%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD008-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 07:10:43 AM UTC 2026
% Result : Unsatisfiable 36.38s 10.02s
% Output : CNFRefutation 36.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of clauses : 42 ( 19 unt; 0 nHn; 42 RR)
% Number of literals : 78 ( 0 equ; 38 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(c_is_defined,hypothesis,
defined(c) ).
cnf(d_is_defined,hypothesis,
defined(d) ).
cnf(sum_5,negated_conjecture,
sum(a,b,c) ).
cnf(sum_6,negated_conjecture,
sum('additive$uinverse'(a),'additive$uinverse'(b),d) ).
cnf(not_sum_7,negated_conjecture,
~ sum('additive$uidentity','additive$uinverse'(c),d) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ) ).
cnf(associativity_addition_2,axiom,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
defined(c),
inference(clausification,[status(esa)],[c_is_defined]) ).
cnf(c3,plain,
defined(d),
inference(clausification,[status(esa)],[d_is_defined]) ).
cnf(c4,plain,
sum(a,b,c),
inference(clausification,[status(esa)],[sum_5]) ).
cnf(c5,plain,
sum('additive$uinverse'(a),'additive$uinverse'(b),d),
inference(clausification,[status(esa)],[sum_6]) ).
cnf(c6,plain,
~ sum('additive$uidentity','additive$uinverse'(c),d),
inference(clausification,[status(esa)],[not_sum_7]) ).
cnf(c7,plain,
( ~ sum(X5,X1,X4)
| ~ sum(X3,X0,X5)
| sum(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_1]) ).
cnf(c8,plain,
( ~ sum(X5,X2,X4)
| ~ sum(X5,X0,X3)
| sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_2]) ).
cnf(c9,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c10,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c11,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(d0,plain,
( ~ defined(X0)
| sum(X0,'additive$uinverse'(X0),'additive$uidentity') ),
inference(resolution,[status(thm)],[c11,c10]) ).
cnf(d1,plain,
( ~ defined(X0)
| sum(X0,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c11,c9]) ).
cnf(d2,plain,
( ~ sum('additive$uinverse'(a),X2,X1)
| ~ sum('additive$uinverse'(b),X0,X2)
| sum(d,X0,X1) ),
inference(resolution,[status(thm)],[c8,c5]) ).
cnf(d3,plain,
sum(b,a,c),
inference(resolution,[status(thm)],[c11,c4]) ).
cnf(d4,plain,
( ~ sum(X2,b,X0)
| sum(X2,c,X1)
| ~ sum(X0,a,X1) ),
inference(resolution,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
( ~ defined(a)
| sum(X0,c,a)
| ~ sum(X0,b,'additive$uidentity') ),
inference(resolution,[status(thm)],[d4,c9]) ).
cnf(d6,plain,
( sum(X0,c,a)
| ~ sum(X0,b,'additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
( ~ defined(b)
| sum('additive$uinverse'(b),c,a) ),
inference(resolution,[status(thm)],[d6,c10]) ).
cnf(d8,plain,
sum('additive$uinverse'(b),c,a),
inference(resolution,[status(thm)],[c1,d7]) ).
cnf(d9,plain,
( ~ sum('additive$uinverse'(a),a,X0)
| sum(d,c,X0) ),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( ~ defined(a)
| sum(d,c,'additive$uidentity') ),
inference(resolution,[status(thm)],[d9,c10]) ).
cnf(d11,plain,
sum(d,c,'additive$uidentity'),
inference(resolution,[status(thm)],[c0,d10]) ).
cnf(d12,plain,
( ~ sum(d,X2,X1)
| ~ sum(c,X0,X2)
| sum('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[d11,c8]) ).
cnf(d13,plain,
( ~ defined(d)
| sum('additive$uidentity',X0,d)
| ~ sum(c,X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
( sum('additive$uidentity',X0,d)
| ~ sum(c,X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[c3,d13]) ).
cnf(d15,plain,
( ~ defined(c)
| sum('additive$uidentity','additive$uinverse'(c),d) ),
inference(resolution,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
sum('additive$uidentity','additive$uinverse'(c),d),
inference(resolution,[status(thm)],[c2,d15]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[c6,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : FLD008-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/5.31 % Computer : n012.cluster.edu
% 0.03/5.31 % Model : x86_64 x86_64
% 0.03/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.31 % Memory : 8046.5625MB
% 0.03/5.31 % OS : Linux 6.8.0-71-generic
% 0.03/5.31 % CPULimit : 300
% 0.03/5.31 % WCLimit : 300
% 0.03/5.31 % DateTime : Sun Sep 27 02:20:55 UTC 2026
% 0.03/5.31 % CPUTime :
% 0.03/5.31 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.38/10.02 % SZS status Unsatisfiable for theBenchmark.p
% 36.38/10.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------