%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG005-1 : 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 : n010.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 30.87s 12.30s
% Output : CNFRefutation 30.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 47 ( 28 unt; 0 nHn; 33 RR)
% Number of literals : 85 ( 9 equ; 40 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_times_b,hypothesis,
product(a,b,d) ).
cnf(a_inverse_times_b,hypothesis,
product('additive$uinverse'(a),b,c) ).
cnf(prove_sum_is_additive_id,negated_conjecture,
~ sum(c,d,'additive$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(right_inverse,axiom,
sum(X0,'additive$uinverse'(X0),'additive$uidentity') ).
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(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(c0,plain,
product(a,b,d),
inference(clausification,[status(esa)],[a_times_b]) ).
cnf(c1,plain,
product('additive$uinverse'(a),b,c),
inference(clausification,[status(esa)],[a_inverse_times_b]) ).
cnf(c2,plain,
~ sum(c,d,'additive$uidentity'),
inference(clausification,[status(esa)],[prove_sum_is_additive_id]) ).
cnf(c3,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c4,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c5,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c6,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c8,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c10,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,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c16,plain,
( ~ product(X5,X4,X0)
| ~ product(X6,X4,X2)
| ~ sum(X5,X3,X6)
| ~ product(X3,X4,X1)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity3]) ).
cnf(c18,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(d0,plain,
( ~ sum(X1,'additive$uinverse'(X1),X0)
| X0 = 'additive$uidentity' ),
inference(resolution,[status(thm)],[c18,c8]) ).
cnf(d1,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c11,c6]) ).
cnf(d2,plain,
( ~ sum(X3,'additive$uidentity',X2)
| ~ sum(X3,X1,X0)
| sum(X0,'additive$uinverse'(X1),X2) ),
inference(resolution,[status(thm)],[c10,c8]) ).
cnf(d3,plain,
( sum(add(X2,X0),'additive$uinverse'(X2),X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
sum(add(X0,X1),'additive$uinverse'(X0),X1),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
( ~ sum(X2,X1,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[c18,d1]) ).
cnf(d6,plain,
add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
( ~ sum(X1,X2,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[c18,c6]) ).
cnf(d8,plain,
( ~ sum(X5,X0,X3)
| sum(multiply(X5,X1),X2,X4)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c16,c5]) ).
cnf(d9,plain,
( sum(multiply(X2,b),X1,d)
| ~ sum(X2,X0,a)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
( sum(multiply(X0,b),d,d)
| ~ sum(X0,a,a) ),
inference(resolution,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
sum(multiply('additive$uidentity',b),d,d),
inference(resolution,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
d = add(multiply('additive$uidentity',b),d),
inference(resolution,[status(thm)],[d11,d7]) ).
cnf(d13,plain,
d = add(d,multiply('additive$uidentity',b)),
inference(demodulation,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
sum(d,'additive$uinverse'(d),multiply('additive$uidentity',b)),
inference(superposition,[status(thm)],[d13,d4]) ).
cnf(d15,plain,
multiply('additive$uidentity',b) = 'additive$uidentity',
inference(resolution,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
( ~ sum(a,X0,X2)
| sum(d,X1,X3)
| ~ product(X2,b,X3)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[c16,c0]) ).
cnf(d17,plain,
( sum(d,X1,multiply(X2,b))
| ~ sum(a,X0,X2)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
( sum(d,c,multiply(X0,b))
| ~ sum(a,'additive$uinverse'(a),X0) ),
inference(resolution,[status(thm)],[d17,c1]) ).
cnf(d19,plain,
sum(d,c,multiply('additive$uidentity',b)),
inference(resolution,[status(thm)],[d18,c8]) ).
cnf(d20,plain,
sum(c,d,multiply('additive$uidentity',b)),
inference(resolution,[status(thm)],[d19,c11]) ).
cnf(d21,plain,
sum(c,d,'additive$uidentity'),
inference(demodulation,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[c2,d21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.46 % Computer : n010.cluster.edu
% 0.17/5.46 % Model : x86_64 x86_64
% 0.17/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.46 % Memory : 8046.5625MB
% 0.17/5.46 % OS : Linux 6.8.0-71-generic
% 0.17/5.46 % CPULimit : 300
% 0.17/5.46 % WCLimit : 300
% 0.17/5.46 % DateTime : Sat Sep 26 05:44:07 UTC 2026
% 0.17/5.47 % CPUTime :
% 0.17/5.47 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.87/12.30 % SZS status Unsatisfiable for theBenchmark.p
% 30.87/12.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------