%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO001-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 07:16:42 AM UTC 2026
% Result : Unsatisfiable 40.73s 5.54s
% Output : CNFRefutation 40.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 32 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-5 aty)
% Number of variables : 38 ( 3 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(identity_for_betweeness,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ between(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',identity_for_betweeness) ).
cnf(c_7,plain,
( A = B
| ~ between(A,B,A) ),
inference(clausify,[status(thm)],[identity_for_betweeness]) ).
fof(inner_pasch1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_1,inner_pasch(VAR_0,VAR_1,VAR_2,VAR_4,VAR_3),VAR_3)
| ~ between(VAR_3,VAR_4,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',inner_pasch1) ).
cnf(c_8,plain,
( between(B,inner_pasch(A,B,C,E,D),D)
| ~ between(D,E,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[inner_pasch1]) ).
fof(inner_pasch2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_4,inner_pasch(VAR_0,VAR_1,VAR_2,VAR_4,VAR_3),VAR_0)
| ~ between(VAR_3,VAR_4,VAR_2)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',inner_pasch2) ).
cnf(c_9,plain,
( between(E,inner_pasch(A,B,C,E,D),A)
| ~ between(D,E,C)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[inner_pasch2]) ).
fof(t3,axiom,
! [VAR_0,VAR_1] : between(VAR_0,VAR_1,VAR_1),
file('theBenchmark.p',t3) ).
cnf(c_52,plain,
between(A,B,B),
inference(clausify,[status(thm)],[t3]) ).
fof(b_between_a_and_c,axiom,
between(a,b,c),
file('theBenchmark.p',b_between_a_and_c) ).
cnf(c_54,plain,
between(a,b,c),
inference(clausify,[status(thm)],[b_between_a_and_c]) ).
fof(prove_b_between_c_and_a,axiom,
~ between(c,b,a),
file('theBenchmark.p',prove_b_between_c_and_a) ).
cnf(c_55,plain,
~ between(c,b,a),
inference(clausify,[status(thm)],[prove_b_between_c_and_a]) ).
cnf(c_2895,plain,
( between(B,inner_pasch(D,C,C,B,A),D)
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_9,c_52]) ).
cnf(c_238,plain,
between(b,inner_pasch(A,c,c,b,a),A),
inference(resolve,[status(thm)],[c_2895,c_54]) ).
cnf(c_2896,plain,
( between(C,inner_pasch(D,C,C,B,A),A)
| ~ between(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_52]) ).
cnf(c_240,plain,
between(c,inner_pasch(A,c,c,b,a),a),
inference(resolve,[status(thm)],[c_2896,c_54]) ).
cnf(c_2897,plain,
b = inner_pasch(b,c,c,b,a),
inference(resolve,[status(thm)],[c_238,c_7]) ).
cnf(c_2084,plain,
inner_pasch(b,c,c,b,a) = b,
inference(copy,[status(thm)],[c_2897]) ).
cnf(c_2898,plain,
between(c,b,a),
inference(paramod,[status(thm)],[c_2084,c_240]) ).
cnf(c_2894,plain,
$false,
inference(resolve,[status(thm)],[c_55,c_2898]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO001-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n006.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 12:29:56 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.34 % Process 2906745 was started by sandbox2 on n006,
% 0.09/0.34 % Fri Sep 25 12:29:56 2026
% 0.09/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 40.73/5.54
% 40.73/5.54 % SZS status Unsatisfiable for theBenchmark
% 40.73/5.54
% 40.73/5.54 % Proof 1 at 4.97 (+ 0.21) seconds.
% 40.73/5.54 % Length of proof is 10.
% 40.73/5.54 % Level of proof is 3.
% 40.73/5.54 % Maximum clause weight is 27.000.
% 40.73/5.54 % Given clauses 126.
% 40.73/5.54
% 40.73/5.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------