%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO026-2 : 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 : n020.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 37.11s 15.82s
% Output : CNFRefutation 37.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 16 unt; 7 nHn; 21 RR)
% Number of literals : 71 ( 14 equ; 39 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 65 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(v_between_u_and_x,hypothesis,
between(u,v,x) ).
cnf(v_to_w_equals_v_to_x,hypothesis,
equidistant(v,w,v,x) ).
cnf(u_not_v,hypothesis,
u != v ).
cnf(prove_w_is_x,negated_conjecture,
w != x ).
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(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,
between(u,v,x),
inference(clausification,[status(esa)],[v_between_u_and_x]) ).
cnf(c2,plain,
equidistant(v,w,v,x),
inference(clausification,[status(esa)],[v_to_w_equals_v_to_x]) ).
cnf(c3,plain,
u != v,
inference(clausification,[status(esa)],[u_not_v]) ).
cnf(c4,plain,
w != x,
inference(clausification,[status(esa)],[prove_w_is_x]) ).
cnf(c5,plain,
equidistant(X0,X1,X1,X0),
inference(clausification,[status(esa)],[reflexivity_for_equidistance]) ).
cnf(c6,plain,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[transitivity_for_equidistance]) ).
cnf(c7,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c10,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)],[c6,c5]) ).
cnf(d1,plain,
equidistant(X0,X1,X0,X1),
inference(resolution,[status(thm)],[d0,c5]) ).
cnf(d2,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,c10]) ).
cnf(d3,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)],[d2,d1]) ).
cnf(d4,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,d3]) ).
cnf(d5,plain,
( equidistant(w,X1,x,X1)
| ~ between(X0,v,x)
| ~ between(X0,v,w)
| X0 = v ),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
( equidistant(w,X0,x,X0)
| ~ between(u,v,w)
| u = v ),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
( equidistant(w,X0,x,X0)
| ~ between(u,v,w) ),
inference(resolution,[status(thm)],[c3,d6]) ).
cnf(d8,plain,
equidistant(w,X0,x,X0),
inference(resolution,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
w = x,
inference(resolution,[status(thm)],[d8,c7]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c4,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO026-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/10.45 % Computer : n020.cluster.edu
% 0.17/10.45 % Model : x86_64 x86_64
% 0.17/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.45 % Memory : 8046.5625MB
% 0.17/10.45 % OS : Linux 6.8.0-71-generic
% 0.17/10.45 % CPULimit : 300
% 0.17/10.45 % WCLimit : 300
% 0.17/10.46 % DateTime : Fri Sep 25 12:34:28 UTC 2026
% 0.17/10.46 % CPUTime :
% 0.17/10.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.11/15.82 % SZS status Unsatisfiable for theBenchmark.p
% 37.11/15.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------