_inverse(multiply(X1,X2)),X3) = add(multiply(additive_inverse(X1),X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).
cnf(c_0_94,plain,
product(multiply(X1,multiply(X2,X3)),X4,multiply(X1,multiply(X2,multiply(X3,X4)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_91]),c_0_20]) ).
cnf(c_0_95,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,additive_inverse(X3)),true,product(add(X4,X1),X2,additive_identity),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_28]),c_0_20]) ).
cnf(c_0_96,plain,
additive_inverse(multiply(X1,X2)) = multiply(additive_inverse(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_93]),c_0_54]) ).
cnf(c_0_97,plain,
product(multiply(X1,multiply(X2,multiply(X3,X4))),X5,multiply(X1,multiply(X2,multiply(X3,multiply(X4,X5))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_94]),c_0_20]) ).
cnf(c_0_98,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,additive_identity),true,product(add(X4,X1),X2,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_36]),c_0_20]) ).
cnf(c_0_99,plain,
ifeq(product(X1,X2,multiply(additive_inverse(X3),X2)),true,product(add(X1,X3),X2,additive_identity),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_51]),c_0_96]),c_0_20]) ).
cnf(c_0_100,plain,
product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_85]),c_0_85]) ).
cnf(c_0_101,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,X5),true,ifeq(product(X6,X2,X7),true,ifeq(sum(X6,X4,X1),true,sum(X7,X5,X3),true),true),true),true) = true,
distributivity3 ).
cnf(c_0_102,plain,
ifeq(product(X1,X2,additive_identity),true,product(add(X1,X3),X2,multiply(X3,X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_51]),c_0_20]) ).
cnf(c_0_103,plain,
product(add(X1,multiply(additive_inverse(X1),additive_identity)),additive_identity,additive_identity) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_20]),c_0_33]) ).
cnf(c_0_104,plain,
ifeq(product(add(X1,X2),X3,X4),true,ifeq(product(X2,X3,X5),true,ifeq(product(X1,X3,X6),true,sum(X6,X5,X4),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_19]),c_0_20]) ).
cnf(c_0_105,plain,
product(add(X1,add(multiply(additive_inverse(X1),additive_identity),X2)),additive_identity,multiply(X2,additive_identity)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_70]),c_0_20]) ).
cnf(c_0_106,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,additive_inverse(X3)),true,ifeq(sum(X4,X1,X5),true,product(X5,X2,additive_identity),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_20]) ).
cnf(c_0_107,plain,
sum(additive_inverse(X1),add(X1,X2),X2) = true,
inference(spm,[status(thm)],[c_0_19,c_0_48]) ).
cnf(c_0_108,plain,
product(add(additive_inverse(X1),multiply(X1,additive_identity)),additive_identity,additive_identity) = true,
inference(spm,[status(thm)],[c_0_103,c_0_46]) ).
cnf(c_0_109,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X4,X5),true,ifeq(sum(X5,X3,X6),true,ifeq(sum(X4,X2,X7),true,product(X1,X7,X6),true),true),true),true) = true,
distributivity2 ).
cnf(c_0_110,plain,
ifeq(product(add(multiply(X1,X2),X3),X4,X5),true,ifeq(product(X3,X4,X6),true,sum(multiply(X1,multiply(X2,X4)),X6,X5),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_91]),c_0_20]) ).
cnf(c_0_111,plain,
product(add(multiply(X1,additive_identity),X2),additive_identity,multiply(add(X2,X1),additive_identity)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_69]),c_0_46]) ).
cnf(c_0_112,plain,
ifeq(product(X1,X2,additive_identity),true,product(add(X1,multiply(X3,additive_identity)),X2,multiply(X3,additive_identity)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_100]),c_0_20]) ).
cnf(c_0_113,plain,
multiply(add(X1,add(multiply(additive_inverse(X1),additive_identity),X2)),additive_identity) = multiply(X2,additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_105]),c_0_24]) ).
cnf(c_0_114,plain,
add(X1,add(X2,add(additive_inverse(X1),X3))) = add(X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_54]),c_0_70]) ).
cnf(c_0_115,plain,
ifeq(product(add(X1,X2),X3,X4),true,ifeq(product(additive_inverse(X1),X3,additive_inverse(X4)),true,product(X2,X3,additive_identity),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_20]) ).
cnf(c_0_116,plain,
product(add(additive_inverse(X1),add(multiply(X1,additive_identity),X2)),additive_identity,multiply(X2,additive_identity)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_108]),c_0_70]),c_0_20]) ).
cnf(c_0_117,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,additive_inverse(X2),X4),true,ifeq(sum(X4,X3,X5),true,product(X1,additive_identity,X5),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_28]),c_0_20]) ).
cnf(c_0_118,plain,
ifeq(product(X1,additive_identity,X2),true,sum(multiply(X3,additive_identity),X2,multiply(add(X1,X3),additive_identity)),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_85]),c_0_20]) ).
cnf(c_0_119,plain,
product(add(additive_inverse(X1),add(multiply(X1,additive_identity),multiply(X2,additive_identity))),additive_identity,multiply(X2,additive_identity)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_108]),c_0_70]),c_0_20]) ).
cnf(c_0_120,plain,
multiply(add(X1,add(multiply(X2,additive_identity),X3)),additive_identity) = multiply(add(X2,add(X1,X3)),additive_identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_96]),c_0_46]) ).
cnf(c_0_121,plain,
multiply(add(multiply(X1,additive_identity),X2),additive_identity) = multiply(add(X1,X2),additive_identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_57]),c_0_96]),c_0_46]) ).
cnf(c_0_122,plain,
ifeq(product(X1,additive_identity,multiply(additive_inverse(X2),additive_identity)),true,product(add(multiply(X1,additive_identity),X2),additive_identity,additive_identity),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_46]),c_0_96]),c_0_20]) ).
cnf(c_0_123,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,additive_inverse(X2),X4),true,product(X1,additive_identity,add(X4,X3)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_19]),c_0_20]) ).
cnf(c_0_124,plain,
sum(multiply(X1,additive_identity),multiply(X2,additive_identity),multiply(add(X2,X1),additive_identity)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_70]),c_0_70]),c_0_120]),c_0_57]),c_0_121]),c_0_20]) ).
cnf(c_0_125,plain,
ifeq(product(X1,additive_identity,multiply(add(X1,additive_inverse(X2)),additive_identity)),true,product(X2,additive_identity,additive_identity),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_57]),c_0_96]),c_0_53]),c_0_96]),c_0_46]),c_0_121]) ).
cnf(c_0_126,plain,
ifeq(product(X1,X2,X3),true,product(X1,additive_identity,add(multiply(X1,additive_inverse(X2)),X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_51]),c_0_20]) ).
cnf(c_0_127,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_91]),c_0_24]) ).
cnf(c_0_128,plain,
add(multiply(X1,additive_identity),multiply(X2,additive_identity)) = multiply(add(X2,X1),additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_124]),c_0_24]) ).
cnf(c_0_129,plain,
ifeq(product(multiply(X1,additive_identity),additive_identity,multiply(add(X1,additive_inverse(X2)),additive_identity)),true,product(X2,additive_identity,additive_identity),true) = true,
inference(spm,[status(thm)],[c_0_125,c_0_121]) ).
cnf(c_0_130,plain,
product(multiply(X1,additive_identity),additive_identity,multiply(add(X1,X1),additive_identity)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_100]),c_0_127]),c_0_85]),c_0_128]),c_0_20]) ).
cnf(c_0_131,negated_conjecture,
product(a,additive_identity,additive_identity) != true,
prove_a_times_additive_id_is_additive_id ).
cnf(c_0_132,plain,
product(X1,additive_identity,additive_identity) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_20]) ).
cnf(c_0_133,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_132])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG001-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n003.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 02:07:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 15.26/15.38 % Version : CSE_E---1.5
% 15.26/15.38 % Problem : theBenchmark.p
% 15.26/15.38 % Proof found
% 15.26/15.38 % SZS status Theorem for theBenchmark.p
% 15.26/15.38 % SZS output start Proof
% See solution above
% 15.30/15.39 % Total time : 14.754000 s
% 15.30/15.39 % SZS output end Proof
% 15.30/15.39 % Total time : 14.758000 s
%------------------------------------------------------------------------------