%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO027-2 : 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 07:13:56 AM UTC 2026
% Result : Unsatisfiable 58.25s 13.82s
% Output : CNFRefutation 58.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 31 ( 16 unt; 9 nHn; 20 RR)
% Number of literals : 76 ( 18 equ; 40 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 96 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(u_not_v,hypothesis,
u != v ).
cnf(prove_w_is_an_extension,negated_conjecture,
w != extension(u,v,v,w) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X0,X1,X1,X0) ).
cnf(transitivity_for_equidistance,axiom,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(identity_for_equidistance,axiom,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ).
cnf(segment_construction1,axiom,
between(X0,X1,extension(X0,X1,X2,X3)) ).
cnf(segment_construction2,axiom,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3) ).
cnf(outer_five_segment,axiom,
( equidistant(X4,X6,X5,X7)
| X0 = X1
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(c0,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c1,plain,
u != v,
inference(clausification,[status(esa)],[u_not_v]) ).
cnf(c2,plain,
w != extension(u,v,v,w),
inference(clausification,[status(esa)],[prove_w_is_an_extension]) ).
cnf(c3,plain,
equidistant(X0,X1,X1,X0),
inference(clausification,[status(esa)],[reflexivity_for_equidistance]) ).
cnf(c4,plain,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[transitivity_for_equidistance]) ).
cnf(c5,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c6,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c7,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(c8,plain,
( ~ equidistant(X1,X6,X3,X7)
| X0 = X1
| ~ between(X2,X3,X5)
| equidistant(X4,X6,X5,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[outer_five_segment]) ).
cnf(d0,plain,
( ~ equidistant(X3,X2,X0,X1)
| equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(d1,plain,
equidistant(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( ~ equidistant(X2,X3,X0,X1)
| equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
equidistant(X0,X1,X2,extension(X3,X2,X0,X1)),
inference(resolution,[status(thm)],[d2,c7]) ).
cnf(d4,plain,
( ~ equidistant(X0,X4,X0,X5)
| ~ equidistant(X1,X3,X1,X2)
| ~ equidistant(X1,X4,X1,X5)
| equidistant(X3,X4,X2,X5)
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[d1,c8]) ).
cnf(d5,plain,
( ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X1,X4,X1,X4)
| equidistant(X2,X4,X3,X4)
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( ~ equidistant(X1,X3,X1,X2)
| equidistant(X3,X4,X2,X4)
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[d1,d5]) ).
cnf(d7,plain,
( equidistant(X2,X4,extension(X3,X1,X1,X2),X4)
| ~ between(X0,X1,extension(X3,X1,X1,X2))
| ~ between(X0,X1,X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
( equidistant(X2,X3,extension(X0,X1,X1,X2),X3)
| ~ between(X0,X1,X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[d7,c6]) ).
cnf(d9,plain,
( X2 = extension(X0,X1,X1,X2)
| ~ between(X0,X1,X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[d8,c5]) ).
cnf(d10,plain,
( u = v
| w = extension(u,v,v,w) ),
inference(resolution,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
w = extension(u,v,v,w),
inference(resolution,[status(thm)],[c1,d10]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[c2,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO027-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/5.44 % Computer : n009.cluster.edu
% 0.19/5.44 % Model : x86_64 x86_64
% 0.19/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.44 % Memory : 8046.5625MB
% 0.19/5.44 % OS : Linux 6.8.0-71-generic
% 0.19/5.44 % CPULimit : 300
% 0.19/5.44 % WCLimit : 300
% 0.19/5.44 % DateTime : Fri Sep 25 12:33:34 UTC 2026
% 0.19/5.44 % CPUTime :
% 0.19/5.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.25/13.82 % SZS status Unsatisfiable for theBenchmark.p
% 58.25/13.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------