%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO010-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 7.91s 3.87s
% Output : CNFRefutation 7.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 57 ( 10 unt; 25 nHn; 51 RR)
% Number of literals : 140 ( 6 equ; 47 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 : 86 ( 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_betweeness,axiom,
( X0 = X1
| ~ between(X0,X1,X0) ) ).
cnf(identity_for_equidistance,axiom,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ).
cnf(outer_pasch1,axiom,
( between(X0,'outer$upasch'(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ) ).
cnf(outer_pasch2,axiom,
( between(X4,X1,'outer$upasch'(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,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(colinearity1,axiom,
( between(X0,X2,X1)
| between(X1,X0,X2)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ) ).
cnf(colinearity2,axiom,
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ) ).
cnf(colinearity3,axiom,
( colinear(X1,X0,X2)
| ~ between(X0,X1,X2) ) ).
cnf(colinearity4,axiom,
( colinear(X0,X2,X1)
| ~ between(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(c2,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(clausification,[status(esa)],[identity_for_betweeness]) ).
cnf(c6,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c8,plain,
( between(X0,'outer$upasch'(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[outer_pasch1]) ).
cnf(c9,plain,
( between(X4,X1,'outer$upasch'(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[outer_pasch2]) ).
cnf(c14,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c15,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(c22,plain,
( between(X0,X2,X1)
| between(X1,X0,X2)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
inference(clausification,[status(esa)],[colinearity1]) ).
cnf(c23,plain,
( colinear(X0,X1,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[colinearity2]) ).
cnf(c24,plain,
( colinear(X1,X0,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[colinearity3]) ).
cnf(c25,plain,
( colinear(X0,X2,X1)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[colinearity4]) ).
cnf(d0,plain,
X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[c15,c6]) ).
cnf(d1,plain,
between(X0,X1,X1),
inference(superposition,[status(thm)],[d0,c14]) ).
cnf(d2,plain,
( X0 = 'outer$upasch'(X3,X0,X0,X2,X1)
| ~ between(X0,X3,X1)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(d3,plain,
( ~ between(X1,X3,X2)
| ~ between(X1,X0,X3)
| ~ between(X1,X3,X2)
| ~ between(X1,X0,X3)
| between(X2,X0,X1) ),
inference(superposition,[status(thm)],[d2,c9]) ).
cnf(d4,plain,
( ~ between(X2,X1,X0)
| between(X0,X1,X2) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( between(a,b,c)
| between(a,c,b)
| between(b,a,c) ),
inference(resolution,[status(thm)],[c22,c0]) ).
cnf(d6,plain,
( colinear(b,c,a)
| between(a,c,b)
| between(a,b,c) ),
inference(resolution,[status(thm)],[d5,c25]) ).
cnf(d7,plain,
( between(a,b,c)
| colinear(b,c,a)
| between(b,c,a) ),
inference(resolution,[status(thm)],[d4,d6]) ).
cnf(d8,plain,
( colinear(b,c,a)
| between(a,b,c)
| colinear(b,c,a) ),
inference(resolution,[status(thm)],[d7,c23]) ).
cnf(d9,plain,
( between(c,b,a)
| colinear(b,c,a) ),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
( colinear(b,c,a)
| colinear(b,c,a) ),
inference(resolution,[status(thm)],[d9,c24]) ).
cnf(d11,plain,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(b,a,c)
| ~ colinear(a,c,b) ),
inference(resolution,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
( colinear(b,a,c)
| between(a,c,b)
| between(a,b,c) ),
inference(resolution,[status(thm)],[d5,c23]) ).
cnf(d13,plain,
( between(a,b,c)
| colinear(b,a,c)
| between(b,c,a) ),
inference(resolution,[status(thm)],[d4,d12]) ).
cnf(d14,plain,
( colinear(b,a,c)
| between(a,b,c)
| colinear(b,a,c) ),
inference(resolution,[status(thm)],[d13,c25]) ).
cnf(d15,plain,
( colinear(b,a,c)
| colinear(b,a,c) ),
inference(resolution,[status(thm)],[d14,c24]) ).
cnf(d16,plain,
( ~ colinear(c,b,a)
| ~ colinear(c,a,b)
| ~ colinear(a,c,b) ),
inference(resolution,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
( between(a,c,b)
| between(a,b,c)
| between(c,a,b) ),
inference(resolution,[status(thm)],[d4,d5]) ).
cnf(d18,plain,
( colinear(c,a,b)
| between(a,c,b)
| between(a,b,c) ),
inference(resolution,[status(thm)],[d17,c23]) ).
cnf(d19,plain,
( colinear(c,a,b)
| between(a,b,c)
| colinear(c,a,b) ),
inference(resolution,[status(thm)],[d18,c24]) ).
cnf(d20,plain,
( between(c,b,a)
| colinear(c,a,b) ),
inference(resolution,[status(thm)],[d19,d4]) ).
cnf(d21,plain,
( colinear(c,a,b)
| colinear(c,a,b) ),
inference(resolution,[status(thm)],[d20,c25]) ).
cnf(d22,plain,
( ~ colinear(c,b,a)
| ~ colinear(a,c,b) ),
inference(resolution,[status(thm)],[d21,d16]) ).
cnf(d23,plain,
( colinear(a,c,b)
| between(a,c,b)
| between(a,b,c) ),
inference(resolution,[status(thm)],[d17,c24]) ).
cnf(d24,plain,
( colinear(a,c,b)
| between(a,b,c)
| colinear(a,c,b) ),
inference(resolution,[status(thm)],[d23,c23]) ).
cnf(d25,plain,
( colinear(a,c,b)
| colinear(a,c,b) ),
inference(resolution,[status(thm)],[d24,c25]) ).
cnf(d26,plain,
~ colinear(c,b,a),
inference(resolution,[status(thm)],[d25,d22]) ).
cnf(d27,plain,
( between(b,c,a)
| between(b,a,c)
| between(c,b,a) ),
inference(resolution,[status(thm)],[d10,c22]) ).
cnf(d28,plain,
( colinear(c,b,a)
| between(b,c,a)
| between(b,a,c) ),
inference(resolution,[status(thm)],[d27,c23]) ).
cnf(d29,plain,
( colinear(c,b,a)
| between(b,a,c)
| colinear(c,b,a) ),
inference(resolution,[status(thm)],[d28,c24]) ).
cnf(d30,plain,
( between(c,a,b)
| colinear(c,b,a) ),
inference(resolution,[status(thm)],[d29,d4]) ).
cnf(d31,plain,
( colinear(c,b,a)
| colinear(c,b,a) ),
inference(resolution,[status(thm)],[d30,c25]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[d31,d26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO010-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.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 12:31:49 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.91/3.87 % SZS status Unsatisfiable for theBenchmark.p
% 7.91/3.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------