%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO040-3 : 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 : n018.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 07:13:59 AM UTC 2026
% Result : Unsatisfiable 25.07s 5.99s
% Output : CNFRefutation 25.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 18 unt; 0 nHn; 29 RR)
% Number of literals : 62 ( 19 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 79 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d3,axiom,
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(d5,axiom,
( equidistant(X0,X1,X4,X5)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(r2_2,axiom,
equidistant(X0,reflection(X1,X0),X1,X0) ).
cnf(r6,axiom,
X0 = reflection(reflection(X0,X1),X1) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(u_between_v_and_w,hypothesis,
between(v,u,w) ).
cnf(prove_u_is_v,negated_conjecture,
u != v ).
cnf(identity_for_equidistance,axiom,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ).
cnf(identity_for_betweeness,axiom,
( X0 = X1
| ~ between(X0,X1,X0) ) ).
cnf(inner_pasch1,axiom,
( between(X1,'inner$upasch'(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ) ).
cnf(inner_pasch2,axiom,
( between(X4,'inner$upasch'(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ) ).
cnf(c2,plain,
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d3]) ).
cnf(c8,plain,
( equidistant(X0,X1,X4,X5)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d5]) ).
cnf(c12,plain,
equidistant(X0,reflection(X1,X0),X1,X0),
inference(clausification,[status(esa)],[r2_2]) ).
cnf(c23,plain,
X0 = reflection(reflection(X0,X1),X1),
inference(clausification,[status(esa)],[r6]) ).
cnf(c28,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c29,plain,
between(v,u,w),
inference(clausification,[status(esa)],[u_between_v_and_w]) ).
cnf(c30,plain,
u != v,
inference(clausification,[status(esa)],[prove_u_is_v]) ).
cnf(c33,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c37,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(clausification,[status(esa)],[identity_for_betweeness]) ).
cnf(c38,plain,
( between(X1,'inner$upasch'(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[inner_pasch1]) ).
cnf(c39,plain,
( between(X4,'inner$upasch'(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[inner_pasch2]) ).
cnf(d_0,plain,
( X1 = 'inner$upasch'(X1,X3,X2,X1,X0)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c39,c37]) ).
cnf(d_1,plain,
( ~ between(u,X0,w)
| u = 'inner$upasch'(u,X0,w,u,v) ),
inference(resolution,[status(thm)],[d_0,c29]) ).
cnf(d_2,plain,
u = 'inner$upasch'(u,v,w,u,v),
inference(resolution,[status(thm)],[d_1,c28]) ).
cnf(d_3,plain,
( X1 = 'inner$upasch'(X0,X1,X2,X3,X1)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c38,c37]) ).
cnf(d_4,plain,
( ~ between(v,X0,w)
| v = 'inner$upasch'(u,v,w,X0,v) ),
inference(resolution,[status(thm)],[d_3,c28]) ).
cnf(d_5,plain,
v = 'inner$upasch'(u,v,w,u,v),
inference(resolution,[status(thm)],[d_4,c29]) ).
cnf(d_6,plain,
v = u,
inference(demodulation,[status(thm)],[d_5,d_2]) ).
cnf(d_7,plain,
u != u,
inference(demodulation,[status(thm)],[c30,d_6]) ).
cnf(d_8,plain,
equidistant(reflection(X0,X1),X1,X0,X1),
inference(resolution,[status(thm)],[c12,c2]) ).
cnf(d_9,plain,
( equidistant(X1,reflection(X0,X1),X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c12,c8]) ).
cnf(d_10,plain,
( X1 = reflection(X0,X1)
| ~ equidistant(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[d_9,c33]) ).
cnf(d_11,plain,
X0 = reflection(reflection(X0,X0),X0),
inference(resolution,[status(thm)],[d_10,d_8]) ).
cnf(d_12,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d_11,c23]) ).
cnf(d_13,plain,
$false,
inference(resolution,[status(thm)],[d_12,d_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO040-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 12:37:06 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.07/5.99 % SZS status Unsatisfiable for theBenchmark.p
% 25.07/5.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------