%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT073-1 : 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 : n007.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 7.41s 1.50s
% Output : CNFRefutation 7.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 10 unt; 0 def)
% Number of atoms : 34 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 20 ( 7 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_in__mktop_4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(c_Pair(VAR_0,VAR_1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(VAR_2,VAR_1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| VAR_0 = VAR_1
| VAR_0 = VAR_1 ),
file('theBenchmark.p',cls_in__mktop_4) ).
cnf(c_491,plain,
( c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(C,B),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| A = B
| A = B ),
inference(clausify,[status(thm)],[cls_in__mktop_4]) ).
cnf(c_492,plain,
( c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(C,B),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| A = B ),
inference(copy,[status(thm)],[c_491]) ).
fof(cls_mktop__Lin_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_in(VAR_0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omktop(VAR_0,VAR_1),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_mktop__Lin_0) ).
cnf(c_496,plain,
( ~ c_in(A,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omktop(A,B),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_mktop__Lin_0]) ).
fof(cls_linear__alt_0,axiom,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,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_linear__alt_0) ).
cnf(c_499,plain,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,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_linear__alt_0]) ).
fof(cls_that_0,axiom,
! [VAR_0] :
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),VAR_0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(VAR_0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| v_thesis____ ),
file('theBenchmark.p',cls_that_0) ).
cnf(c_559,plain,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),A,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(A,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| v_thesis____ ),
inference(clausify,[status(thm)],[cls_that_0]) ).
fof(cls_CHAINED_0,axiom,
v_a____ != v_b____,
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_561,plain,
v_a____ != v_b____,
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
cnf(c_562,plain,
v_b____ != v_a____,
inference(copy,[status(thm)],[c_561]) ).
fof(cls_conjecture_0,axiom,
~ v_thesis____,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_563,plain,
~ v_thesis____,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_645,plain,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),A,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(A,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_563,c_559]) ).
cnf(c_2987,plain,
c_in(c_Arrow__Order__Mirabelle_Omktop(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,A),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_499,c_496]) ).
cnf(c_4282,plain,
( v_a____ = v_b____
| ~ c_in(c_Arrow__Order__Mirabelle_Omktop(A,v_b____),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_645,c_492]) ).
cnf(c_4283,plain,
( v_b____ = v_a____
| ~ c_in(c_Arrow__Order__Mirabelle_Omktop(A,v_b____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(copy,[status(thm)],[c_4282]) ).
cnf(c_4280,plain,
~ c_in(c_Arrow__Order__Mirabelle_Omktop(A,v_b____),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_562,c_4283]) ).
cnf(c_4281,plain,
$false,
inference(resolve,[status(thm)],[c_4280,c_2987]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT073-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.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 : Sat Sep 26 06:23:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2990599 was started by sandbox2 on n007,
% 0.09/0.37 % Sat Sep 26 06:23:09 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.41
% 0.15/0.41 % From the command line: assign(max_seconds, 300).
% 7.41/1.50
% 7.41/1.50 % given #500 (I,wt=27): 635 c_Relation_ODomain(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(A,B,C,D),E,tc_prod(C,D)),C,D),D,C) = c_Set_Oinsert(B,c_Relation_ODomain(c_Relation_Oconverse(E,C,D),D,C),D). [back_rewrite(166),rewrite([463(4),463(6)])].
% 7.41/1.50
% 7.41/1.50 % SZS status Unsatisfiable for theBenchmark
% 7.41/1.50
% 7.41/1.50 % Proof 1 at 0.87 (+ 0.15) seconds.
% 7.41/1.50 % Length of proof is 12.
% 7.41/1.50 % Level of proof is 3.
% 7.41/1.50 % Maximum clause weight is 19.000.
% 7.41/1.50 % Given clauses 510.
% 7.41/1.50
% 7.41/1.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------