%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG001-1 : 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 : n026.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 08:25:32 AM UTC 2026
% Result : Unsatisfiable 43.58s 11.71s
% Output : CNFRefutation 43.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of clauses : 56 ( 25 unt; 0 nHn; 34 RR)
% Number of literals : 111 ( 15 equ; 57 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 143 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_a_times_0_is_0,negated_conjecture,
~ product(a,'additive$uidentity','additive$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(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(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(c0,plain,
~ product(a,'additive$uidentity','additive$uidentity'),
inference(clausification,[status(esa)],[prove_a_times_0_is_0]) ).
cnf(c1,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c2,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c3,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c4,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c5,plain,
sum('additive$uinverse'(X0),X0,'additive$uidentity'),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c6,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c7,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(c8,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(c9,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c12,plain,
( ~ product(X0,X3,X5)
| ~ product(X0,X4,X6)
| sum(X5,X2,X6)
| ~ sum(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c16,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(d0,plain,
( ~ sum('additive$uidentity',X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c16,c1]) ).
cnf(d1,plain,
( ~ sum(X2,X3,X0)
| ~ sum(X3,X1,'additive$uidentity')
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(d2,plain,
( sum('additive$uidentity',X1,X0)
| ~ sum('additive$uinverse'(X0),X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
sum('additive$uidentity','additive$uinverse'('additive$uinverse'(X0)),X0),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
X0 = 'additive$uinverse'('additive$uinverse'(X0)),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ sum(X1,'additive$uidentity',X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c16,c2]) ).
cnf(d6,plain,
( ~ sum(X3,'additive$uinverse'(X2),X1)
| ~ sum(X0,X2,X3)
| sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(d7,plain,
( sum(X0,'additive$uidentity','additive$uinverse'(X1))
| ~ sum(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
( 'additive$uinverse'(X1) = X0
| ~ sum(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ sum(X3,X2,X0)
| ~ sum(X2,X1,'additive$uinverse'(X3))
| sum(X0,X1,'additive$uidentity') ),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d10,plain,
( sum(X1,'additive$uinverse'(X0),'additive$uidentity')
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
( 'additive$uinverse'('additive$uinverse'(X0)) = X1
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( ~ sum(X0,'additive$uidentity',X1)
| X0 = X1 ),
inference(demodulation,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c9,c4]) ).
cnf(d14,plain,
( ~ sum(X3,X2,X1)
| ~ sum(X0,'additive$uinverse'(X2),X3)
| sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d15,plain,
( sum(X1,'additive$uidentity',X2)
| ~ sum(add('additive$uinverse'(X0),X1),X0,X2) ),
inference(resolution,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
sum(X0,'additive$uidentity',add(X1,add('additive$uinverse'(X1),X0))),
inference(resolution,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
X0 = add(X1,add('additive$uinverse'(X1),X0)),
inference(resolution,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
X0 = add(X0,'additive$uidentity'),
inference(resolution,[status(thm)],[d12,c4]) ).
cnf(d19,plain,
'additive$uidentity' = add(X0,'additive$uinverse'(X0)),
inference(superposition,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
( ~ sum(X1,X2,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[c16,c4]) ).
cnf(d21,plain,
( ~ sum(X0,'additive$uinverse'(X0),X1)
| 'additive$uidentity' = X1 ),
inference(superposition,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
sum(add('additive$uinverse'(X0),X1),X0,X1),
inference(superposition,[status(thm)],[d17,d13]) ).
cnf(d23,plain,
sum(add(X0,X1),'additive$uinverse'(X0),X1),
inference(superposition,[status(thm)],[d4,d22]) ).
cnf(d24,plain,
( ~ sum(X0,X1,X2)
| sum(X2,'additive$uinverse'(X0),X1) ),
inference(superposition,[status(thm)],[d20,d23]) ).
cnf(d25,plain,
( 'additive$uidentity' = X1
| ~ sum(X0,X1,X0) ),
inference(resolution,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
( sum(X3,X4,X2)
| ~ product(X0,'additive$uidentity',X4)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c12,c2]) ).
cnf(d27,plain,
( sum(X2,multiply(X0,'additive$uidentity'),X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d26,c3]) ).
cnf(d28,plain,
( 'additive$uidentity' = multiply(X0,'additive$uidentity')
| ~ product(X0,X1,X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d27,d25]) ).
cnf(d29,plain,
( ~ product(X0,X1,X2)
| product(X0,'additive$uidentity','additive$uidentity') ),
inference(superposition,[status(thm)],[d28,c3]) ).
cnf(d30,plain,
product(X0,'additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d29,c3]) ).
cnf(d31,plain,
$false,
inference(resolution,[status(thm)],[d30,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n026.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 05:46:00 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.58/11.71 % SZS status Unsatisfiable for theBenchmark.p
% 43.58/11.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------