%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT004-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 08:28:22 AM UTC 2026
% Result : Unsatisfiable 6.68s 6.55s
% Output : CNFRefutation 6.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 7 unt; 0 def)
% Number of atoms : 133 ( 25 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 165 ( 70 ~; 95 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 19 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_17,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| hBOOL(c_in(c_Pair(VAR_3,VAR_2,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(VAR_2,VAR_3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| VAR_0 = VAR_1
| hBOOL(c_in(c_Pair(VAR_1,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)))
| hBOOL(c_in(c_Pair(VAR_0,VAR_1,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_17) ).
cnf(c_157,plain,
( D = C
| hBOOL(c_in(c_Pair(D,C,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(C,D,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| A = B
| hBOOL(c_in(c_Pair(B,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)))
| hBOOL(c_in(c_Pair(A,B,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_17]) ).
fof(cls_conjecture_15,axiom,
( ~ 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)))
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ 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)))
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,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_15) ).
cnf(c_160,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)))
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ 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)))
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,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_15]) ).
cnf(c_4262,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)))
| ~ 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)))
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,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(copy,[status(thm)],[c_160]) ).
cnf(c_4263,plain,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ 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)))
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,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(copy,[status(thm)],[c_4262]) ).
cnf(c_161,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)))
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,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(copy,[status(thm)],[c_4263]) ).
fof(cls_conjecture_13,axiom,
( ~ 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)))
| ~ hBOOL(c_in(c_Pair(v_xa,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)))
| ~ 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)))
| ~ hBOOL(c_in(c_Pair(v_xa,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_13) ).
cnf(c_163,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)))
| ~ hBOOL(c_in(c_Pair(v_xa,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)))
| ~ 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)))
| ~ hBOOL(c_in(c_Pair(v_xa,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_13]) ).
cnf(c_4264,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)))
| ~ 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)))
| ~ hBOOL(c_in(c_Pair(v_xa,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(copy,[status(thm)],[c_163]) ).
cnf(c_4265,plain,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ 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)))
| ~ hBOOL(c_in(c_Pair(v_xa,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(copy,[status(thm)],[c_4264]) ).
cnf(c_164,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)))
| ~ hBOOL(c_in(c_Pair(v_xa,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(copy,[status(thm)],[c_4265]) ).
fof(cls_conjecture_8,axiom,
( ~ 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)))
| v_x != v_xa
| ~ 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)))
| v_x != v_xa ),
file('theBenchmark.p',cls_conjecture_8) ).
cnf(c_169,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)))
| v_x != v_xa
| ~ 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)))
| v_x != v_xa ),
inference(clausify,[status(thm)],[cls_conjecture_8]) ).
cnf(c_4266,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)))
| v_x != v_xa
| ~ 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)))
| v_xa != v_x ),
inference(copy,[status(thm)],[c_169]) ).
cnf(c_4267,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)))
| v_xa != v_x
| ~ 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)))
| v_xa != v_x ),
inference(copy,[status(thm)],[c_4266]) ).
cnf(c_4268,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)))
| ~ 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)))
| v_xa != v_x ),
inference(copy,[status(thm)],[c_4267]) ).
cnf(c_4269,plain,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ 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)))
| v_xa != v_x ),
inference(copy,[status(thm)],[c_4268]) ).
cnf(c_170,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)))
| v_xa != v_x ),
inference(copy,[status(thm)],[c_4269]) ).
fof(cls_conjecture_3,axiom,
! [VAR_0,VAR_1] :
( ~ hBOOL(c_in(c_Pair(VAR_1,VAR_1,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(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_3) ).
cnf(c_173,plain,
( ~ hBOOL(c_in(c_Pair(B,B,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,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_3]) ).
fof(cls_conjecture_0,axiom,
( c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_175,plain,
( c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_176,plain,
c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
inference(copy,[status(thm)],[c_175]) ).
cnf(c_4270,plain,
( A = B
| hBOOL(c_in(c_Pair(B,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)))
| A = B
| hBOOL(c_in(c_Pair(B,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)))
| hBOOL(c_in(c_Pair(A,B,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(factor,[status(thm)],[c_157]) ).
cnf(c_4271,plain,
( A = B
| A = B
| hBOOL(c_in(c_Pair(B,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)))
| hBOOL(c_in(c_Pair(A,B,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(copy,[status(thm)],[c_4270]) ).
cnf(c_816,plain,
( A = B
| hBOOL(c_in(c_Pair(B,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)))
| hBOOL(c_in(c_Pair(A,B,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(copy,[status(thm)],[c_4271]) ).
cnf(c_817,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(factor,[status(thm)],[c_173]) ).
cnf(c_4272,plain,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| v_xa != v_x ),
inference(resolve,[status(thm)],[c_817,c_170]) ).
cnf(c_818,plain,
v_xa != v_x,
inference(resolve,[status(thm)],[c_176,c_4272]) ).
cnf(c_4273,plain,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_xa,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_817,c_164]) ).
cnf(c_819,plain,
~ hBOOL(c_in(c_Pair(v_xa,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_176,c_4273]) ).
cnf(c_4274,plain,
( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(v_x,v_xa,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_817,c_161]) ).
cnf(c_820,plain,
~ hBOOL(c_in(c_Pair(v_x,v_xa,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_176,c_4274]) ).
cnf(c_4275,plain,
( v_x = v_xa
| hBOOL(c_in(c_Pair(v_x,v_xa,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_819,c_816]) ).
cnf(c_4276,plain,
( v_xa = v_x
| hBOOL(c_in(c_Pair(v_x,v_xa,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(copy,[status(thm)],[c_4275]) ).
cnf(c_4277,plain,
v_xa = v_x,
inference(resolve,[status(thm)],[c_820,c_4276]) ).
cnf(c_4261,plain,
$false,
inference(resolve,[status(thm)],[c_818,c_4277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT004-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/5.60 % Computer : n002.cluster.edu
% 0.02/5.60 % Model : x86_64 x86_64
% 0.02/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/5.60 % Memory : 8046.5625MB
% 0.02/5.60 % OS : Linux 6.8.0-71-generic
% 0.02/5.60 % CPULimit : 300
% 0.02/5.60 % WCLimit : 300
% 0.02/5.60 % DateTime : Sat Sep 26 06:20:27 UTC 2026
% 0.02/5.60 % CPUTime :
% 0.02/5.60 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/5.60 % Process 1023543 was started by sandbox on n002,
% 0.02/5.60 % Sat Sep 26 06:20:27 2026
% 0.02/5.60 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/5.63
% 0.02/5.63 % From the command line: assign(max_seconds, 300).
% 6.68/6.55
% 6.68/6.55 % given #500 (I,wt=52): 716 c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(tc_prod(C,D),tc_bool)),C,D),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(A,C,D),c_Relation_ODomain(B,C,D),tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) # tptp_name(cls_Domain__Int__subset_0) # clausal_fof(1). [assumption].
% 6.68/6.55
% 6.68/6.55 % SZS status Unsatisfiable for theBenchmark
% 6.68/6.55
% 6.68/6.55 % Proof 1 at 0.66 (+ 0.12) seconds.
% 6.68/6.55 % Length of proof is 16.
% 6.68/6.55 % Level of proof is 3.
% 6.68/6.55 % Maximum clause weight is 65.000.
% 6.68/6.55 % Given clauses 583.
% 6.68/6.55
% 6.68/6.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------