%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO013-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 07:16:46 AM UTC 2026
% Result : Unsatisfiable 1.81s 0.66s
% Output : CNFRefutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 18 unt; 0 def)
% Number of atoms : 56 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 44 ( 20 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 22 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t10_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( colinear(VAR_2,VAR_1,VAR_0)
| ~ colinear(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',t10_1) ).
cnf(c_104,plain,
( colinear(C,B,A)
| ~ colinear(A,B,C) ),
inference(clausify,[status(thm)],[t10_1]) ).
fof(t12_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_1
| colinear(VAR_1,VAR_2,VAR_3)
| ~ colinear(VAR_0,VAR_1,VAR_3)
| ~ colinear(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',t12_2) ).
cnf(c_116,plain,
( A = B
| colinear(B,C,D)
| ~ colinear(A,B,D)
| ~ colinear(A,B,C) ),
inference(clausify,[status(thm)],[t12_2]) ).
fof(a_not_b,axiom,
a != b,
file('theBenchmark.p',a_not_b) ).
cnf(c_119,plain,
a != b,
inference(clausify,[status(thm)],[a_not_b]) ).
cnf(c_120,plain,
b != a,
inference(copy,[status(thm)],[c_119]) ).
fof(and1_colinear,axiom,
colinear(a,b,d1),
file('theBenchmark.p',and1_colinear) ).
cnf(c_121,plain,
colinear(a,b,d1),
inference(clausify,[status(thm)],[and1_colinear]) ).
fof(abd2_colinear,axiom,
colinear(a,b,d2),
file('theBenchmark.p',abd2_colinear) ).
cnf(c_122,plain,
colinear(a,b,d2),
inference(clausify,[status(thm)],[abd2_colinear]) ).
fof(abd3_colinear,axiom,
colinear(a,b,d3),
file('theBenchmark.p',abd3_colinear) ).
cnf(c_123,plain,
colinear(a,b,d3),
inference(clausify,[status(thm)],[abd3_colinear]) ).
fof(prove_d1d2d3_colinear,axiom,
~ colinear(d1,d2,d3),
file('theBenchmark.p',prove_d1d2d3_colinear) ).
cnf(c_124,plain,
~ colinear(d1,d2,d3),
inference(clausify,[status(thm)],[prove_d1d2d3_colinear]) ).
cnf(c_1270,plain,
( a = b
| colinear(b,A,d1)
| ~ colinear(a,b,A) ),
inference(resolve,[status(thm)],[c_121,c_116]) ).
cnf(c_1271,plain,
( b = a
| colinear(b,A,d1)
| ~ colinear(a,b,A) ),
inference(copy,[status(thm)],[c_1270]) ).
cnf(c_479,plain,
( colinear(b,A,d1)
| ~ colinear(a,b,A) ),
inference(resolve,[status(thm)],[c_120,c_1271]) ).
cnf(c_1272,plain,
( a = b
| colinear(b,A,d2)
| ~ colinear(a,b,A) ),
inference(resolve,[status(thm)],[c_122,c_116]) ).
cnf(c_1273,plain,
( b = a
| colinear(b,A,d2)
| ~ colinear(a,b,A) ),
inference(copy,[status(thm)],[c_1272]) ).
cnf(c_494,plain,
( colinear(b,A,d2)
| ~ colinear(a,b,A) ),
inference(resolve,[status(thm)],[c_120,c_1273]) ).
cnf(c_719,plain,
colinear(b,d3,d1),
inference(resolve,[status(thm)],[c_479,c_123]) ).
cnf(c_720,plain,
colinear(b,d2,d1),
inference(resolve,[status(thm)],[c_479,c_122]) ).
cnf(c_1274,plain,
( b = d3
| colinear(d3,A,d1)
| ~ colinear(b,d3,A) ),
inference(resolve,[status(thm)],[c_719,c_116]) ).
cnf(c_725,plain,
( d3 = b
| colinear(d3,A,d1)
| ~ colinear(b,d3,A) ),
inference(copy,[status(thm)],[c_1274]) ).
cnf(c_749,plain,
colinear(d1,d2,b),
inference(resolve,[status(thm)],[c_720,c_104]) ).
cnf(c_1018,plain,
colinear(b,d3,d2),
inference(resolve,[status(thm)],[c_494,c_123]) ).
cnf(c_1254,plain,
( d3 = b
| colinear(d3,d2,d1) ),
inference(resolve,[status(thm)],[c_725,c_1018]) ).
cnf(c_1275,plain,
( colinear(d1,d2,d3)
| d3 = b ),
inference(resolve,[status(thm)],[c_1254,c_104]) ).
cnf(c_1268,plain,
d3 = b,
inference(resolve,[status(thm)],[c_124,c_1275]) ).
cnf(c_1276,plain,
~ colinear(d1,d2,b),
inference(paramod,[status(thm)],[c_1268,c_124]) ).
cnf(c_1269,plain,
$false,
inference(resolve,[status(thm)],[c_749,c_1276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO013-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.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 : Fri Sep 25 12:33:11 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 1044705 was started by sandbox on n008,
% 0.09/0.38 % Fri Sep 25 12:33:11 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 1.81/0.66
% 1.81/0.66 % SZS status Unsatisfiable for theBenchmark
% 1.81/0.66
% 1.81/0.66 % Proof 1 at 0.17 (+ 0.07) seconds.
% 1.81/0.66 % Length of proof is 18.
% 1.81/0.66 % Level of proof is 7.
% 1.81/0.66 % Maximum clause weight is 20.000.
% 1.81/0.66 % Given clauses 364.
% 1.81/0.66
% 1.81/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------