%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO034-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:13:57 AM UTC 2026
% Result : Unsatisfiable 46.69s 6.49s
% Output : CNFRefutation 46.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 28 ( 15 unt; 0 nHn; 26 RR)
% Number of literals : 59 ( 5 equ; 34 neg)
% Maximal clause size : 7 ( 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 : 51 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d1,axiom,
equidistant(X0,X1,X0,X1) ).
cnf(d2,axiom,
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(t1,axiom,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ) ).
cnf(d12,axiom,
( equidistant(X1,X6,X3,X7)
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X4,X6,X5,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(u_to_v_equals_u_to_x,hypothesis,
equidistant(u,v,u,x) ).
cnf(w_to_v_equals_w_to_x,hypothesis,
equidistant(w,v,w,x) ).
cnf(prove_v_is_x,negated_conjecture,
v != x ).
cnf(identity_for_equidistance,axiom,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ).
cnf(c0,plain,
equidistant(X0,X1,X0,X1),
inference(clausification,[status(esa)],[d1]) ).
cnf(c1,plain,
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d2]) ).
cnf(c26,plain,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[t1]) ).
cnf(c46,plain,
( ~ equidistant(X4,X6,X2,X7)
| ~ equidistant(X3,X6,X0,X7)
| equidistant(X5,X6,X1,X7)
| ~ equidistant(X3,X5,X0,X1)
| ~ between(X3,X5,X4)
| ~ equidistant(X3,X4,X0,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[d12]) ).
cnf(c49,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c50,plain,
equidistant(u,v,u,x),
inference(clausification,[status(esa)],[u_to_v_equals_u_to_x]) ).
cnf(c51,plain,
equidistant(w,v,w,x),
inference(clausification,[status(esa)],[w_to_v_equals_w_to_x]) ).
cnf(c52,plain,
v != x,
inference(clausification,[status(esa)],[prove_v_is_x]) ).
cnf(c55,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(d_0,plain,
equidistant(w,x,w,v),
inference(resolution,[status(thm)],[c51,c1]) ).
cnf(d_1,plain,
equidistant(u,x,u,v),
inference(resolution,[status(thm)],[c50,c1]) ).
cnf(d_2,plain,
( ~ between(X5,X4,X0)
| ~ between(X5,X4,X2)
| ~ equidistant(X5,X0,X5,X2)
| ~ equidistant(X5,X1,X5,X3)
| equidistant(X4,X1,X4,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c46,c0]) ).
cnf(d_3,plain,
( ~ between(X0,X1,u)
| ~ between(X0,X1,u)
| equidistant(X1,x,X1,v)
| ~ equidistant(X0,u,X0,u)
| ~ equidistant(X0,x,X0,v) ),
inference(resolution,[status(thm)],[d_2,d_1]) ).
cnf(d_4,plain,
( ~ between(X1,X0,u)
| ~ equidistant(X1,x,X1,v)
| equidistant(X0,x,X0,v) ),
inference(resolution,[status(thm)],[c0,d_3]) ).
cnf(d_5,plain,
( ~ between(w,X0,u)
| equidistant(X0,x,X0,v) ),
inference(resolution,[status(thm)],[d_4,d_0]) ).
cnf(d_6,plain,
( v = x
| ~ between(w,v,u) ),
inference(resolution,[status(thm)],[d_5,c55]) ).
cnf(d_7,plain,
~ between(w,v,u),
inference(resolution,[status(thm)],[c52,d_6]) ).
cnf(d_8,plain,
between(w,v,u),
inference(resolution,[status(thm)],[c26,c49]) ).
cnf(d_9,plain,
$false,
inference(resolution,[status(thm)],[d_8,d_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO034-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n004.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 12:33:52 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.69/6.49 % SZS status Unsatisfiable for theBenchmark.p
% 46.69/6.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------