%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO033-3 : 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 : n026.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 60.11s 8.06s
% Output : CNFRefutation 60.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 17 unt; 0 nHn; 29 RR)
% Number of literals : 70 ( 0 equ; 44 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d8,axiom,
( equidistant(X0,X4,X2,X5)
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ) ).
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(u_to_v_equals_u1_to_v1,hypothesis,
equidistant(u,v,u1,v1) ).
cnf(v_to_w_equals_v1_to_w1,hypothesis,
equidistant(v,w,v1,w1) ).
cnf(u_to_x_equals_u1_to_x1,hypothesis,
equidistant(u,x,u1,x1) ).
cnf(w_to_x_equals_w1_to_x1,hypothesis,
equidistant(w,x,w1,x1) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(v1_between_u1_and_w1,hypothesis,
between(u1,v1,w1) ).
cnf(prove_v_to_x_equals_v1_to_x1,negated_conjecture,
~ equidistant(v,x,v1,x1) ).
cnf(c17,plain,
( ~ equidistant(X4,X0,X5,X2)
| ~ between(X5,X2,X3)
| ~ between(X4,X0,X1)
| equidistant(X4,X1,X5,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d8]) ).
cnf(c45,plain,
( ~ equidistant(X6,X1,X7,X3)
| ~ between(X7,X5,X2)
| ~ between(X6,X4,X0)
| ~ equidistant(X6,X0,X7,X2)
| ~ equidistant(X6,X4,X7,X5)
| equidistant(X4,X1,X5,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d12]) ).
cnf(c47,plain,
equidistant(u,v,u1,v1),
inference(clausification,[status(esa)],[u_to_v_equals_u1_to_v1]) ).
cnf(c48,plain,
equidistant(v,w,v1,w1),
inference(clausification,[status(esa)],[v_to_w_equals_v1_to_w1]) ).
cnf(c49,plain,
equidistant(u,x,u1,x1),
inference(clausification,[status(esa)],[u_to_x_equals_u1_to_x1]) ).
cnf(c50,plain,
equidistant(w,x,w1,x1),
inference(clausification,[status(esa)],[w_to_x_equals_w1_to_x1]) ).
cnf(c51,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c52,plain,
between(u1,v1,w1),
inference(clausification,[status(esa)],[v1_between_u1_and_w1]) ).
cnf(c53,plain,
~ equidistant(v,x,v1,x1),
inference(clausification,[status(esa)],[prove_v_to_x_equals_v1_to_x1]) ).
cnf(d_0,plain,
( ~ between(u,v,X2)
| ~ between(u1,v1,X3)
| ~ equidistant(X2,X0,X3,X1)
| ~ equidistant(u,X2,u1,X3)
| ~ equidistant(u,X0,u1,X1)
| equidistant(v,X0,v1,X1) ),
inference(resolution,[status(thm)],[c45,c47]) ).
cnf(d_1,plain,
( ~ between(u1,v1,w1)
| ~ between(u,v,w)
| equidistant(v,x,v1,x1)
| ~ equidistant(u,x,u1,x1)
| ~ equidistant(u,w,u1,w1) ),
inference(resolution,[status(thm)],[d_0,c50]) ).
cnf(d_2,plain,
( ~ between(u1,v1,w1)
| equidistant(v,x,v1,x1)
| ~ equidistant(u,x,u1,x1)
| ~ equidistant(u,w,u1,w1) ),
inference(resolution,[status(thm)],[c51,d_1]) ).
cnf(d_3,plain,
( equidistant(v,x,v1,x1)
| ~ equidistant(u,x,u1,x1)
| ~ equidistant(u,w,u1,w1) ),
inference(resolution,[status(thm)],[c52,d_2]) ).
cnf(d_4,plain,
( equidistant(v,x,v1,x1)
| ~ equidistant(u,w,u1,w1) ),
inference(resolution,[status(thm)],[c49,d_3]) ).
cnf(d_5,plain,
~ equidistant(u,w,u1,w1),
inference(resolution,[status(thm)],[c53,d_4]) ).
cnf(d_6,plain,
( ~ between(u,v,X0)
| ~ between(u1,v1,X1)
| ~ equidistant(v,X0,v1,X1)
| equidistant(u,X0,u1,X1) ),
inference(resolution,[status(thm)],[c17,c47]) ).
cnf(d_7,plain,
( ~ between(u1,v1,w1)
| ~ between(u,v,w)
| equidistant(u,w,u1,w1) ),
inference(resolution,[status(thm)],[d_6,c48]) ).
cnf(d_8,plain,
( ~ between(u1,v1,w1)
| equidistant(u,w,u1,w1) ),
inference(resolution,[status(thm)],[c51,d_7]) ).
cnf(d_9,plain,
equidistant(u,w,u1,w1),
inference(resolution,[status(thm)],[c52,d_8]) ).
cnf(d_10,plain,
$false,
inference(resolution,[status(thm)],[d_9,d_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO033-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 12:36:54 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 60.11/8.06 % SZS status Unsatisfiable for theBenchmark.p
% 60.11/8.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------