%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG003-1 : 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 : n004.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 16.56s 4.15s
% Output : CNFRefutation 16.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 34 ( 23 unt; 0 nHn; 26 RR)
% Number of literals : 52 ( 13 equ; 21 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_plus_c_is_d,hypothesis,
sum(a,c,d) ).
cnf(b_plus_c_is_d,hypothesis,
sum(b,c,d) ).
cnf(prove_a_equals_b,negated_conjecture,
a != b ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) ).
cnf(closure_of_addition,axiom,
sum(X0,X1,add(X0,X1)) ).
cnf(right_inverse,axiom,
sum(X0,'additive$uinverse'(X0),'additive$uidentity') ).
cnf(associativity_of_addition2,axiom,
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(commutativity_of_addition,axiom,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(c0,plain,
sum(a,c,d),
inference(clausification,[status(esa)],[a_plus_c_is_d]) ).
cnf(c1,plain,
sum(b,c,d),
inference(clausification,[status(esa)],[b_plus_c_is_d]) ).
cnf(c2,plain,
a != b,
inference(clausification,[status(esa)],[prove_a_equals_b]) ).
cnf(c4,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
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(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,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(c18,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(d0,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c11,c6]) ).
cnf(d1,plain,
( ~ sum(X1,X2,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[c18,c6]) ).
cnf(d2,plain,
add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ sum(X2,X1,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[d0,c18]) ).
cnf(d4,plain,
( ~ sum(X2,X3,X0)
| ~ sum(X3,X1,'additive$uidentity')
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c4]) ).
cnf(d5,plain,
( sum(d,X0,a)
| ~ sum(c,X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
sum(d,'additive$uinverse'(c),a),
inference(resolution,[status(thm)],[d5,c8]) ).
cnf(d7,plain,
a = add('additive$uinverse'(c),d),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
a = add(d,'additive$uinverse'(c)),
inference(demodulation,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
( sum(d,X0,b)
| ~ sum(c,X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[d4,c1]) ).
cnf(d10,plain,
sum(d,'additive$uinverse'(c),b),
inference(resolution,[status(thm)],[d9,c8]) ).
cnf(d11,plain,
b = add('additive$uinverse'(c),d),
inference(resolution,[status(thm)],[d10,d3]) ).
cnf(d12,plain,
b = add(d,'additive$uinverse'(c)),
inference(demodulation,[status(thm)],[d11,d2]) ).
cnf(d13,plain,
b = a,
inference(demodulation,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
a != a,
inference(demodulation,[status(thm)],[c2,d13]) ).
cnf(d15,plain,
$false,
inference(equality_resolution,[status(thm)],[d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43 % Computer : n004.cluster.edu
% 0.20/0.43 % Model : x86_64 x86_64
% 0.20/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.43 % Memory : 8046.5625MB
% 0.20/0.43 % OS : Linux 6.8.0-71-generic
% 0.20/0.43 % CPULimit : 300
% 0.20/0.43 % WCLimit : 300
% 0.20/0.43 % DateTime : Sat Sep 26 05:43:21 UTC 2026
% 0.20/0.44 % CPUTime :
% 0.20/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.56/4.15 % SZS status Unsatisfiable for theBenchmark.p
% 16.56/4.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------