%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG004-2 : 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 : n005.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 08:25:33 AM UTC 2026
% Result : Unsatisfiable 35.44s 4.75s
% Output : CNFRefutation 35.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 55 ( 28 unt; 0 nHn; 47 RR)
% Number of literals : 110 ( 17 equ; 57 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cancellation1,axiom,
( X1 = X3
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(a_times_b,hypothesis,
product(a,b,c) ).
cnf(a_inverse_times_b_inverse,hypothesis,
product('additive$uinverse'(a),'additive$uinverse'(b),d) ).
cnf(prove_c_equals_d,negated_conjecture,
c != d ).
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$uidentity') ).
cnf(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity3,axiom,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ) ).
cnf(multiplication_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
( X1 = X3
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[cancellation1]) ).
cnf(c2,plain,
product(a,b,c),
inference(clausification,[status(esa)],[a_times_b]) ).
cnf(c3,plain,
product('additive$uinverse'(a),'additive$uinverse'(b),d),
inference(clausification,[status(esa)],[a_inverse_times_b_inverse]) ).
cnf(c4,plain,
d != c,
inference(clausification,[status(esa)],[prove_c_equals_d]) ).
cnf(c6,plain,
sum(X0,'additive$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(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(c16,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(c18,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(c21,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(d0,plain,
( ~ sum('additive$uinverse'(X1),X0,'additive$uidentity')
| X0 = X1 ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d1,plain,
( ~ sum(X1,X0,'additive$uidentity')
| X0 = 'additive$uinverse'(X1) ),
inference(resolution,[status(thm)],[c10,c0]) ).
cnf(d2,plain,
( ~ product(X3,'additive$uinverse'(X4),X1)
| ~ product(X3,X4,X0)
| ~ product(X3,'additive$uidentity',X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c16,c10]) ).
cnf(d3,plain,
( ~ product(a,'additive$uidentity',X1)
| ~ product(a,'additive$uinverse'(b),X0)
| sum(c,X0,X1) ),
inference(resolution,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
( ~ product(a,'additive$uidentity',X0)
| sum(c,multiply(a,'additive$uinverse'(b)),X0) ),
inference(resolution,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
( ~ sum(X1,X0,X1)
| X0 = 'additive$uidentity' ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(d6,plain,
( ~ product(a,b,X0)
| X0 = c ),
inference(resolution,[status(thm)],[c21,c2]) ).
cnf(d7,plain,
multiply(a,b) = c,
inference(resolution,[status(thm)],[d6,c7]) ).
cnf(d8,plain,
( ~ product(X3,'additive$uidentity',X1)
| ~ product(X3,X4,X0)
| ~ product(X3,X4,X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c16,c6]) ).
cnf(d9,plain,
( ~ product(X2,'additive$uidentity',X1)
| ~ product(X2,X3,X0)
| sum(X0,X1,multiply(X2,X3)) ),
inference(resolution,[status(thm)],[d8,c7]) ).
cnf(d10,plain,
( ~ product(a,'additive$uidentity',X0)
| sum(c,X0,multiply(a,b)) ),
inference(resolution,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
( ~ product(a,'additive$uidentity',X0)
| sum(c,X0,c) ),
inference(demodulation,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
sum(c,multiply(a,'additive$uidentity'),c),
inference(resolution,[status(thm)],[d11,c7]) ).
cnf(d13,plain,
multiply(a,'additive$uidentity') = 'additive$uidentity',
inference(resolution,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
product(a,'additive$uidentity','additive$uidentity'),
inference(superposition,[status(thm)],[d13,c7]) ).
cnf(d15,plain,
sum(c,multiply(a,'additive$uinverse'(b)),'additive$uidentity'),
inference(resolution,[status(thm)],[d14,d4]) ).
cnf(d16,plain,
multiply(a,'additive$uinverse'(b)) = 'additive$uinverse'(c),
inference(resolution,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
( ~ product('additive$uinverse'(X3),X4,X1)
| ~ product('additive$uidentity',X4,X2)
| ~ product(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c18,c10]) ).
cnf(d18,plain,
( ~ product('additive$uidentity',X1,X3)
| ~ product('additive$uinverse'(X0),X1,X2)
| sum(multiply(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[d17,c7]) ).
cnf(d19,plain,
( ~ product('additive$uidentity','additive$uinverse'(b),X0)
| sum(multiply(a,'additive$uinverse'(b)),d,X0) ),
inference(resolution,[status(thm)],[d18,c3]) ).
cnf(d20,plain,
( ~ product(X1,X2,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[c21,c7]) ).
cnf(d21,plain,
d = multiply('additive$uinverse'(a),'additive$uinverse'(b)),
inference(resolution,[status(thm)],[d20,c3]) ).
cnf(d22,plain,
( ~ product('additive$uidentity',X4,X1)
| ~ product(X3,X4,X2)
| ~ product(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c18,c6]) ).
cnf(d23,plain,
( ~ product('additive$uidentity',X3,X1)
| ~ product(X2,X3,X0)
| sum(X0,X1,multiply(X2,X3)) ),
inference(resolution,[status(thm)],[d22,c7]) ).
cnf(d24,plain,
( ~ product('additive$uidentity','additive$uinverse'(b),X0)
| sum(d,X0,multiply('additive$uinverse'(a),'additive$uinverse'(b))) ),
inference(resolution,[status(thm)],[d23,c3]) ).
cnf(d25,plain,
( ~ product('additive$uidentity','additive$uinverse'(b),X0)
| sum(d,X0,d) ),
inference(demodulation,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
sum(d,multiply('additive$uidentity','additive$uinverse'(b)),d),
inference(resolution,[status(thm)],[d25,c7]) ).
cnf(d27,plain,
multiply('additive$uidentity','additive$uinverse'(b)) = 'additive$uidentity',
inference(resolution,[status(thm)],[d26,d5]) ).
cnf(d28,plain,
product('additive$uidentity','additive$uinverse'(b),'additive$uidentity'),
inference(superposition,[status(thm)],[d27,c7]) ).
cnf(d29,plain,
sum(multiply(a,'additive$uinverse'(b)),d,'additive$uidentity'),
inference(resolution,[status(thm)],[d28,d19]) ).
cnf(d30,plain,
sum('additive$uinverse'(c),d,'additive$uidentity'),
inference(demodulation,[status(thm)],[d29,d16]) ).
cnf(d31,plain,
d = c,
inference(resolution,[status(thm)],[d30,d0]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[c4,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n005.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 05:43:47 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.44/4.75 % SZS status Unsatisfiable for theBenchmark.p
% 35.44/4.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------