%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO026-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 : Thu Sep 24 08:39:17 AM UTC 2026
% Result : Unsatisfiable 192.76s 193.03s
% Output : Proof 192.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 27 ( 23 unt; 2 nHn; 26 RR)
% Number of literals : 43 ( 8 equ; 18 neg)
% Maximal clause size : 8 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_for_equidistance,axiom,
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('GEO002-0.ax',identity_for_equidistance) ).
cnf(outer_five_segment,axiom,
( equidistant(Z,V,Z1,V1)
| X = Y
| ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ),
file('GEO002-0.ax',outer_five_segment) ).
cnf(d1,axiom,
equidistant(U,V,U,V),
file('theBenchmark.p',d1) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(v_between_u_and_x,hypothesis,
between(u,v,x),
file('theBenchmark.p',v_between_u_and_x) ).
cnf(v_to_w_equals_v_to_x,hypothesis,
equidistant(v,w,v,x),
file('theBenchmark.p',v_to_w_equals_v_to_x) ).
cnf(u_not_v,hypothesis,
u != v,
file('theBenchmark.p',u_not_v) ).
cnf(prove_w_is_x,negated_conjecture,
w != x,
file('theBenchmark.p',prove_w_is_x) ).
cnf(t1,plain,
w != x,
inference(start,[status(thm),parent(0:0)],[prove_w_is_x]) ).
cnf(t2,plain,
( ~ equidistant(w,x,x,x)
| w = x ),
inference(extension,[status(thm),parent(t1:1)],[identity_for_equidistance]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ equidistant(u,x,u,x)
| ~ equidistant(v,x,v,x)
| ~ equidistant(u,v,u,v)
| ~ between(u,v,x)
| u = v
| ~ between(u,v,w)
| ~ equidistant(v,w,v,x)
| equidistant(w,x,x,x) ),
inference(extension,[status(thm),parent(t2:2)],[outer_five_segment]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
equidistant(v,w,v,x),
inference(extension,[status(thm),parent(t4:2)],[v_to_w_equals_v_to_x]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
between(u,v,w),
inference(extension,[status(thm),parent(t4:3)],[v_between_u_and_w]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
u != v,
inference(extension,[status(thm),parent(t4:4)],[u_not_v]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
cnf(t12,plain,
between(u,v,x),
inference(extension,[status(thm),parent(t4:5)],[v_between_u_and_x]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:5]) ).
cnf(t14,plain,
equidistant(u,v,u,v),
inference(extension,[status(thm),parent(t4:6)],[d1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t4:6]) ).
cnf(t16,plain,
equidistant(v,x,v,x),
inference(extension,[status(thm),parent(t4:7)],[d1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t4:7]) ).
cnf(t18,plain,
equidistant(u,x,u,x),
inference(extension,[status(thm),parent(t4:8)],[d1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t4:8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO026-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n015.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sat Sep 19 07:11:49 UTC 2026
% 0.07/0.36 % CPUTime :
% 192.76/193.03 % SZS status Unsatisfiable for theBenchmark
% 192.76/193.03 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------