%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG008-2 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.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 : Tue May 5 05:04:58 PM UTC 2026
% Result : Unsatisfiable 3.95s 3.16s
% Output : CNFRefutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 22
% Syntax : Number of clauses : 150 ( 73 unt; 0 nHn; 102 RR)
% Number of literals : 303 ( 52 equ; 155 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 358 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
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_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
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(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_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(x_squared_is_x,hypothesis,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_squared_is_x) ).
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(a_times_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
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_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(distributivity3,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity3) ).
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/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity1) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
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(associativity_of_addition1,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition1) ).
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(cancellation1,axiom,
( X2 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation1) ).
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(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
cnf(c_0_22,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_23,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_24,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_25,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_26,plain,
( X1 = X2
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_28,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity_of_multiplication2 ).
cnf(c_0_29,hypothesis,
product(X1,X1,X1),
x_squared_is_x ).
cnf(c_0_30,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_31,hypothesis,
product(a,b,c),
a_times_b_is_c ).
cnf(c_0_32,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_35,hypothesis,
( product(X1,X2,X3)
| ~ product(X4,X2,X3)
| ~ product(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,hypothesis,
( X1 = c
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_38,axiom,
( X1 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X3) ),
cancellation2 ).
cnf(c_0_39,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_27]),c_0_33]) ).
cnf(c_0_40,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_41,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_27]) ).
cnf(c_0_42,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
distributivity3 ).
cnf(c_0_43,hypothesis,
( product(X1,b,c)
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_31]) ).
cnf(c_0_44,hypothesis,
multiply(a,b) = c,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,plain,
( X1 = X2
| ~ sum(X1,X3,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_38,c_0_27]) ).
cnf(c_0_46,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_39,c_0_27]) ).
cnf(c_0_47,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,hypothesis,
( sum(X1,X2,c)
| ~ product(X3,b,X2)
| ~ product(X4,b,X1)
| ~ sum(X4,X3,a) ),
inference(spm,[status(thm)],[c_0_42,c_0_31]) ).
cnf(c_0_49,hypothesis,
product(c,b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_37]),c_0_44]) ).
cnf(c_0_50,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_51,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_52,hypothesis,
( sum(X1,c,c)
| ~ product(X2,b,X1)
| ~ sum(X2,c,a) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_54,hypothesis,
( sum(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X5,X3,X1)
| ~ sum(X5,X4,X3) ),
inference(spm,[status(thm)],[c_0_42,c_0_29]) ).
cnf(c_0_55,hypothesis,
( sum(X1,X2,X3)
| ~ product(X3,X4,X2)
| ~ product(X3,X5,X1)
| ~ sum(X5,X4,X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_29]) ).
cnf(c_0_56,plain,
( X1 = additive_inverse(X2)
| ~ sum(X1,add(X3,X2),X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_51]) ).
cnf(c_0_57,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_46]),c_0_47]) ).
cnf(c_0_58,hypothesis,
( sum(multiply(X1,b),c,c)
| ~ sum(X1,c,a) ),
inference(spm,[status(thm)],[c_0_52,c_0_37]) ).
cnf(c_0_59,plain,
sum(add(additive_inverse(X1),X2),X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_41]) ).
cnf(c_0_60,plain,
( X1 = additive_identity
| ~ sum(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_61,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_53]) ).
cnf(c_0_62,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_63,hypothesis,
( sum(X1,X2,X2)
| ~ product(X3,X2,X1)
| ~ sum(X3,X2,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_29]) ).
cnf(c_0_64,hypothesis,
( sum(X1,X2,X2)
| ~ product(X2,X3,X1)
| ~ sum(X3,X2,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_29]) ).
cnf(c_0_65,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity_of_multiplication1 ).
cnf(c_0_66,plain,
( X1 = additive_inverse(add(X2,additive_inverse(X3)))
| ~ sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_67,hypothesis,
sum(multiply(add(a,additive_inverse(c)),b),c,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_47]) ).
cnf(c_0_68,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_60,c_0_41]) ).
cnf(c_0_69,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_70,hypothesis,
( sum(multiply(X1,X2),X2,X2)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_37]) ).
cnf(c_0_71,hypothesis,
( sum(multiply(X1,X2),X1,X1)
| ~ sum(X2,X1,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_37]) ).
cnf(c_0_72,plain,
( product(X1,X2,multiply(X3,X4))
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_65,c_0_37]) ).
cnf(c_0_73,hypothesis,
multiply(add(a,additive_inverse(c)),b) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_69]) ).
cnf(c_0_74,plain,
( X1 = additive_identity
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_53]) ).
cnf(c_0_75,hypothesis,
sum(multiply(additive_identity,X1),X1,X1),
inference(spm,[status(thm)],[c_0_70,c_0_53]) ).
cnf(c_0_76,hypothesis,
sum(multiply(X1,additive_identity),X1,X1),
inference(spm,[status(thm)],[c_0_71,c_0_53]) ).
cnf(c_0_77,hypothesis,
( product(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_65,c_0_29]) ).
cnf(c_0_78,plain,
( product(X1,multiply(X2,X3),multiply(X4,X3))
| ~ product(X1,X2,X4) ),
inference(spm,[status(thm)],[c_0_72,c_0_37]) ).
cnf(c_0_79,hypothesis,
product(add(a,additive_inverse(c)),b,additive_identity),
inference(spm,[status(thm)],[c_0_37,c_0_73]) ).
cnf(c_0_80,hypothesis,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_81,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_74,c_0_76]) ).
cnf(c_0_82,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_37]) ).
cnf(c_0_83,hypothesis,
( product(X1,multiply(X2,X3),X3)
| ~ product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_77,c_0_37]) ).
cnf(c_0_84,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_85,hypothesis,
product(add(a,additive_inverse(c)),multiply(b,X1),additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_86,hypothesis,
product(X1,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_37,c_0_81]) ).
cnf(c_0_87,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1 ).
cnf(c_0_88,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_89,hypothesis,
( product(c,X1,X2)
| ~ product(a,multiply(b,X1),X2) ),
inference(spm,[status(thm)],[c_0_82,c_0_31]) ).
cnf(c_0_90,hypothesis,
product(X1,multiply(X2,multiply(X1,X2)),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_83,c_0_37]) ).
cnf(c_0_91,hypothesis,
multiply(add(a,additive_inverse(c)),multiply(b,X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_92,axiom,
( X2 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X3) ),
cancellation1 ).
cnf(c_0_93,hypothesis,
( sum(X1,X2,additive_identity)
| ~ product(X3,X4,X2)
| ~ product(X3,X5,X1)
| ~ sum(X5,X4,additive_identity) ),
inference(spm,[status(thm)],[c_0_50,c_0_86]) ).
cnf(c_0_94,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_87,c_0_53]) ).
cnf(c_0_95,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_88,c_0_37]) ).
cnf(c_0_96,hypothesis,
product(c,X1,multiply(a,multiply(b,X1))),
inference(spm,[status(thm)],[c_0_89,c_0_37]) ).
cnf(c_0_97,hypothesis,
product(b,additive_identity,multiply(b,add(a,additive_inverse(c)))),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_98,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_99,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_51]),c_0_47]) ).
cnf(c_0_100,plain,
( X1 = X2
| ~ sum(additive_inverse(X2),X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_92,c_0_25]) ).
cnf(c_0_101,hypothesis,
( sum(X1,X2,additive_identity)
| ~ product(X2,X3,X1)
| ~ sum(X3,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_93,c_0_29]) ).
cnf(c_0_102,plain,
( sum(X1,add(X2,X3),X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_94,c_0_41]) ).
cnf(c_0_103,hypothesis,
( product(X1,X2,X3)
| ~ sum(X1,multiply(X1,X4),X3)
| ~ sum(X1,X4,X2) ),
inference(spm,[status(thm)],[c_0_95,c_0_29]) ).
cnf(c_0_104,hypothesis,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_84,c_0_96]) ).
cnf(c_0_105,hypothesis,
multiply(b,add(a,additive_inverse(c))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_97]),c_0_81]) ).
cnf(c_0_106,hypothesis,
( sum(X1,c,c)
| ~ product(c,X2,X1)
| ~ sum(X2,b,c) ),
inference(spm,[status(thm)],[c_0_55,c_0_49]) ).
cnf(c_0_107,hypothesis,
( product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X5,X2,X3)
| ~ sum(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_29]) ).
cnf(c_0_108,plain,
( X1 = X2
| ~ sum(X1,additive_inverse(add(X2,X3)),additive_inverse(X3)) ),
inference(spm,[status(thm)],[c_0_45,c_0_99]) ).
cnf(c_0_109,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_100,c_0_62]) ).
cnf(c_0_110,hypothesis,
( sum(multiply(X1,X2),X1,additive_identity)
| ~ sum(X2,X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_101,c_0_37]) ).
cnf(c_0_111,plain,
sum(additive_inverse(X1),add(X2,X1),X2),
inference(spm,[status(thm)],[c_0_102,c_0_25]) ).
cnf(c_0_112,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_61,c_0_27]) ).
cnf(c_0_113,hypothesis,
( product(X1,add(X2,X1),X3)
| ~ sum(X1,multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_103,c_0_41]) ).
cnf(c_0_114,hypothesis,
multiply(c,add(a,additive_inverse(c))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_81]) ).
cnf(c_0_115,hypothesis,
( sum(multiply(c,X1),c,c)
| ~ sum(X1,b,c) ),
inference(spm,[status(thm)],[c_0_106,c_0_37]) ).
cnf(c_0_116,hypothesis,
( product(X1,X2,X3)
| ~ sum(multiply(X4,X2),X2,X3)
| ~ sum(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_107,c_0_37]) ).
cnf(c_0_117,plain,
( X1 = X2
| ~ sum(X1,additive_inverse(add(X2,additive_inverse(X3))),X3) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_118,hypothesis,
sum(multiply(X1,additive_inverse(X1)),X1,additive_identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]),c_0_112]) ).
cnf(c_0_119,hypothesis,
( product(c,a,X1)
| ~ sum(c,additive_identity,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_47]),c_0_57]) ).
cnf(c_0_120,hypothesis,
sum(multiply(c,add(c,additive_inverse(b))),c,c),
inference(spm,[status(thm)],[c_0_115,c_0_46]) ).
cnf(c_0_121,hypothesis,
( product(additive_identity,X1,X2)
| ~ sum(multiply(additive_inverse(X1),X1),X1,X2) ),
inference(spm,[status(thm)],[c_0_116,c_0_25]) ).
cnf(c_0_122,hypothesis,
multiply(additive_inverse(X1),X1) = X1,
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_117,c_0_118]),c_0_69]),c_0_33]),c_0_69]),c_0_33]),c_0_109]) ).
cnf(c_0_123,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_98,c_0_37]) ).
cnf(c_0_124,hypothesis,
product(b,multiply(c,a),multiply(b,a)),
inference(spm,[status(thm)],[c_0_90,c_0_104]) ).
cnf(c_0_125,hypothesis,
product(c,a,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_27]),c_0_33]) ).
cnf(c_0_126,hypothesis,
multiply(c,add(c,additive_inverse(b))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_120]),c_0_68]),c_0_69]) ).
cnf(c_0_127,hypothesis,
( product(additive_identity,X1,X2)
| ~ sum(X1,X1,X2) ),
inference(rw,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_128,hypothesis,
( product(X1,X2,X3)
| ~ sum(X2,multiply(X4,X2),X3)
| ~ sum(X2,X4,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_29]) ).
cnf(c_0_129,hypothesis,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(spm,[status(thm)],[c_0_84,c_0_124]) ).
cnf(c_0_130,hypothesis,
multiply(c,a) = c,
inference(spm,[status(thm)],[c_0_84,c_0_125]) ).
cnf(c_0_131,hypothesis,
product(c,add(c,additive_inverse(b)),additive_identity),
inference(spm,[status(thm)],[c_0_37,c_0_126]) ).
cnf(c_0_132,hypothesis,
product(additive_identity,X1,add(X1,X1)),
inference(spm,[status(thm)],[c_0_127,c_0_27]) ).
cnf(c_0_133,hypothesis,
( product(add(X1,X2),X2,X3)
| ~ sum(X2,multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_128,c_0_41]) ).
cnf(c_0_134,hypothesis,
multiply(b,c) = multiply(b,a),
inference(rw,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_135,hypothesis,
product(c,multiply(add(c,additive_inverse(b)),X1),additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_131]),c_0_80]) ).
cnf(c_0_136,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_59]),c_0_47]) ).
cnf(c_0_137,hypothesis,
add(X1,X1) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_132]),c_0_80]) ).
cnf(c_0_138,hypothesis,
( product(add(b,c),c,X1)
| ~ sum(c,multiply(b,a),X1) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_139,hypothesis,
multiply(c,multiply(add(c,additive_inverse(b)),X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_84,c_0_135]) ).
cnf(c_0_140,hypothesis,
additive_inverse(X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_33]) ).
cnf(c_0_141,hypothesis,
product(add(b,c),c,add(c,multiply(b,a))),
inference(spm,[status(thm)],[c_0_138,c_0_27]) ).
cnf(c_0_142,hypothesis,
multiply(c,multiply(add(b,c),X1)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140]),c_0_47]) ).
cnf(c_0_143,hypothesis,
multiply(add(b,c),c) = add(c,multiply(b,a)),
inference(spm,[status(thm)],[c_0_84,c_0_141]) ).
cnf(c_0_144,hypothesis,
product(add(b,c),additive_identity,add(c,multiply(b,a))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_142]),c_0_143]) ).
cnf(c_0_145,plain,
add(X1,add(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_136,c_0_140]) ).
cnf(c_0_146,hypothesis,
add(c,multiply(b,a)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_144]),c_0_81]) ).
cnf(c_0_147,hypothesis,
multiply(b,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_33]) ).
cnf(c_0_148,negated_conjecture,
~ product(b,a,c),
prove_b_times_a_is_c ).
cnf(c_0_149,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_147]),c_0_148]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG008-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:45:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 3.95/3.16 % Version : CSE_E---1.7
% 3.95/3.16 % Problem : theBenchmark.p
% 3.95/3.16 % SZS status Unsatisfiable for theBenchmark.p
% 3.95/3.16 % SZS output start CNFRefutation
% See solution above
% 3.95/3.18 % Total time : 2.370s
%------------------------------------------------------------------------------