%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO021-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 08:39:16 AM UTC 2026
% Result : Unsatisfiable 138.15s 138.47s
% Output : Proof 138.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 15 ( 12 unt; 0 nHn; 14 RR)
% Number of literals : 21 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(reflexivity_for_equidistance,axiom,
equidistant(X,Y,Y,X),
file('GEO002-0.ax',reflexivity_for_equidistance) ).
cnf(transitivity_for_equidistance,axiom,
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
file('GEO002-0.ax',transitivity_for_equidistance) ).
cnf(u_to_v_equals_w_to_x,hypothesis,
equidistant(u,v,w,x),
file('theBenchmark.p',u_to_v_equals_w_to_x) ).
cnf(prove_symmetry,negated_conjecture,
~ equidistant(x,w,v,u),
file('theBenchmark.p',prove_symmetry) ).
cnf(t1,plain,
~ equidistant(x,w,v,u),
inference(start,[status(thm),parent(0:0)],[prove_symmetry]) ).
cnf(t2,plain,
( ~ equidistant(w,x,v,u)
| ~ equidistant(w,x,x,w)
| equidistant(x,w,v,u) ),
inference(extension,[status(thm),parent(t1:1)],[transitivity_for_equidistance]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
equidistant(w,x,x,w),
inference(extension,[status(thm),parent(t2:2)],[reflexivity_for_equidistance]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ equidistant(u,v,v,u)
| ~ equidistant(u,v,w,x)
| equidistant(w,x,v,u) ),
inference(extension,[status(thm),parent(t2:3)],[transitivity_for_equidistance]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
equidistant(u,v,w,x),
inference(extension,[status(thm),parent(t6:2)],[u_to_v_equals_w_to_x]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
equidistant(u,v,v,u),
inference(extension,[status(thm),parent(t6:3)],[reflexivity_for_equidistance]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO021-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n013.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 19 07:08:06 UTC 2026
% 0.07/0.35 % CPUTime :
% 138.15/138.47 % SZS status Unsatisfiable for theBenchmark
% 138.15/138.47 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------