%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT002-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 08:28:21 AM UTC 2026
% Result : Unsatisfiable 0.39s 15.88s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 13 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_4,axiom,
hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_152,plain,
hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_3,axiom,
hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_153,plain,
hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0] : ~ hBOOL(c_in(c_Pair(VAR_0,VAR_0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_154,plain,
~ hBOOL(c_in(c_Pair(A,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_155,plain,
c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_transD_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ c_Relation_Otrans(VAR_3,VAR_2)
| ~ hBOOL(c_in(c_Pair(VAR_0,VAR_4,VAR_2,VAR_2),VAR_3,tc_prod(VAR_2,VAR_2)))
| ~ hBOOL(c_in(c_Pair(VAR_4,VAR_1,VAR_2,VAR_2),VAR_3,tc_prod(VAR_2,VAR_2)))
| hBOOL(c_in(c_Pair(VAR_0,VAR_1,VAR_2,VAR_2),VAR_3,tc_prod(VAR_2,VAR_2))) ),
file('theBenchmark.p',cls_transD_0) ).
cnf(c_160,plain,
( ~ c_Relation_Otrans(D,C)
| ~ hBOOL(c_in(c_Pair(A,E,C,C),D,tc_prod(C,C)))
| ~ hBOOL(c_in(c_Pair(E,B,C,C),D,tc_prod(C,C)))
| hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) ),
inference(clausify,[status(thm)],[cls_transD_0]) ).
cnf(c_920,plain,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(A,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(A,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolve,[status(thm)],[c_160,c_153]) ).
cnf(c_921,plain,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolve,[status(thm)],[c_920,c_152]) ).
cnf(c_922,plain,
hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(resolve,[status(thm)],[c_921,c_155]) ).
cnf(c_919,plain,
$false,
inference(resolve,[status(thm)],[c_154,c_922]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT002-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.13/15.48 % CPULimit : 300
% 0.13/15.48 % WCLimit : 300
% 0.13/15.48 % DateTime : Sat Sep 26 06:17:33 UTC 2026
% 0.13/15.48 % CPUTime :
% 0.13/15.49 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/15.49 % Process 2103871 was started by sandbox2 on n013,
% 0.13/15.49 % Sat Sep 26 06:17:33 2026
% 0.13/15.49 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.39/15.51
% 0.39/15.51 % From the command line: assign(max_seconds, 300).
% 0.39/15.88
% 0.39/15.88 % SZS status Unsatisfiable for theBenchmark
% 0.39/15.88
% 0.39/15.88 % Proof 1 at 0.32 (+ 0.02) seconds.
% 0.39/15.88 % Length of proof is 6.
% 0.39/15.88 % Level of proof is 1.
% 0.39/15.88 % Maximum clause weight is 51.000.
% 0.39/15.88 % Given clauses 85.
% 0.39/15.88
% 0.39/15.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------