%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ROB002-1 : 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 : n009.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 08:26:49 AM UTC 2026
% Result : Unsatisfiable 29.02s 4.61s
% Output : CNFRefutation 29.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 6 RR)
% Number of literals : 14 ( 13 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(double_negation,hypothesis,
negate(negate(X0)) = X0 ).
cnf(prove_huntingtons_axiom,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b ).
cnf(commutativity_of_add,axiom,
add(X0,X1) = add(X1,X0) ).
cnf(robbins_axiom,axiom,
negate(add(negate(add(X0,X1)),negate(add(X0,negate(X1))))) = X0 ).
cnf(c0,plain,
negate(negate(X0)) = X0,
inference(clausification,[status(esa)],[double_negation]) ).
cnf(c1,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
inference(clausification,[status(esa)],[prove_huntingtons_axiom]) ).
cnf(c2,plain,
add(X0,X1) = add(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_add]) ).
cnf(c4,plain,
negate(add(negate(add(X0,X1)),negate(add(X0,negate(X1))))) = X0,
inference(clausification,[status(esa)],[robbins_axiom]) ).
cnf(d0,plain,
negate(X0) = add(negate(add(X0,X1)),negate(add(X0,negate(X1)))),
inference(superposition,[status(thm)],[c4,c0]) ).
cnf(d1,plain,
negate(X0) = add(negate(add(X1,X0)),negate(add(X0,negate(X1)))),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
add(negate(add(a,negate(b))),negate(add(negate(b),negate(a)))) != b,
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d3,plain,
negate(negate(b)) != b,
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
b != b,
inference(demodulation,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
$false,
inference(equality_resolution,[status(thm)],[d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ROB002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 06:13:14 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.02/4.61 % SZS status Unsatisfiable for theBenchmark.p
% 29.02/4.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------