%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG008-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:25:34 AM UTC 2026
% Result : Unsatisfiable 227.57s 40.72s
% Output : CNFRefutation 227.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 21
% Syntax : Number of clauses : 164 ( 72 unt; 0 nHn; 111 RR)
% Number of literals : 335 ( 38 equ; 173 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 : 422 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cancellation1,axiom,
( X1 = X3
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(cancellation2,axiom,
( X0 = X3
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(x_squared_is_x,hypothesis,
product(X0,X0,X0) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c) ).
cnf(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c) ).
cnf(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) ).
cnf(closure_of_multiplication,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(closure_of_addition,axiom,
sum(X0,X1,add(X0,X1)) ).
cnf(left_inverse,axiom,
sum('additive$uinverse'(X0),X0,'additive$uidentity') ).
cnf(right_inverse,axiom,
sum(X0,'additive$uinverse'(X0),'additive$uidentity') ).
cnf(associativity_of_addition1,axiom,
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(associativity_of_addition2,axiom,
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(commutativity_of_addition,axiom,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(associativity_of_multiplication1,axiom,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(associativity_of_multiplication2,axiom,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity2,axiom,
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity3,axiom,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity4,axiom,
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ) ).
cnf(multiplication_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
( X1 = X3
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[cancellation1]) ).
cnf(c1,plain,
( X0 = X3
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[cancellation2]) ).
cnf(c2,plain,
product(X0,X0,X0),
inference(clausification,[status(esa)],[x_squared_is_x]) ).
cnf(c3,plain,
product(a,b,c),
inference(clausification,[status(esa)],[a_times_b_is_c]) ).
cnf(c4,plain,
~ product(b,a,c),
inference(clausification,[status(esa)],[prove_b_times_a_is_c]) ).
cnf(c5,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c6,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c7,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c8,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c9,plain,
sum('additive$uinverse'(X0),X0,'additive$uidentity'),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c10,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c11,plain,
( sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_of_addition1]) ).
cnf(c12,plain,
( sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_of_addition2]) ).
cnf(c13,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c14,plain,
( product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_of_multiplication1]) ).
cnf(c15,plain,
( product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_of_multiplication2]) ).
cnf(c16,plain,
( ~ product(X6,X5,X2)
| ~ product(X6,X4,X1)
| ~ product(X6,X3,X0)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c17,plain,
( ~ sum(X4,X2,X6)
| ~ sum(X3,X1,X5)
| product(X0,X5,X6)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c18,plain,
( ~ product(X6,X1,X3)
| ~ sum(X0,X6,X5)
| ~ product(X5,X1,X4)
| sum(X2,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity3]) ).
cnf(c19,plain,
( ~ product(X6,X1,X5)
| ~ sum(X6,X0,X3)
| ~ sum(X5,X2,X4)
| product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity4]) ).
cnf(c21,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(d0,plain,
( ~ sum(X0,X1,'additive$uidentity')
| X0 = 'additive$uinverse'(X1) ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d1,plain,
( ~ sum(X1,X0,X1)
| X0 = 'additive$uidentity' ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(d2,plain,
( ~ product(X1,X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c21,c2]) ).
cnf(d3,plain,
multiply(X0,X0) = X0,
inference(resolution,[status(thm)],[d2,c7]) ).
cnf(d4,plain,
( ~ product('additive$uidentity',X4,X1)
| ~ product(X3,X4,X0)
| ~ product(X3,X4,X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c18,c6]) ).
cnf(d5,plain,
( ~ product('additive$uidentity',X3,X1)
| ~ product(X2,X3,X0)
| sum(X0,X1,multiply(X2,X3)) ),
inference(resolution,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
( ~ product('additive$uidentity',X0,X1)
| sum(X0,X1,multiply(X0,X0)) ),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
( ~ product('additive$uidentity',X0,X1)
| sum(X0,X1,X0) ),
inference(demodulation,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
sum(X0,multiply('additive$uidentity',X0),X0),
inference(resolution,[status(thm)],[d7,c7]) ).
cnf(d9,plain,
multiply('additive$uidentity',X0) = 'additive$uidentity',
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
( ~ product(X4,X3,X1)
| ~ product('additive$uinverse'(X4),X3,X0)
| ~ product('additive$uidentity',X3,X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c18,c9]) ).
cnf(d11,plain,
( ~ product('additive$uinverse'(X1),X1,X0)
| ~ product('additive$uidentity',X1,X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d10,c2]) ).
cnf(d12,plain,
( ~ product('additive$uinverse'(X1),X1,X0)
| sum(X0,X1,multiply('additive$uidentity',X1)) ),
inference(resolution,[status(thm)],[d11,c7]) ).
cnf(d13,plain,
( ~ product('additive$uinverse'(X0),X0,X1)
| sum(X1,X0,'additive$uidentity') ),
inference(demodulation,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
X0 = 'additive$uinverse'('additive$uinverse'(X0)),
inference(resolution,[status(thm)],[d0,c10]) ).
cnf(d15,plain,
( ~ product(X3,X4,X2)
| ~ product(X3,X4,X0)
| ~ product(X3,'additive$uidentity',X1)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c16,c6]) ).
cnf(d16,plain,
( ~ product(X2,'additive$uidentity',X1)
| ~ product(X2,X3,X0)
| sum(X0,X1,multiply(X2,X3)) ),
inference(resolution,[status(thm)],[d15,c7]) ).
cnf(d17,plain,
( ~ product(X0,'additive$uidentity',X1)
| sum(X0,X1,multiply(X0,X0)) ),
inference(resolution,[status(thm)],[d16,c2]) ).
cnf(d18,plain,
( ~ product(X0,'additive$uidentity',X1)
| sum(X0,X1,X0) ),
inference(demodulation,[status(thm)],[d17,d3]) ).
cnf(d19,plain,
sum(X0,multiply(X0,'additive$uidentity'),X0),
inference(resolution,[status(thm)],[d18,c7]) ).
cnf(d20,plain,
multiply(X0,'additive$uidentity') = 'additive$uidentity',
inference(resolution,[status(thm)],[d19,d1]) ).
cnf(d21,plain,
( ~ product(X3,'additive$uidentity',X2)
| ~ product(X3,'additive$uinverse'(X4),X0)
| ~ product(X3,X4,X1)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c16,c9]) ).
cnf(d22,plain,
( ~ product(X1,'additive$uinverse'(X1),X0)
| ~ product(X1,'additive$uidentity',X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d21,c2]) ).
cnf(d23,plain,
( ~ product(X1,'additive$uinverse'(X1),X0)
| sum(X0,X1,multiply(X1,'additive$uidentity')) ),
inference(resolution,[status(thm)],[d22,c7]) ).
cnf(d24,plain,
( ~ product(X0,'additive$uinverse'(X0),X1)
| sum(X1,X0,'additive$uidentity') ),
inference(demodulation,[status(thm)],[d23,d20]) ).
cnf(d25,plain,
sum(multiply(X0,'additive$uinverse'(X0)),X0,'additive$uidentity'),
inference(resolution,[status(thm)],[d24,c7]) ).
cnf(d26,plain,
multiply(X0,'additive$uinverse'(X0)) = 'additive$uinverse'(X0),
inference(resolution,[status(thm)],[d25,d0]) ).
cnf(d27,plain,
product(X0,'additive$uinverse'(X0),'additive$uinverse'(X0)),
inference(superposition,[status(thm)],[d26,c7]) ).
cnf(d28,plain,
( ~ sum('additive$uinverse'(X1),X0,'additive$uidentity')
| X0 = X1 ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d29,plain,
'additive$uinverse'('additive$uinverse'(X0)) = X0,
inference(resolution,[status(thm)],[d28,c10]) ).
cnf(d30,plain,
product('additive$uinverse'(X0),X0,'additive$uinverse'('additive$uinverse'(X0))),
inference(superposition,[status(thm)],[d29,d27]) ).
cnf(d31,plain,
product('additive$uinverse'(X0),X0,X0),
inference(demodulation,[status(thm)],[d30,d14]) ).
cnf(d32,plain,
sum(X0,X0,'additive$uidentity'),
inference(resolution,[status(thm)],[d31,d13]) ).
cnf(d33,plain,
X0 = 'additive$uinverse'(X0),
inference(resolution,[status(thm)],[d32,d0]) ).
cnf(d34,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c13,c8]) ).
cnf(d35,plain,
( ~ sum(X4,X2,X3)
| ~ sum(X0,X1,X4)
| sum(X0,add(X1,X2),X3) ),
inference(resolution,[status(thm)],[c11,c8]) ).
cnf(d36,plain,
( sum(X0,add(X1,'additive$uinverse'(X2)),'additive$uidentity')
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d35,c10]) ).
cnf(d37,plain,
sum(X0,add(X1,'additive$uinverse'(add(X1,X0))),'additive$uidentity'),
inference(resolution,[status(thm)],[d36,d34]) ).
cnf(d38,plain,
X0 = 'additive$uinverse'(add(X1,'additive$uinverse'(add(X1,X0)))),
inference(resolution,[status(thm)],[d37,d0]) ).
cnf(d39,plain,
X1 = add(X0,'additive$uinverse'(add(X0,X1))),
inference(demodulation,[status(thm)],[d38,d33]) ).
cnf(d40,plain,
X1 = add(X0,add(X0,X1)),
inference(demodulation,[status(thm)],[d39,d33]) ).
cnf(d41,plain,
( ~ sum(X2,X0,'additive$uidentity')
| X0 = add(X1,'additive$uinverse'(add(X1,X2))) ),
inference(resolution,[status(thm)],[d37,c0]) ).
cnf(d42,plain,
( ~ sum(X1,X2,'additive$uidentity')
| X2 = add(X0,add(X0,X1)) ),
inference(demodulation,[status(thm)],[d41,d33]) ).
cnf(d43,plain,
( ~ sum(X1,X2,'additive$uidentity')
| X2 = X1 ),
inference(demodulation,[status(thm)],[d42,d40]) ).
cnf(d44,plain,
( ~ product(X1,X2,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[c21,c7]) ).
cnf(d45,plain,
( ~ product(X0,X3,X2)
| ~ product(X0,X3,X1)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c2]) ).
cnf(d46,plain,
( product(a,X0,c)
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[d45,c3]) ).
cnf(d47,plain,
product(a,c,c),
inference(resolution,[status(thm)],[d46,c3]) ).
cnf(d48,plain,
( ~ product(X0,X3,X4)
| ~ product(X1,X3,'additive$uidentity')
| product(X2,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c19,c6]) ).
cnf(d49,plain,
( sum(X0,add(X1,X2),X2)
| ~ sum(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[d35,c5]) ).
cnf(d50,plain,
sum(X0,add('additive$uinverse'(X0),X1),X1),
inference(resolution,[status(thm)],[d49,c10]) ).
cnf(d51,plain,
( ~ product(X3,X1,X2)
| ~ product(add('additive$uinverse'(X3),X0),X1,'additive$uidentity')
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d50,d48]) ).
cnf(d52,plain,
( ~ product(add('additive$uinverse'(a),X0),c,'additive$uidentity')
| product(X0,c,c) ),
inference(resolution,[status(thm)],[d51,d47]) ).
cnf(d53,plain,
( ~ product(add(a,X0),c,'additive$uidentity')
| product(X0,c,c) ),
inference(demodulation,[status(thm)],[d52,d33]) ).
cnf(d54,plain,
( ~ product(X3,multiply(X4,X1),X2)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,c7]) ).
cnf(d55,plain,
( product(X0,X1,X2)
| ~ product(X0,multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[d54,c2]) ).
cnf(d56,plain,
product(X0,X1,multiply(X0,multiply(X0,X1))),
inference(resolution,[status(thm)],[d55,c7]) ).
cnf(d57,plain,
( ~ product(multiply(X0,X3),X4,X2)
| ~ product(X3,X4,X1)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c7]) ).
cnf(d58,plain,
( ~ product(multiply(X0,X1),X2,X3)
| product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[d57,c7]) ).
cnf(d59,plain,
product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)),
inference(resolution,[status(thm)],[d58,c7]) ).
cnf(d60,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(resolution,[status(thm)],[d59,d44]) ).
cnf(d61,plain,
( ~ product(X3,X0,X4)
| ~ product(X3,X1,'additive$uinverse'(X4))
| product(X3,X2,'additive$uidentity')
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c17,c10]) ).
cnf(d62,plain,
( ~ product(X0,X2,X3)
| ~ product(X0,X1,'additive$uinverse'(X3))
| product(X0,add(X1,X2),'additive$uidentity') ),
inference(resolution,[status(thm)],[d61,d34]) ).
cnf(d63,plain,
( ~ product(multiply(X0,X1),X1,X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d57,c2]) ).
cnf(d64,plain,
product(X0,X1,multiply(multiply(X0,X1),X1)),
inference(resolution,[status(thm)],[d63,c7]) ).
cnf(d65,plain,
( product(X0,add(X1,X2),'additive$uidentity')
| ~ product(X0,X1,'additive$uinverse'(multiply(multiply(X0,X2),X2))) ),
inference(resolution,[status(thm)],[d64,d62]) ).
cnf(d66,plain,
( product(X0,add(X2,X1),'additive$uidentity')
| ~ product(X0,X2,multiply(multiply(X0,X1),X1)) ),
inference(demodulation,[status(thm)],[d65,d33]) ).
cnf(d67,plain,
( product(X0,add(X2,X1),'additive$uidentity')
| ~ product(X0,X2,multiply(X0,multiply(X1,X1))) ),
inference(demodulation,[status(thm)],[d66,d60]) ).
cnf(d68,plain,
( product(X1,add(X2,X0),'additive$uidentity')
| ~ product(X1,X2,multiply(X1,X0)) ),
inference(demodulation,[status(thm)],[d67,d3]) ).
cnf(d69,plain,
product(X0,add(X1,multiply(X0,X1)),'additive$uidentity'),
inference(resolution,[status(thm)],[d68,d56]) ).
cnf(d70,plain,
( ~ sum('additive$uidentity',X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(d71,plain,
X0 = add(X0,'additive$uidentity'),
inference(resolution,[status(thm)],[d70,d34]) ).
cnf(d72,plain,
( ~ sum(X4,X1,X3)
| ~ sum(X2,X4,X0)
| sum(X0,X1,add(X2,X3)) ),
inference(resolution,[status(thm)],[c12,c8]) ).
cnf(d73,plain,
( sum(X2,'additive$uinverse'(X1),add(X0,'additive$uidentity'))
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d72,c10]) ).
cnf(d74,plain,
( ~ sum(X0,X2,X1)
| sum(X1,'additive$uinverse'(X2),X0) ),
inference(demodulation,[status(thm)],[d73,d71]) ).
cnf(d75,plain,
sum(add(X0,X1),'additive$uinverse'(X0),X1),
inference(resolution,[status(thm)],[d74,d34]) ).
cnf(d76,plain,
( ~ sum(X0,'additive$uinverse'(X1),X2)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[d75,c1]) ).
cnf(d77,plain,
( ~ sum(X1,X0,X2)
| X1 = add(X0,X2) ),
inference(demodulation,[status(thm)],[d76,d33]) ).
cnf(d78,plain,
( ~ product(X4,X5,X1)
| ~ product(X3,X5,X0)
| ~ product(add(X3,X4),X5,X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c18,c8]) ).
cnf(d79,plain,
( ~ product(add(X3,X1),X1,X2)
| ~ product(X3,X1,X0)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d78,c2]) ).
cnf(d80,plain,
( ~ product(add(a,b),b,X0)
| sum(c,b,X0) ),
inference(resolution,[status(thm)],[d79,c3]) ).
cnf(d81,plain,
sum(c,b,multiply(add(a,b),b)),
inference(resolution,[status(thm)],[d80,c7]) ).
cnf(d82,plain,
c = add(b,multiply(add(a,b),b)),
inference(resolution,[status(thm)],[d81,d77]) ).
cnf(d83,plain,
product(add(a,b),c,'additive$uidentity'),
inference(superposition,[status(thm)],[d82,d69]) ).
cnf(d84,plain,
product(b,c,c),
inference(resolution,[status(thm)],[d83,d53]) ).
cnf(d85,plain,
c = multiply(b,c),
inference(resolution,[status(thm)],[d84,d44]) ).
cnf(d86,plain,
( product(multiply(X0,X1),X2,X3)
| ~ product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[d54,c7]) ).
cnf(d87,plain,
product(multiply(X0,X1),X2,multiply(X0,multiply(X1,X2))),
inference(resolution,[status(thm)],[d86,c7]) ).
cnf(d88,plain,
X0 = multiply(X0,X0),
inference(resolution,[status(thm)],[d44,c2]) ).
cnf(d89,plain,
product(multiply(multiply(X0,X1),X0),X1,multiply(X0,X1)),
inference(superposition,[status(thm)],[d88,d87]) ).
cnf(d90,plain,
product(multiply(X0,multiply(X1,X0)),X1,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d89,d60]) ).
cnf(d91,plain,
( ~ product(a,b,X0)
| X0 = c ),
inference(resolution,[status(thm)],[c21,c3]) ).
cnf(d92,plain,
multiply(a,b) = c,
inference(resolution,[status(thm)],[d91,c7]) ).
cnf(d93,plain,
product(multiply(b,c),a,multiply(b,a)),
inference(superposition,[status(thm)],[d92,d90]) ).
cnf(d94,plain,
product(c,a,multiply(b,a)),
inference(demodulation,[status(thm)],[d93,d85]) ).
cnf(d95,plain,
multiply(b,a) = multiply(c,a),
inference(resolution,[status(thm)],[d94,d44]) ).
cnf(d96,plain,
( ~ product(X3,add(X4,X5),X2)
| ~ product(X3,X5,X0)
| ~ product(X3,X4,X1)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d34,c16]) ).
cnf(d97,plain,
( ~ product(X0,add(X3,X0),X2)
| ~ product(X0,X3,X1)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d96,c2]) ).
cnf(d98,plain,
( ~ product(X0,add(X1,X0),X2)
| sum(X0,multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[d97,c7]) ).
cnf(d99,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,'additive$uidentity','additive$uinverse'(X2))
| product(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[d61,c6]) ).
cnf(d100,plain,
( ~ product(X0,'additive$uidentity','additive$uinverse'(multiply(multiply(X0,X1),X1)))
| product(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[d64,d99]) ).
cnf(d101,plain,
( ~ product(X0,'additive$uidentity',multiply(multiply(X0,X1),X1))
| product(X0,X1,'additive$uidentity') ),
inference(demodulation,[status(thm)],[d100,d33]) ).
cnf(d102,plain,
( ~ product(X0,'additive$uidentity',multiply(X0,multiply(X1,X1)))
| product(X0,X1,'additive$uidentity') ),
inference(demodulation,[status(thm)],[d101,d60]) ).
cnf(d103,plain,
( ~ product(X1,'additive$uidentity',multiply(X1,X0))
| product(X1,X0,'additive$uidentity') ),
inference(demodulation,[status(thm)],[d102,d3]) ).
cnf(d104,plain,
product(X0,multiply(X1,multiply(X0,X1)),multiply(X0,X1)),
inference(resolution,[status(thm)],[d58,c2]) ).
cnf(d105,plain,
c = multiply(a,c),
inference(resolution,[status(thm)],[d47,d44]) ).
cnf(d106,plain,
product(a,multiply(c,X0),multiply(c,X0)),
inference(superposition,[status(thm)],[d105,d59]) ).
cnf(d107,plain,
( ~ product(X0,X3,X4)
| ~ product(X1,X3,'additive$uinverse'(X4))
| product(X2,X3,'additive$uidentity')
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c19,c10]) ).
cnf(d108,plain,
( ~ product(X1,X2,X3)
| ~ product(X0,X2,'additive$uinverse'(X3))
| product(add(X0,X1),X2,'additive$uidentity') ),
inference(resolution,[status(thm)],[d107,d34]) ).
cnf(d109,plain,
( product(X0,X2,multiply(X0,X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d45,c7]) ).
cnf(d110,plain,
product(X0,multiply(X0,X1),multiply(X0,X1)),
inference(resolution,[status(thm)],[d109,c7]) ).
cnf(d111,plain,
( product(add(X0,X1),multiply(X1,X2),'additive$uidentity')
| ~ product(X0,multiply(X1,X2),'additive$uinverse'(multiply(X1,X2))) ),
inference(resolution,[status(thm)],[d110,d108]) ).
cnf(d112,plain,
( product(add(X2,X0),multiply(X0,X1),'additive$uidentity')
| ~ product(X2,multiply(X0,X1),multiply(X0,X1)) ),
inference(demodulation,[status(thm)],[d111,d33]) ).
cnf(d113,plain,
product(add(a,c),multiply(c,X0),'additive$uidentity'),
inference(resolution,[status(thm)],[d112,d106]) ).
cnf(d114,plain,
'additive$uidentity' = multiply(add(a,c),multiply(c,X0)),
inference(resolution,[status(thm)],[d113,d44]) ).
cnf(d115,plain,
product(c,'additive$uidentity',multiply(c,add(a,c))),
inference(superposition,[status(thm)],[d114,d104]) ).
cnf(d116,plain,
product(c,add(a,c),'additive$uidentity'),
inference(resolution,[status(thm)],[d115,d103]) ).
cnf(d117,plain,
sum(c,multiply(c,a),'additive$uidentity'),
inference(resolution,[status(thm)],[d116,d98]) ).
cnf(d118,plain,
sum(c,multiply(b,a),'additive$uidentity'),
inference(demodulation,[status(thm)],[d117,d95]) ).
cnf(d119,plain,
multiply(b,a) = c,
inference(resolution,[status(thm)],[d118,d43]) ).
cnf(d120,plain,
product(b,a,c),
inference(superposition,[status(thm)],[d119,c7]) ).
cnf(d121,plain,
$false,
inference(resolution,[status(thm)],[c4,d120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n002.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 05:47:26 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 227.57/40.72 % SZS status Unsatisfiable for theBenchmark.p
% 227.57/40.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------