%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO053-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 07:14:01 AM UTC 2026
% Result : Unsatisfiable 25.47s 6.59s
% Output : CNFRefutation 25.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 41 ( 28 unt; 0 nHn; 23 RR)
% Number of literals : 62 ( 25 equ; 24 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 75 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d1,axiom,
equidistant(X0,X1,X0,X1) ).
cnf(d4_5,axiom,
( equidistant(X3,X2,X1,X0)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(r2_2,axiom,
equidistant(X0,reflection(X1,X0),X1,X0) ).
cnf(r3_2,axiom,
X0 = reflection(X0,X0) ).
cnf(t3,axiom,
between(X0,X1,X1) ).
cnf(d15,axiom,
( X1 = X3
| ~ equidistant(X2,X1,X2,X3)
| ~ equidistant(X0,X1,X0,X3)
| ~ between(X0,X1,X2) ) ).
cnf(i3,axiom,
( X1 = insertion(X0,X2,X0,X1)
| ~ between(X0,X1,X2) ) ).
cnf(i4,axiom,
( insertion(X4,X5,X0,X1) = insertion(X4,X5,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(u_to_v_equals_u_to_w,hypothesis,
equidistant(u,v,u,w) ).
cnf(prove_v_equals_w,negated_conjecture,
v != w ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X0,X1,X1,X0) ).
cnf(c0,plain,
equidistant(X0,X1,X0,X1),
inference(clausification,[status(esa)],[d1]) ).
cnf(c7,plain,
( equidistant(X3,X2,X1,X0)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d4_5]) ).
cnf(c12,plain,
equidistant(X0,reflection(X1,X0),X1,X0),
inference(clausification,[status(esa)],[r2_2]) ).
cnf(c14,plain,
X0 = reflection(X0,X0),
inference(clausification,[status(esa)],[r3_2]) ).
cnf(c24,plain,
between(X0,X1,X1),
inference(clausification,[status(esa)],[t3]) ).
cnf(c49,plain,
( X1 = X3
| ~ equidistant(X2,X1,X2,X3)
| ~ equidistant(X0,X1,X0,X3)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[d15]) ).
cnf(c53,plain,
( X1 = insertion(X0,X2,X0,X1)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[i3]) ).
cnf(c54,plain,
( insertion(X4,X5,X0,X1) = insertion(X4,X5,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[i4]) ).
cnf(c62,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c63,plain,
equidistant(u,v,u,w),
inference(clausification,[status(esa)],[u_to_v_equals_u_to_w]) ).
cnf(c64,plain,
v != w,
inference(clausification,[status(esa)],[prove_v_equals_w]) ).
cnf(c65,plain,
equidistant(X0,X1,X1,X0),
inference(clausification,[status(esa)],[reflexivity_for_equidistance]) ).
cnf(d_0,plain,
v = insertion(u,w,u,v),
inference(resolution,[status(thm)],[c53,c62]) ).
cnf(d_1,plain,
X0 = insertion(X1,X0,X1,X0),
inference(resolution,[status(thm)],[c53,c24]) ).
cnf(d_2,plain,
insertion(X0,X1,X2,X3) = insertion(X0,X1,X3,X2),
inference(resolution,[status(thm)],[c54,c65]) ).
cnf(d_3,plain,
equidistant(w,u,v,u),
inference(resolution,[status(thm)],[c63,c7]) ).
cnf(d_4,plain,
insertion(X0,X1,w,u) = insertion(X0,X1,v,u),
inference(resolution,[status(thm)],[c54,d_3]) ).
cnf(d_5,plain,
insertion(X0,X1,u,w) = insertion(X0,X1,v,u),
inference(demodulation,[status(thm)],[d_4,d_2]) ).
cnf(d_6,plain,
insertion(X0,X1,u,w) = insertion(X0,X1,u,v),
inference(demodulation,[status(thm)],[d_5,d_2]) ).
cnf(d_7,plain,
w = insertion(u,w,u,v),
inference(superposition,[status(thm)],[d_6,d_1]) ).
cnf(d_8,plain,
w = v,
inference(demodulation,[status(thm)],[d_7,d_0]) ).
cnf(d_9,plain,
v != v,
inference(demodulation,[status(thm)],[c64,d_8]) ).
cnf(d_10,plain,
( ~ between(X1,reflection(X0,X0),X0)
| ~ equidistant(X1,reflection(X0,X0),X1,X0)
| reflection(X0,X0) = X0 ),
inference(resolution,[status(thm)],[c49,c12]) ).
cnf(d_11,plain,
( ~ between(X1,reflection(X0,X0),X0)
| ~ equidistant(X1,reflection(X0,X0),X1,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d_10,c14]) ).
cnf(d_12,plain,
( ~ between(X1,reflection(X0,X0),X0)
| ~ equidistant(X1,X0,X1,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d_11,c14]) ).
cnf(d_13,plain,
( ~ between(X1,X0,X0)
| ~ equidistant(X1,X0,X1,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d_12,c14]) ).
cnf(d_14,plain,
( ~ between(X1,X0,X0)
| X0 = X0 ),
inference(resolution,[status(thm)],[c0,d_13]) ).
cnf(d_15,plain,
X0 = X0,
inference(resolution,[status(thm)],[c24,d_14]) ).
cnf(d_16,plain,
$false,
inference(resolution,[status(thm)],[d_15,d_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO053-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n002.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.37 % CPULimit : 300
% 0.07/0.37 % WCLimit : 300
% 0.07/0.37 % DateTime : Fri Sep 25 12:39:34 UTC 2026
% 0.07/0.37 % CPUTime :
% 0.07/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.47/6.59 % SZS status Unsatisfiable for theBenchmark.p
% 25.47/6.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------