%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO056-3 : 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 : n014.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 07:14:02 AM UTC 2026
% Result : Unsatisfiable 12.10s 7.03s
% Output : CNFRefutation 12.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 8 RR)
% Number of literals : 13 ( 8 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(r2_2,axiom,
equidistant(X0,reflection(X1,X0),X1,X0) ).
cnf(u_equals_v,hypothesis,
u = v ).
cnf(prove_v_equals_reflection,negated_conjecture,
v != reflection(u,v) ).
cnf(identity_for_equidistance,axiom,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ).
cnf(c12,plain,
equidistant(X0,reflection(X1,X0),X1,X0),
inference(clausification,[status(esa)],[r2_2]) ).
cnf(c13,plain,
u = v,
inference(clausification,[status(esa)],[u_equals_v]) ).
cnf(c14,plain,
v != reflection(u,v),
inference(clausification,[status(esa)],[prove_v_equals_reflection]) ).
cnf(c17,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(d_0,plain,
v != reflection(v,v),
inference(demodulation,[status(thm)],[c14,c13]) ).
cnf(d_1,plain,
X0 = reflection(X0,X0),
inference(resolution,[status(thm)],[c17,c12]) ).
cnf(d_2,plain,
$false,
inference(resolution,[status(thm)],[d_1,d_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO056-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n014.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Fri Sep 25 12:37:39 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.10/7.03 % SZS status Unsatisfiable for theBenchmark.p
% 12.10/7.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------