%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT074-1 : 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 : n001.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 08:28:27 AM UTC 2026
% Result : Unsatisfiable 2.11s 0.80s
% Output : CNFRefutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_125,plain,
c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0_01,axiom,
c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_126,plain,
c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(clausify,[status(thm)],[cls_CHAINED_0_01]) ).
fof(cls_CHAINED_0,axiom,
c_in(v_Lab____,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_127,plain,
c_in(v_Lab____,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_Lin__irrefl_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_in(VAR_2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(VAR_1,VAR_0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),VAR_2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(VAR_0,VAR_1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),VAR_2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_Lin__irrefl_0) ).
cnf(c_204,plain,
( ~ c_in(C,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(B,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),C,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(clausify,[status(thm)],[cls_Lin__irrefl_0]) ).
cnf(c_1206,plain,
( ~ c_in(v_Lab____,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lab____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(resolve,[status(thm)],[c_204,c_126]) ).
cnf(c_1207,plain,
~ c_in(v_Lab____,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(resolve,[status(thm)],[c_125,c_1206]) ).
cnf(c_1205,plain,
$false,
inference(resolve,[status(thm)],[c_127,c_1207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT074-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.39 % Computer : n001.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8046.5625MB
% 0.15/0.39 % OS : Linux 6.8.0-71-generic
% 0.15/0.39 % CPULimit : 300
% 0.15/0.39 % WCLimit : 300
% 0.15/0.39 % DateTime : Sat Sep 26 06:30:42 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.40 % Process 1108343 was started by sandbox2 on n001,
% 0.15/0.40 % Sat Sep 26 06:30:42 2026
% 0.15/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 2.11/0.80
% 2.11/0.80 % SZS status Unsatisfiable for theBenchmark
% 2.11/0.80
% 2.11/0.80 % Proof 1 at 0.32 (+ 0.03) seconds.
% 2.11/0.80 % Length of proof is 5.
% 2.11/0.80 % Level of proof is 1.
% 2.11/0.80 % Maximum clause weight is 28.000.
% 2.11/0.80 % Given clauses 116.
% 2.11/0.80
% 2.11/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------