%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO025-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 07:13:55 AM UTC 2026
% Result : Unsatisfiable 147.29s 29.06s
% Output : CNFRefutation 147.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 20 unt; 9 nHn; 33 RR)
% Number of literals : 77 ( 13 equ; 35 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 : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 52 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d2,axiom,
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(d4_2,axiom,
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(d7,axiom,
equidistant(X0,X0,X1,X1) ).
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(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(v1_between_u1_and_w1,hypothesis,
between(u1,v1,w1) ).
cnf(prove_equal_sums,negated_conjecture,
~ equidistant(u,w,u1,w1) ).
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(c1,plain,
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d2]) ).
cnf(c4,plain,
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d4_2]) ).
cnf(c16,plain,
equidistant(X0,X0,X1,X1),
inference(clausification,[status(esa)],[d7]) ).
cnf(c17,plain,
equidistant(u,v,u1,v1),
inference(clausification,[status(esa)],[u_to_v_equals_u1_to_v1]) ).
cnf(c18,plain,
equidistant(v,w,v1,w1),
inference(clausification,[status(esa)],[v_to_w_equals_v1_to_w1]) ).
cnf(c19,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c20,plain,
between(u1,v1,w1),
inference(clausification,[status(esa)],[v1_between_u1_and_w1]) ).
cnf(c21,plain,
~ equidistant(u,w,u1,w1),
inference(clausification,[status(esa)],[prove_equal_sums]) ).
cnf(c24,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c27,plain,
( X0 = X1
| ~ between(X0,X1,X5)
| equidistant(X5,X6,X4,X7)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X5,X3,X4)
| ~ between(X2,X3,X4)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[outer_five_segment]) ).
cnf(d_0,plain,
equidistant(v,u,v1,u1),
inference(resolution,[status(thm)],[c17,c4]) ).
cnf(d_1,plain,
( ~ between(u,v,X0)
| ~ between(u1,v1,X2)
| ~ equidistant(u,X1,u1,X3)
| ~ equidistant(v,X0,v1,X2)
| ~ equidistant(v,X1,v1,X3)
| equidistant(X0,X1,X2,X3)
| u = v ),
inference(resolution,[status(thm)],[c27,c17]) ).
cnf(d_2,plain,
( ~ between(u1,v1,w1)
| ~ between(u,v,w)
| ~ equidistant(v,X0,v1,X1)
| ~ equidistant(u,X0,u1,X1)
| equidistant(w,X0,w1,X1)
| u = v ),
inference(resolution,[status(thm)],[d_1,c18]) ).
cnf(d_3,plain,
( ~ between(u1,v1,w1)
| equidistant(w,X0,w1,X1)
| ~ equidistant(v,X0,v1,X1)
| ~ equidistant(u,X0,u1,X1)
| u = v ),
inference(resolution,[status(thm)],[c19,d_2]) ).
cnf(d_4,plain,
( equidistant(w,X0,w1,X1)
| ~ equidistant(v,X0,v1,X1)
| ~ equidistant(u,X0,u1,X1)
| u = v ),
inference(resolution,[status(thm)],[c20,d_3]) ).
cnf(d_5,plain,
( equidistant(w,u,w1,u1)
| ~ equidistant(u,u,u1,u1)
| u = v ),
inference(resolution,[status(thm)],[d_4,d_0]) ).
cnf(d_6,plain,
( equidistant(w,u,w1,u1)
| u = v ),
inference(resolution,[status(thm)],[c16,d_5]) ).
cnf(d_7,plain,
( equidistant(u,w,u1,w1)
| u = v ),
inference(resolution,[status(thm)],[d_6,c4]) ).
cnf(d_8,plain,
u = v,
inference(resolution,[status(thm)],[c21,d_7]) ).
cnf(d_9,plain,
equidistant(u1,v1,u,v),
inference(resolution,[status(thm)],[c17,c1]) ).
cnf(d_10,plain,
equidistant(u1,v1,u,u),
inference(demodulation,[status(thm)],[d_9,d_8]) ).
cnf(d_11,plain,
u1 = v1,
inference(resolution,[status(thm)],[d_10,c24]) ).
cnf(d_12,plain,
equidistant(u,w,v1,w1),
inference(demodulation,[status(thm)],[c18,d_8]) ).
cnf(d_13,plain,
equidistant(u,w,u1,w1),
inference(demodulation,[status(thm)],[d_12,d_11]) ).
cnf(d_14,plain,
$false,
inference(resolution,[status(thm)],[c21,d_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO025-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n005.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % 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 12:32:47 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 147.29/29.06 % SZS status Unsatisfiable for theBenchmark.p
% 147.29/29.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------