%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO062-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 08:39:23 AM UTC 2026
% Result : Unsatisfiable 41.79s 42.13s
% Output : Proof 41.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 17 unt; 0 nHn; 21 RR)
% Number of literals : 35 ( 4 equ; 14 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 19 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d1,axiom,
equidistant(U,V,U,V),
file('theBenchmark.p',d1) ).
cnf(d4_2,axiom,
( equidistant(V,U,X,W)
| ~ equidistant(U,V,W,X) ),
file('theBenchmark.p',d4_2) ).
cnf(d15,axiom,
( V = X
| ~ equidistant(W,V,W,X)
| ~ equidistant(U,V,U,X)
| ~ between(U,V,W) ),
file('theBenchmark.p',d15) ).
cnf(i2_1,axiom,
equidistant(U,V,U1,insertion(U1,W1,U,V)),
file('theBenchmark.p',i2_1) ).
cnf(i2_3,axiom,
( equidistant(V,W,insertion(U1,W1,U,V),W1)
| ~ equidistant(U,W,U1,W1)
| ~ between(U,V,W) ),
file('theBenchmark.p',i2_3) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(prove_v_equals_insertion,negated_conjecture,
v != insertion(u,w,u,v),
file('theBenchmark.p',prove_v_equals_insertion) ).
cnf(t1,plain,
v != insertion(u,w,u,v),
inference(start,[status(thm),parent(0:0)],[prove_v_equals_insertion]) ).
cnf(t2,plain,
( ~ equidistant(u,v,u,insertion(u,w,u,v))
| ~ equidistant(w,v,w,insertion(u,w,u,v))
| ~ between(u,v,w)
| v = insertion(u,w,u,v) ),
inference(extension,[status(thm),parent(t1:1)],[d15]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
between(u,v,w),
inference(extension,[status(thm),parent(t2:2)],[v_between_u_and_w]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(l2,lemma,
between(u,v,w),
inference(lemma,[status(cth),parent(t2:2),below(t1:1)],[t2:2]) ).
cnf(t6,plain,
( ~ equidistant(v,w,insertion(u,w,u,v),w)
| equidistant(w,v,w,insertion(u,w,u,v)) ),
inference(extension,[status(thm),parent(t2:3)],[d4_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ equidistant(u,w,u,w)
| ~ between(u,v,w)
| equidistant(v,w,insertion(u,w,u,v),w) ),
inference(extension,[status(thm),parent(t6:2)],[i2_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
between(u,v,w),
inference(lemma_extension,[status(thm),parent(t8:2)],[l2:1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
equidistant(u,w,u,w),
inference(extension,[status(thm),parent(t8:3)],[d1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
equidistant(u,v,u,insertion(u,w,u,v)),
inference(extension,[status(thm),parent(t2:4)],[i2_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO062-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 07:15:17 UTC 2026
% 0.09/0.38 % CPUTime :
% 41.79/42.13 % SZS status Unsatisfiable for theBenchmark
% 41.79/42.13 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------