%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO009-3 : 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 : n017.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 36.83s 41.48s
% Output : CNFRefutation 36.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of clauses : 62 ( 37 unt; 13 nHn; 37 RR)
% Number of literals : 106 ( 30 equ; 37 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 143 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ) ).
cnf(t2,axiom,
between(X0,X0,X1) ).
cnf(b5,axiom,
( between(X1,X2,X3)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ) ).
cnf(b7,axiom,
( X1 = X2
| between(X0,X1,X3)
| ~ between(X1,X2,X3)
| ~ between(X0,X1,X2) ) ).
cnf(b8,axiom,
( between(X0,X3,X2)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ) ).
cnf(e3_1,axiom,
X0 != extension(X1,X0,'lower$udimension$upoint$u1','lower$udimension$upoint$u2') ).
cnf(e3_3,axiom,
between(X0,X1,extension(X0,X1,'lower$udimension$upoint$u1','lower$udimension$upoint$u2')) ).
cnf(i3,axiom,
( X1 = insertion(X0,X2,X0,X1)
| ~ between(X0,X1,X2) ) ).
cnf(i4,axiom,
( insertion(X4,X5,X0,X1) = insertion(X4,X5,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(b13,axiom,
( between(X1,X3,X2)
| between(X1,X2,X3)
| X0 = X1
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ) ).
cnf(c_between_a_and_e,hypothesis,
between(a,c,e) ).
cnf(d_between_a_and_e,hypothesis,
between(a,d,e) ).
cnf(c_not_between_a_and_d,hypothesis,
~ between(a,c,d) ).
cnf(prove_d_between_a_and_c,negated_conjecture,
~ between(a,d,c) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X0,X1,X1,X0) ).
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(insertion,axiom,
insertion(X0,X1,X2,X3) = extension(extension(X1,X0,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),X0,X2,X3) ).
cnf(c26,plain,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[t1]) ).
cnf(c27,plain,
between(X0,X0,X1),
inference(clausification,[status(esa)],[t2]) ).
cnf(c32,plain,
( between(X3,X1,X2)
| ~ between(X0,X3,X1)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[b5]) ).
cnf(c34,plain,
( X3 = X1
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X3)
| between(X0,X1,X2) ),
inference(clausification,[status(esa)],[b7]) ).
cnf(c35,plain,
( between(X3,X1,X2)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[b8]) ).
cnf(c40,plain,
extension(X0,X1,'lower$udimension$upoint$u1','lower$udimension$upoint$u2') != X1,
inference(clausification,[status(esa)],[e3_1]) ).
cnf(c42,plain,
between(X0,X1,extension(X0,X1,'lower$udimension$upoint$u1','lower$udimension$upoint$u2')),
inference(clausification,[status(esa)],[e3_3]) ).
cnf(c52,plain,
( insertion(X0,X2,X0,X1) = X1
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[i3]) ).
cnf(c53,plain,
( insertion(X4,X5,X2,X3) = insertion(X4,X5,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[i4]) ).
cnf(c56,plain,
( X1 = X0
| ~ between(X0,X1,X3)
| between(X1,X3,X2)
| between(X1,X2,X3)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[b13]) ).
cnf(c58,plain,
between(a,c,e),
inference(clausification,[status(esa)],[c_between_a_and_e]) ).
cnf(c59,plain,
between(a,d,e),
inference(clausification,[status(esa)],[d_between_a_and_e]) ).
cnf(c60,plain,
~ between(a,c,d),
inference(clausification,[status(esa)],[c_not_between_a_and_d]) ).
cnf(c61,plain,
~ between(a,d,c),
inference(clausification,[status(esa)],[prove_d_between_a_and_c]) ).
cnf(c62,plain,
equidistant(X0,X1,X1,X0),
inference(clausification,[status(esa)],[reflexivity_for_equidistance]) ).
cnf(c65,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c66,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(c81,plain,
extension(extension(X0,X1,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),X1,X2,X3) = insertion(X1,X0,X2,X3),
inference(clausification,[status(esa)],[insertion]) ).
cnf(d_0,plain,
between(extension(X0,X1,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),X1,X0),
inference(resolution,[status(thm)],[c42,c26]) ).
cnf(d_1,plain,
( ~ between(extension(X1,X0,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),X0,X2)
| between(X0,X1,X2)
| between(X0,X2,X1)
| X0 = extension(X1,X0,'lower$udimension$upoint$u1','lower$udimension$upoint$u2') ),
inference(resolution,[status(thm)],[d_0,c56]) ).
cnf(d_2,plain,
insertion(X0,X1,X2,X3) = insertion(X0,X1,X3,X2),
inference(resolution,[status(thm)],[c53,c62]) ).
cnf(d_3,plain,
insertion(X1,X0,'lower$udimension$upoint$u1','lower$udimension$upoint$u2') != X1,
inference(superposition,[status(thm)],[c81,c40]) ).
cnf(d_4,plain,
insertion(X0,X1,'lower$udimension$upoint$u2','lower$udimension$upoint$u1') != X0,
inference(demodulation,[status(thm)],[d_3,d_2]) ).
cnf(d_5,plain,
insertion(X0,X1,X2,X3) = insertion(X0,X1,X4,extension(X5,X4,X2,X3)),
inference(resolution,[status(thm)],[c66,c53]) ).
cnf(d_6,plain,
insertion(extension(X0,X1,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),X0,extension(X0,X1,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),X1) = X1,
inference(resolution,[status(thm)],[d_0,c52]) ).
cnf(d_7,plain,
insertion(extension(X0,X1,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),X0,X1,extension(X0,X1,'lower$udimension$upoint$u1','lower$udimension$upoint$u2')) = X1,
inference(demodulation,[status(thm)],[d_6,d_2]) ).
cnf(d_8,plain,
insertion(extension(X0,X1,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),X0,'lower$udimension$upoint$u1','lower$udimension$upoint$u2') = X1,
inference(demodulation,[status(thm)],[d_7,d_5]) ).
cnf(d_9,plain,
insertion(extension(X0,X1,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),X0,'lower$udimension$upoint$u2','lower$udimension$upoint$u1') = X1,
inference(demodulation,[status(thm)],[d_8,d_2]) ).
cnf(d_10,plain,
X1 != extension(X0,X1,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),
inference(superposition,[status(thm)],[d_9,d_4]) ).
cnf(d_11,plain,
( ~ between(extension(X2,X0,'lower$udimension$upoint$u1','lower$udimension$upoint$u2'),X0,X1)
| between(X0,X2,X1)
| between(X0,X1,X2) ),
inference(resolution,[status(thm)],[d_10,d_1]) ).
cnf(d_12,plain,
between(e,c,a),
inference(resolution,[status(thm)],[c26,c58]) ).
cnf(d_13,plain,
( ~ between(e,a,X0)
| between(c,a,X0) ),
inference(resolution,[status(thm)],[c32,d_12]) ).
cnf(d_14,plain,
( ~ between(X0,X2,extension(X2,X1,X3,X4))
| between(X0,X1,extension(X2,X1,X3,X4)) ),
inference(resolution,[status(thm)],[c65,c35]) ).
cnf(d_15,plain,
between(e,d,a),
inference(resolution,[status(thm)],[c26,c59]) ).
cnf(d_16,plain,
( between(e,d,X0)
| ~ between(d,a,X0)
| a = d ),
inference(resolution,[status(thm)],[c34,d_15]) ).
cnf(d_17,plain,
( between(e,d,extension(d,a,X0,X1))
| a = d ),
inference(resolution,[status(thm)],[d_16,c65]) ).
cnf(d_18,plain,
( between(e,a,extension(d,a,X0,X1))
| a = d ),
inference(resolution,[status(thm)],[d_17,d_14]) ).
cnf(d_19,plain,
( between(c,a,extension(d,a,X0,X1))
| a = d ),
inference(resolution,[status(thm)],[d_18,d_13]) ).
cnf(d_20,plain,
( between(extension(d,a,X0,X1),a,c)
| a = d ),
inference(resolution,[status(thm)],[d_19,c26]) ).
cnf(d_21,plain,
( between(a,c,d)
| between(a,d,c)
| a = d ),
inference(resolution,[status(thm)],[d_20,d_11]) ).
cnf(d_22,plain,
( between(a,d,c)
| a = d ),
inference(resolution,[status(thm)],[c60,d_21]) ).
cnf(d_23,plain,
a = d,
inference(resolution,[status(thm)],[c61,d_22]) ).
cnf(d_24,plain,
~ between(a,a,c),
inference(demodulation,[status(thm)],[c61,d_23]) ).
cnf(d_25,plain,
$false,
inference(resolution,[status(thm)],[c27,d_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO009-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/10.43 % Computer : n017.cluster.edu
% 0.16/10.43 % Model : x86_64 x86_64
% 0.16/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.43 % Memory : 8046.5625MB
% 0.16/10.43 % OS : Linux 6.8.0-71-generic
% 0.16/10.43 % CPULimit : 300
% 0.16/10.43 % WCLimit : 300
% 0.16/10.43 % DateTime : Fri Sep 25 12:26:27 UTC 2026
% 0.16/10.44 % CPUTime :
% 0.16/10.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.83/41.48 % SZS status Unsatisfiable for theBenchmark.p
% 36.83/41.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------