%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG007-1 : 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 : n001.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 38.76s 10.73s
% Output : CNFRefutation 38.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 74 ( 37 unt; 0 nHn; 38 RR)
% Number of literals : 153 ( 17 equ; 81 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 210 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(x_squared_is_x,hypothesis,
product(X0,X0,X0) ).
cnf(prove_a_plus_a_is_id,negated_conjecture,
~ sum(a,a,'additive$uidentity') ).
cnf(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) ).
cnf(closure_of_multiplication,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(left_inverse,axiom,
sum('additive$uinverse'(X0),X0,'additive$uidentity') ).
cnf(right_inverse,axiom,
sum(X0,'additive$uinverse'(X0),'additive$uidentity') ).
cnf(associativity_of_addition1,axiom,
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(associativity_of_addition2,axiom,
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(associativity_of_multiplication1,axiom,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity3,axiom,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ) ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(multiplication_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
product(X0,X0,X0),
inference(clausification,[status(esa)],[x_squared_is_x]) ).
cnf(c1,plain,
~ sum(a,a,'additive$uidentity'),
inference(clausification,[status(esa)],[prove_a_plus_a_is_id]) ).
cnf(c2,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c3,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c4,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c6,plain,
sum('additive$uinverse'(X0),X0,'additive$uidentity'),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c7,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c8,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(c9,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(c11,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(c13,plain,
( sum(X4,X6,X2)
| ~ sum(X3,X5,X1)
| ~ product(X0,X5,X6)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c15,plain,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity3]) ).
cnf(c17,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(c18,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(d0,plain,
( ~ product(X1,X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c18,c0]) ).
cnf(d1,plain,
multiply(X0,X0) = X0,
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( ~ sum(X1,'additive$uidentity',X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c17,c3]) ).
cnf(d3,plain,
( ~ sum(X2,'additive$uinverse'(X3),X1)
| ~ sum(X0,X2,X3)
| sum(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[c8,c7]) ).
cnf(d4,plain,
( sum(X0,'additive$uidentity','additive$uidentity')
| ~ sum(X0,X1,X1) ),
inference(resolution,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
( ~ sum(X3,X0,X1)
| sum(X4,X2,X1)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,c0]) ).
cnf(d6,plain,
( ~ sum(X3,X0,X1)
| sum(multiply(X3,X1),X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
( sum(multiply(X0,X1),X1,X1)
| ~ sum(X0,X1,X1) ),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
sum(multiply('additive$uidentity',X0),X0,X0),
inference(resolution,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
sum(multiply('additive$uidentity',X0),'additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
'additive$uidentity' = multiply('additive$uidentity',X0),
inference(resolution,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
( ~ sum(X3,X0,X5)
| sum(X4,X2,multiply(X5,X1))
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,c4]) ).
cnf(d12,plain,
( ~ sum(X3,X0,X4)
| sum(multiply(X3,X1),X2,multiply(X4,X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d11,c4]) ).
cnf(d13,plain,
( sum(multiply(X0,X3),multiply(X1,X3),multiply(X2,X3))
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d12,c4]) ).
cnf(d14,plain,
sum(multiply(X0,X1),multiply('additive$uinverse'(X0),X1),multiply('additive$uidentity',X1)),
inference(resolution,[status(thm)],[d13,c7]) ).
cnf(d15,plain,
sum(multiply(X1,X0),multiply('additive$uinverse'(X1),X0),'additive$uidentity'),
inference(demodulation,[status(thm)],[d14,d10]) ).
cnf(d16,plain,
( ~ product(X1,X2,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[c18,c4]) ).
cnf(d17,plain,
( ~ product(X4,X2,X3)
| ~ product(X0,X1,X4)
| product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[c11,c4]) ).
cnf(d18,plain,
( product(X0,multiply(X1,X3),multiply(X2,X3))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d17,c4]) ).
cnf(d19,plain,
product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)),
inference(resolution,[status(thm)],[d18,c4]) ).
cnf(d20,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(resolution,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
( ~ product(X3,X1,X2)
| ~ product(X0,X1,X3)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,c0]) ).
cnf(d22,plain,
( product(X0,X1,multiply(X2,X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d21,c4]) ).
cnf(d23,plain,
product(X0,X1,multiply(multiply(X0,X1),X1)),
inference(resolution,[status(thm)],[d22,c4]) ).
cnf(d24,plain,
multiply(multiply(X0,X1),X1) = multiply(X0,X1),
inference(resolution,[status(thm)],[d23,d16]) ).
cnf(d25,plain,
multiply(X0,multiply(X1,X1)) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d24,d20]) ).
cnf(d26,plain,
multiply(X1,X0) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d25,d1]) ).
cnf(d27,plain,
( ~ sum('additive$uidentity',X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c17,c2]) ).
cnf(d28,plain,
( ~ sum(X3,'additive$uidentity',X2)
| ~ sum(X3,'additive$uinverse'(X1),X0)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,c6]) ).
cnf(d29,plain,
( sum(X2,X1,X0)
| ~ sum(X0,'additive$uinverse'(X1),X2) ),
inference(resolution,[status(thm)],[d28,c3]) ).
cnf(d30,plain,
( ~ sum(X5,X1,X3)
| sum(multiply(X0,X5),X2,X4)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c13,c4]) ).
cnf(d31,plain,
( sum(multiply(X0,X3),X2,X0)
| ~ sum(X3,X1,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d30,c0]) ).
cnf(d32,plain,
( sum(multiply(X1,X0),X1,X1)
| ~ sum(X0,X1,X1) ),
inference(resolution,[status(thm)],[d31,c0]) ).
cnf(d33,plain,
sum(multiply(X0,'additive$uidentity'),X0,X0),
inference(resolution,[status(thm)],[d32,c2]) ).
cnf(d34,plain,
sum(multiply(X0,'additive$uidentity'),'additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d33,d4]) ).
cnf(d35,plain,
'additive$uidentity' = multiply(X0,'additive$uidentity'),
inference(resolution,[status(thm)],[d34,d2]) ).
cnf(d36,plain,
( sum(multiply(X0,X3),X2,multiply(X0,X4))
| ~ sum(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d30,c4]) ).
cnf(d37,plain,
( sum(multiply(X1,X0),X1,multiply(X1,X2))
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d36,c0]) ).
cnf(d38,plain,
sum(multiply('additive$uinverse'(X0),X0),'additive$uinverse'(X0),multiply('additive$uinverse'(X0),'additive$uidentity')),
inference(resolution,[status(thm)],[d37,c7]) ).
cnf(d39,plain,
sum(multiply('additive$uinverse'(X0),X0),'additive$uinverse'(X0),'additive$uidentity'),
inference(demodulation,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
sum('additive$uidentity',X0,multiply('additive$uinverse'(X0),X0)),
inference(resolution,[status(thm)],[d39,d29]) ).
cnf(d41,plain,
multiply('additive$uinverse'(X0),X0) = X0,
inference(resolution,[status(thm)],[d40,d27]) ).
cnf(d42,plain,
X0 = multiply('additive$uinverse'(X0),X0),
inference(superposition,[status(thm)],[d41,d26]) ).
cnf(d43,plain,
sum(multiply(X0,X0),X0,'additive$uidentity'),
inference(superposition,[status(thm)],[d42,d15]) ).
cnf(d44,plain,
sum(X0,X0,'additive$uidentity'),
inference(demodulation,[status(thm)],[d43,d1]) ).
cnf(d45,plain,
$false,
inference(resolution,[status(thm)],[d44,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 05:50:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.76/10.73 % SZS status Unsatisfiable for theBenchmark.p
% 38.76/10.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------