%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO010-2 : 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 : n002.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 07:13:51 AM UTC 2026
% Result : Unsatisfiable 46.61s 11.07s
% Output : CNFRefutation 46.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of clauses : 61 ( 12 unt; 22 nHn; 55 RR)
% Number of literals : 155 ( 7 equ; 63 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 110 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(abc_colinear,hypothesis,
colinear(a,b,c) ).
cnf(prove_colinear_in_all_orders,negated_conjecture,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ) ).
cnf(identity_for_equidistance,axiom,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ).
cnf(segment_construction1,axiom,
between(X0,X1,extension(X0,X1,X2,X3)) ).
cnf(segment_construction2,axiom,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3) ).
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(colinearity1,axiom,
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ) ).
cnf(colinearity2,axiom,
( colinear(X2,X0,X1)
| ~ between(X0,X1,X2) ) ).
cnf(colinearity3,axiom,
( colinear(X1,X2,X0)
| ~ between(X0,X1,X2) ) ).
cnf(colinearity4,axiom,
( between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ) ).
cnf(c0,plain,
colinear(a,b,c),
inference(clausification,[status(esa)],[abc_colinear]) ).
cnf(c1,plain,
( ~ colinear(c,b,a)
| ~ colinear(a,c,b)
| ~ colinear(b,a,c)
| ~ colinear(c,a,b)
| ~ colinear(b,c,a) ),
inference(clausification,[status(esa)],[prove_colinear_in_all_orders]) ).
cnf(c4,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c5,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c6,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(c8,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(clausification,[status(esa)],[identity_for_betweeness]) ).
cnf(c9,plain,
( between(X1,'inner$upasch'(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[inner_pasch1]) ).
cnf(c10,plain,
( between(X4,'inner$upasch'(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[inner_pasch2]) ).
cnf(c20,plain,
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[colinearity1]) ).
cnf(c21,plain,
( colinear(X2,X0,X1)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[colinearity2]) ).
cnf(c22,plain,
( colinear(X1,X2,X0)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[colinearity3]) ).
cnf(c23,plain,
( between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
inference(clausification,[status(esa)],[colinearity4]) ).
cnf(d0,plain,
X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(d1,plain,
between(X0,X1,X1),
inference(superposition,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
( colinear(X3,X1,'inner$upasch'(X3,X4,X2,X1,X0))
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c21]) ).
cnf(d3,plain,
( X0 = 'inner$upasch'(X3,X0,X2,X1,X0)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,c8]) ).
cnf(d4,plain,
( ~ between(X1,X3,X2)
| ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2)
| colinear(X0,X3,X1) ),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( colinear(X4,'inner$upasch'(X3,X4,X2,X1,X0),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,c20]) ).
cnf(d6,plain,
( X1 = 'inner$upasch'(X1,X3,X2,X1,X0)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c8]) ).
cnf(d7,plain,
( ~ between(X3,X0,X2)
| ~ between(X0,X1,X2)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2)
| colinear(X1,X0,X3) ),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( ~ between(X2,X1,X0)
| colinear(X0,X1,X2) ),
inference(resolution,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
( between(a,b,c)
| between(b,c,a)
| between(c,a,b) ),
inference(resolution,[status(thm)],[c23,c0]) ).
cnf(d10,plain,
( ~ between(X1,X3,X2)
| ~ between(X0,X1,X2)
| ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| between(X3,X1,X0) ),
inference(superposition,[status(thm)],[d3,c10]) ).
cnf(d11,plain,
( between(b,c,a)
| between(a,b,c)
| ~ between(a,X0,b)
| between(X0,a,c) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( between(b,c,a)
| between(a,b,c)
| between(b,a,c) ),
inference(resolution,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
( colinear(a,c,b)
| between(b,a,c)
| between(a,b,c) ),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( colinear(a,c,b)
| between(a,b,c)
| colinear(a,c,b) ),
inference(resolution,[status(thm)],[d13,c22]) ).
cnf(d15,plain,
( ~ between(b,X0,c)
| colinear(a,X0,b)
| colinear(a,c,b) ),
inference(resolution,[status(thm)],[d14,d4]) ).
cnf(d16,plain,
( colinear(a,c,b)
| colinear(a,c,b) ),
inference(resolution,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
( between(a,c,b)
| between(c,b,a)
| between(b,a,c) ),
inference(resolution,[status(thm)],[d16,c23]) ).
cnf(d18,plain,
( colinear(c,b,a)
| between(b,a,c)
| between(a,c,b) ),
inference(resolution,[status(thm)],[d17,c20]) ).
cnf(d19,plain,
( colinear(b,c,a)
| between(b,c,a)
| between(a,b,c) ),
inference(resolution,[status(thm)],[d9,c21]) ).
cnf(d20,plain,
( colinear(b,c,a)
| between(a,b,c)
| colinear(b,c,a) ),
inference(resolution,[status(thm)],[d19,c20]) ).
cnf(d21,plain,
( colinear(b,c,a)
| colinear(b,c,a) ),
inference(resolution,[status(thm)],[d20,c22]) ).
cnf(d22,plain,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
inference(resolution,[status(thm)],[d21,c1]) ).
cnf(d23,plain,
( colinear(c,a,b)
| between(b,c,a)
| between(a,b,c) ),
inference(resolution,[status(thm)],[d9,c20]) ).
cnf(d24,plain,
( colinear(c,a,b)
| between(a,b,c)
| colinear(c,a,b) ),
inference(resolution,[status(thm)],[d23,c22]) ).
cnf(d25,plain,
( colinear(c,a,b)
| colinear(c,a,b) ),
inference(resolution,[status(thm)],[d24,c21]) ).
cnf(d26,plain,
( ~ colinear(c,b,a)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
inference(resolution,[status(thm)],[d25,d22]) ).
cnf(d27,plain,
( ~ colinear(c,b,a)
| ~ colinear(b,a,c) ),
inference(resolution,[status(thm)],[d16,d26]) ).
cnf(d28,plain,
( colinear(b,a,c)
| between(b,a,c)
| between(a,c,b) ),
inference(resolution,[status(thm)],[d17,c22]) ).
cnf(d29,plain,
( colinear(b,a,c)
| between(a,c,b)
| colinear(b,a,c) ),
inference(resolution,[status(thm)],[d28,c20]) ).
cnf(d30,plain,
( colinear(b,a,c)
| colinear(b,a,c) ),
inference(resolution,[status(thm)],[d29,c21]) ).
cnf(d31,plain,
~ colinear(c,b,a),
inference(resolution,[status(thm)],[d30,d27]) ).
cnf(d32,plain,
( between(b,a,c)
| between(a,c,b) ),
inference(resolution,[status(thm)],[d31,d18]) ).
cnf(d33,plain,
( colinear(c,b,a)
| between(a,c,b) ),
inference(resolution,[status(thm)],[d32,c21]) ).
cnf(d34,plain,
between(a,c,b),
inference(resolution,[status(thm)],[d31,d33]) ).
cnf(d35,plain,
colinear(c,b,a),
inference(resolution,[status(thm)],[d34,c22]) ).
cnf(d36,plain,
$false,
inference(resolution,[status(thm)],[d31,d35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n002.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 12:33:42 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.61/11.07 % SZS status Unsatisfiable for theBenchmark.p
% 46.61/11.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------