%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG008-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 50.47s 8.94s
% Output : CNFRefutation 50.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 25
% Syntax : Number of clauses : 143 ( 66 unt; 0 nHn; 101 RR)
% Number of literals : 293 ( 31 equ; 152 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 : 350 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_inverse_additive_inverse,axiom,
sum('additive$uinverse'('additive$uinverse'(X0)),'additive$uidentity',X0) ).
cnf(multiply_additive_id1,axiom,
product(X0,'additive$uidentity','additive$uidentity') ).
cnf(multiply_additive_id2,axiom,
product('additive$uidentity',X0,'additive$uidentity') ).
cnf(distribute_additive_inverse,axiom,
sum('additive$uinverse'(X0),'additive$uinverse'(X1),'additive$uinverse'(add(X0,X1))) ).
cnf(multiply_additive_inverse,axiom,
product(X0,'additive$uinverse'(X1),'additive$uinverse'(multiply(X0,X1))) ).
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(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(multiplication_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c1,plain,
sum('additive$uinverse'('additive$uinverse'(X0)),'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_inverse_additive_inverse]) ).
cnf(c2,plain,
product(X0,'additive$uidentity','additive$uidentity'),
inference(clausification,[status(esa)],[multiply_additive_id1]) ).
cnf(c3,plain,
product('additive$uidentity',X0,'additive$uidentity'),
inference(clausification,[status(esa)],[multiply_additive_id2]) ).
cnf(c4,plain,
sum('additive$uinverse'(X0),'additive$uinverse'(X1),'additive$uinverse'(add(X0,X1))),
inference(clausification,[status(esa)],[distribute_additive_inverse]) ).
cnf(c5,plain,
product(X0,'additive$uinverse'(X1),'additive$uinverse'(multiply(X0,X1))),
inference(clausification,[status(esa)],[multiply_additive_inverse]) ).
cnf(c6,plain,
product(X0,X0,X0),
inference(clausification,[status(esa)],[x_squared_is_x]) ).
cnf(c7,plain,
product(a,b,c),
inference(clausification,[status(esa)],[a_times_b_is_c]) ).
cnf(c8,plain,
~ product(b,a,c),
inference(clausification,[status(esa)],[prove_b_times_a_is_c]) ).
cnf(c9,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c10,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c11,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c12,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c13,plain,
sum('additive$uinverse'(X0),X0,'additive$uidentity'),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c14,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c15,plain,
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_of_addition1]) ).
cnf(c16,plain,
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_of_addition2]) ).
cnf(c17,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c18,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_of_multiplication1]) ).
cnf(c19,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_of_multiplication2]) ).
cnf(c20,plain,
( ~ product(X0,X5,X3)
| ~ product(X0,X6,X4)
| ~ sum(X5,X1,X6)
| sum(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c21,plain,
( ~ sum(X4,X6,X2)
| ~ product(X0,X5,X6)
| ~ sum(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c22,plain,
( ~ product(X1,X3,X6)
| sum(X4,X6,X5)
| ~ product(X2,X3,X5)
| ~ product(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity3]) ).
cnf(c23,plain,
( ~ sum(X4,X6,X2)
| ~ sum(X3,X5,X0)
| ~ product(X5,X1,X6)
| ~ product(X3,X1,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity4]) ).
cnf(c24,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(c25,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(d0,plain,
( ~ sum('additive$uidentity',X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c24,c9]) ).
cnf(d1,plain,
( ~ sum('additive$uinverse'(X2),X3,X1)
| ~ sum(X2,X0,X3)
| sum('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[c16,c13]) ).
cnf(d2,plain,
( sum('additive$uidentity',X1,'additive$uinverse'(X0))
| ~ sum(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[d1,c10]) ).
cnf(d3,plain,
( X1 = 'additive$uinverse'(X0)
| ~ sum(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( ~ product(X4,X1,X2)
| ~ product(X3,X1,X0)
| ~ sum(X3,X1,X4)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c22,c6]) ).
cnf(d5,plain,
( ~ sum(X0,'additive$uidentity',X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c24,c10]) ).
cnf(d6,plain,
'additive$uinverse'('additive$uinverse'(X0)) = X0,
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
( ~ product(X1,X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c25,c6]) ).
cnf(d8,plain,
multiply(X0,X0) = X0,
inference(resolution,[status(thm)],[d7,c11]) ).
cnf(d9,plain,
product(X0,'additive$uinverse'(X0),'additive$uinverse'(X0)),
inference(superposition,[status(thm)],[d8,c5]) ).
cnf(d10,plain,
product('additive$uinverse'(X0),X0,'additive$uinverse'('additive$uinverse'(X0))),
inference(superposition,[status(thm)],[d6,d9]) ).
cnf(d11,plain,
product('additive$uinverse'(X0),X0,X0),
inference(demodulation,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( ~ product(X1,X0,X2)
| sum(X0,X0,X2)
| ~ sum('additive$uinverse'(X0),X0,X1) ),
inference(resolution,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
( ~ product('additive$uidentity',X0,X1)
| sum(X0,X0,X1) ),
inference(resolution,[status(thm)],[d12,c13]) ).
cnf(d14,plain,
sum(X0,X0,'additive$uidentity'),
inference(resolution,[status(thm)],[d13,c3]) ).
cnf(d15,plain,
X0 = 'additive$uinverse'(X0),
inference(resolution,[status(thm)],[d14,d3]) ).
cnf(d16,plain,
( ~ sum(X3,X0,'additive$uidentity')
| sum(X3,X2,X1)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,c9]) ).
cnf(d17,plain,
( ~ sum(X0,X1,'additive$uidentity')
| sum(X0,'additive$uidentity','additive$uinverse'(X1)) ),
inference(resolution,[status(thm)],[d16,c14]) ).
cnf(d18,plain,
( X0 = 'additive$uinverse'(X1)
| ~ sum(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[d17,d5]) ).
cnf(d19,plain,
( ~ sum(X1,X0,'additive$uidentity')
| X1 = X0 ),
inference(demodulation,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
( ~ product(X1,X4,X0)
| ~ product(X1,X5,X3)
| ~ sum(X4,'additive$uinverse'(X2),X5)
| sum(X0,'additive$uinverse'(multiply(X1,X2)),X3) ),
inference(resolution,[status(thm)],[c20,c5]) ).
cnf(d21,plain,
( ~ product(X1,'additive$uidentity',X0)
| ~ product(X1,'additive$uinverse'(X2),X3)
| sum(X0,'additive$uinverse'(multiply(X1,X2)),X3) ),
inference(resolution,[status(thm)],[d20,c9]) ).
cnf(d22,plain,
( 'additive$uinverse'(multiply(X0,X1)) = X2
| ~ product(X0,'additive$uidentity','additive$uidentity')
| ~ product(X0,'additive$uinverse'(X1),X2) ),
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
( ~ product(X0,'additive$uidentity','additive$uidentity')
| ~ product(X0,'additive$uinverse'(X1),X2)
| multiply(X0,X1) = X2 ),
inference(demodulation,[status(thm)],[d22,d15]) ).
cnf(d24,plain,
( ~ product(X1,'additive$uidentity','additive$uidentity')
| ~ product(X1,X0,X2)
| multiply(X1,X0) = X2 ),
inference(demodulation,[status(thm)],[d23,d15]) ).
cnf(d25,plain,
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[c2,d24]) ).
cnf(d26,plain,
sum('additive$uinverse'(X0),'additive$uinverse'(X1),'additive$uinverse'(add(X1,X0))),
inference(resolution,[status(thm)],[c17,c4]) ).
cnf(d27,plain,
sum('additive$uinverse'(X1),X0,'additive$uinverse'(add('additive$uinverse'(X0),X1))),
inference(superposition,[status(thm)],[d6,d26]) ).
cnf(d28,plain,
( ~ product(X1,X4,X0)
| ~ product(X1,X5,X3)
| ~ sum(X4,X2,X5)
| sum(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[c20,c11]) ).
cnf(d29,plain,
( ~ product(X0,X2,X3)
| sum('additive$uinverse'(X0),multiply(X0,X1),X3)
| ~ sum('additive$uinverse'(X0),X1,X2) ),
inference(resolution,[status(thm)],[d28,d9]) ).
cnf(d30,plain,
( ~ product(X0,'additive$uinverse'(add('additive$uinverse'(X1),X0)),X2)
| sum('additive$uinverse'(X0),multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[d29,d27]) ).
cnf(d31,plain,
( ~ product(X0,'additive$uinverse'(add('additive$uinverse'(X1),X0)),X2)
| sum(X0,multiply(X0,X1),X2) ),
inference(demodulation,[status(thm)],[d30,d15]) ).
cnf(d32,plain,
( ~ product(X1,add('additive$uinverse'(X0),X1),X2)
| sum(X1,multiply(X1,X0),X2) ),
inference(demodulation,[status(thm)],[d31,d15]) ).
cnf(d33,plain,
( ~ product(X1,add(X0,X1),X2)
| sum(X1,multiply(X1,X0),X2) ),
inference(demodulation,[status(thm)],[d32,d15]) ).
cnf(d34,plain,
( ~ product(X0,X4,X3)
| ~ product(X1,X2,X4)
| product(multiply(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[c19,c11]) ).
cnf(d35,plain,
( product(multiply(X2,X0),X1,'additive$uidentity')
| ~ product(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[d34,c2]) ).
cnf(d36,plain,
( ~ product(a,b,X0)
| X0 = c ),
inference(resolution,[status(thm)],[c25,c7]) ).
cnf(d37,plain,
multiply(a,b) = c,
inference(resolution,[status(thm)],[d36,c11]) ).
cnf(d38,plain,
( ~ product(b,X0,'additive$uidentity')
| product(c,X0,'additive$uidentity') ),
inference(superposition,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c17,c12]) ).
cnf(d40,plain,
( ~ product(X0,b,X2)
| product(X1,b,X3)
| ~ sum(X2,c,X3)
| ~ sum(X0,a,X1) ),
inference(resolution,[status(thm)],[c23,c7]) ).
cnf(d41,plain,
( ~ product(X3,X1,X2)
| ~ product(X0,X1,X3)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c18,c6]) ).
cnf(d42,plain,
( product(a,b,X0)
| ~ product(c,b,X0) ),
inference(resolution,[status(thm)],[d41,c7]) ).
cnf(d43,plain,
product(a,b,multiply(c,b)),
inference(resolution,[status(thm)],[d42,c11]) ).
cnf(d44,plain,
multiply(c,b) = c,
inference(resolution,[status(thm)],[d43,d36]) ).
cnf(d45,plain,
product(c,b,c),
inference(superposition,[status(thm)],[d44,c11]) ).
cnf(d46,plain,
( product(X1,b,X0)
| ~ sum(c,a,X1)
| ~ sum(c,c,X0) ),
inference(resolution,[status(thm)],[d45,d40]) ).
cnf(d47,plain,
( product(X0,b,'additive$uidentity')
| ~ sum(c,a,X0) ),
inference(resolution,[status(thm)],[d46,d14]) ).
cnf(d48,plain,
product(add(a,c),b,'additive$uidentity'),
inference(resolution,[status(thm)],[d47,d39]) ).
cnf(d49,plain,
( ~ product(X4,'additive$uinverse'(X2),X3)
| ~ product(X0,X1,X4)
| product(X0,'additive$uinverse'(multiply(X1,X2)),X3) ),
inference(resolution,[status(thm)],[c18,c5]) ).
cnf(d50,plain,
( product(X0,'additive$uinverse'(multiply(X1,X2)),'additive$uidentity')
| ~ product(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[d49,c3]) ).
cnf(d51,plain,
( 'additive$uidentity' = 'additive$uinverse'(multiply(X0,X1))
| ~ product('additive$uinverse'(multiply(X0,X1)),X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[d50,d7]) ).
cnf(d52,plain,
( ~ product('additive$uinverse'(multiply(X0,X1)),X0,'additive$uidentity')
| 'additive$uidentity' = multiply(X0,X1) ),
inference(demodulation,[status(thm)],[d51,d15]) ).
cnf(d53,plain,
( ~ product(multiply(X0,X1),X0,'additive$uidentity')
| 'additive$uidentity' = multiply(X0,X1) ),
inference(demodulation,[status(thm)],[d52,d15]) ).
cnf(d54,plain,
( ~ product(X1,X0,'additive$uidentity')
| 'additive$uidentity' = multiply(X0,X1) ),
inference(resolution,[status(thm)],[d53,d35]) ).
cnf(d55,plain,
'additive$uidentity' = multiply(b,add(a,c)),
inference(resolution,[status(thm)],[d54,d48]) ).
cnf(d56,plain,
product(b,add(a,c),'additive$uidentity'),
inference(superposition,[status(thm)],[d55,c11]) ).
cnf(d57,plain,
product(c,add(a,c),'additive$uidentity'),
inference(resolution,[status(thm)],[d56,d38]) ).
cnf(d58,plain,
sum(c,multiply(c,a),'additive$uidentity'),
inference(resolution,[status(thm)],[d57,d33]) ).
cnf(d59,plain,
c = multiply(c,a),
inference(resolution,[status(thm)],[d58,d19]) ).
cnf(d60,plain,
( ~ product(X4,X2,X3)
| ~ product(X0,X1,X4)
| product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[c18,c11]) ).
cnf(d61,plain,
( product(X0,multiply(X1,X2),X3)
| ~ product(multiply(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[d60,c11]) ).
cnf(d62,plain,
( ~ product(X0,X4,X3)
| ~ product('additive$uinverse'(X1),X2,X4)
| product('additive$uinverse'(multiply(X0,X1)),X2,X3) ),
inference(resolution,[status(thm)],[c19,c5]) ).
cnf(d63,plain,
( product('additive$uinverse'(multiply(X0,X1)),X2,X3)
| ~ product(X0,multiply('additive$uinverse'(X1),X2),X3) ),
inference(resolution,[status(thm)],[d62,c11]) ).
cnf(d64,plain,
product('additive$uinverse'(multiply(multiply('additive$uinverse'(X0),X1),X0)),X1,multiply('additive$uinverse'(X0),X1)),
inference(resolution,[status(thm)],[d63,c6]) ).
cnf(d65,plain,
product(multiply(multiply('additive$uinverse'(X0),X1),X0),X1,multiply('additive$uinverse'(X0),X1)),
inference(demodulation,[status(thm)],[d64,d15]) ).
cnf(d66,plain,
product(multiply(multiply(X0,X1),X0),X1,multiply('additive$uinverse'(X0),X1)),
inference(demodulation,[status(thm)],[d65,d15]) ).
cnf(d67,plain,
product(multiply(multiply(X0,X1),X0),X1,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d66,d15]) ).
cnf(d68,plain,
( ~ product(X1,X2,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[c25,c11]) ).
cnf(d69,plain,
( ~ product(X2,b,X1)
| ~ product(X0,a,X2)
| product(X0,c,X1) ),
inference(resolution,[status(thm)],[c18,c7]) ).
cnf(d70,plain,
( product(X0,c,X1)
| ~ product(multiply(X0,a),b,X1) ),
inference(resolution,[status(thm)],[d69,c11]) ).
cnf(d71,plain,
product(X0,c,multiply(multiply(X0,a),b)),
inference(resolution,[status(thm)],[d70,c11]) ).
cnf(d72,plain,
multiply(multiply(X0,a),b) = multiply(X0,c),
inference(resolution,[status(thm)],[d71,d68]) ).
cnf(d73,plain,
product(multiply(b,c),a,multiply(b,a)),
inference(superposition,[status(thm)],[d72,d67]) ).
cnf(d74,plain,
product(b,multiply(c,a),multiply(b,a)),
inference(resolution,[status(thm)],[d73,d61]) ).
cnf(d75,plain,
product(b,c,multiply(b,a)),
inference(demodulation,[status(thm)],[d74,d59]) ).
cnf(d76,plain,
multiply(b,c) = multiply(b,a),
inference(resolution,[status(thm)],[d75,d25]) ).
cnf(d77,plain,
( ~ product(X0,X1,X3)
| product(X0,X2,X4)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c21,c6]) ).
cnf(d78,plain,
( product(c,X1,X0)
| ~ sum(c,b,X1)
| ~ sum(c,c,X0) ),
inference(resolution,[status(thm)],[d45,d77]) ).
cnf(d79,plain,
( product(c,X0,'additive$uidentity')
| ~ sum(c,b,X0) ),
inference(resolution,[status(thm)],[d78,d14]) ).
cnf(d80,plain,
product(c,add(b,c),'additive$uidentity'),
inference(resolution,[status(thm)],[d79,d39]) ).
cnf(d81,plain,
'additive$uidentity' = multiply(add(b,c),c),
inference(resolution,[status(thm)],[d54,d80]) ).
cnf(d82,plain,
product(add(b,c),c,'additive$uidentity'),
inference(superposition,[status(thm)],[d81,c11]) ).
cnf(d83,plain,
( ~ product(X5,X2,X3)
| ~ product(X4,X2,X0)
| ~ sum(X4,X1,X5)
| sum(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[c22,c11]) ).
cnf(d84,plain,
( ~ product(X2,X0,X3)
| sum(X0,multiply(X1,X0),X3)
| ~ sum('additive$uinverse'(X0),X1,X2) ),
inference(resolution,[status(thm)],[d11,d83]) ).
cnf(d85,plain,
( ~ product('additive$uinverse'(add('additive$uinverse'(X1),X0)),X0,X2)
| sum(X0,multiply(X1,X0),X2) ),
inference(resolution,[status(thm)],[d84,d27]) ).
cnf(d86,plain,
( ~ product(add('additive$uinverse'(X0),X1),X1,X2)
| sum(X1,multiply(X0,X1),X2) ),
inference(demodulation,[status(thm)],[d85,d15]) ).
cnf(d87,plain,
( ~ product(add(X0,X1),X1,X2)
| sum(X1,multiply(X0,X1),X2) ),
inference(demodulation,[status(thm)],[d86,d15]) ).
cnf(d88,plain,
sum(c,multiply(b,c),'additive$uidentity'),
inference(resolution,[status(thm)],[d87,d82]) ).
cnf(d89,plain,
sum(c,multiply(b,a),'additive$uidentity'),
inference(demodulation,[status(thm)],[d88,d76]) ).
cnf(d90,plain,
c = multiply(b,a),
inference(resolution,[status(thm)],[d89,d19]) ).
cnf(d91,plain,
product(b,a,c),
inference(superposition,[status(thm)],[d90,c11]) ).
cnf(d92,plain,
$false,
inference(resolution,[status(thm)],[c8,d91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n014.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 05:45:01 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.47/8.94 % SZS status Unsatisfiable for theBenchmark.p
% 50.47/8.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------