%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV885-1 : 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 : n006.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 09:09:17 AM UTC 2026
% Result : Unsatisfiable 23.20s 3.44s
% Output : CNFRefutation 23.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 72 ( 50 unt; 0 def)
% Number of atoms : 105 ( 58 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 69 ( 36 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-4 aty)
% Number of variables : 83 ( 7 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_6,axiom,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_350,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
cnf(c_351,plain,
c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) != c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a),
inference(copy,[status(thm)],[c_350]) ).
fof(cls_conjecture_5,axiom,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_352,plain,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_3,axiom,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_354,plain,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_355,plain,
c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat) = c_Finite__Set_Ocard(v_G,t_a),
inference(copy,[status(thm)],[c_354]) ).
fof(cls_conjecture_2,axiom,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_356,plain,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_357,plain,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_358,plain,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_card__insert__if_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_Finite__Set_Ofinite(VAR_1,VAR_2)
| c_in(VAR_0,VAR_1,VAR_2)
| c_Finite__Set_Ocard(c_Set_Oinsert(VAR_0,VAR_1,VAR_2),VAR_2) = c_Suc(c_Finite__Set_Ocard(VAR_1,VAR_2)) ),
file('theBenchmark.p',cls_card__insert__if_1) ).
cnf(c_386,plain,
( ~ c_Finite__Set_Ofinite(B,C)
| c_in(A,B,C)
| c_Finite__Set_Ocard(c_Set_Oinsert(A,B,C),C) = c_Suc(c_Finite__Set_Ocard(B,C)) ),
inference(clausify,[status(thm)],[cls_card__insert__if_1]) ).
fof(cls_finite__surj_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ c_Finite__Set_Ofinite(VAR_3,VAR_4)
| ~ c_lessequals(VAR_0,c_Set_Oimage(VAR_2,VAR_3,VAR_4,VAR_1),tc_fun(VAR_1,tc_bool))
| c_Finite__Set_Ofinite(VAR_0,VAR_1) ),
file('theBenchmark.p',cls_finite__surj_0) ).
cnf(c_392,plain,
( ~ c_Finite__Set_Ofinite(D,E)
| ~ c_lessequals(A,c_Set_Oimage(C,D,E,B),tc_fun(B,tc_bool))
| c_Finite__Set_Ofinite(A,B) ),
inference(clausify,[status(thm)],[cls_finite__surj_0]) ).
fof(cls_card__Suc__eq_4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_Finite__Set_Ocard(VAR_1,VAR_2) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ocard(c_Set_Oinsert(VAR_0,VAR_1,VAR_2),VAR_2) = c_Suc(c_Finite__Set_Ocard(VAR_1,VAR_2))
| c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_card__Suc__eq_4) ).
cnf(c_439,plain,
( c_Finite__Set_Ocard(B,C) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ocard(c_Set_Oinsert(A,B,C),C) = c_Suc(c_Finite__Set_Ocard(B,C))
| c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_card__Suc__eq_4]) ).
fof(cls_card__Suc__Diff1_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_Finite__Set_Ofinite(VAR_0,VAR_2)
| ~ c_in(VAR_1,VAR_0,VAR_2)
| c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(VAR_0,c_Set_Oinsert(VAR_1,c_Orderings_Obot__class_Obot(tc_fun(VAR_2,tc_bool)),VAR_2),tc_fun(VAR_2,tc_bool)),VAR_2)) = c_Finite__Set_Ocard(VAR_0,VAR_2) ),
file('theBenchmark.p',cls_card__Suc__Diff1_0) ).
cnf(c_462,plain,
( ~ c_Finite__Set_Ofinite(A,C)
| ~ c_in(B,A,C)
| c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),tc_fun(C,tc_bool)),C)) = c_Finite__Set_Ocard(A,C) ),
inference(clausify,[status(thm)],[cls_card__Suc__Diff1_0]) ).
fof(cls_add__diff__assoc_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_lessequals(VAR_2,VAR_1,tc_nat)
| c_HOL_Oplus__class_Oplus(VAR_0,c_HOL_Ominus__class_Ominus(VAR_1,VAR_2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(VAR_0,VAR_1,tc_nat),VAR_2,tc_nat) ),
file('theBenchmark.p',cls_add__diff__assoc_0) ).
cnf(c_467,plain,
( ~ c_lessequals(C,B,tc_nat)
| c_HOL_Oplus__class_Oplus(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) ),
inference(clausify,[status(thm)],[cls_add__diff__assoc_0]) ).
fof(cls_le__add__diff__inverse_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_lessequals(VAR_0,VAR_1,tc_nat)
| c_HOL_Oplus__class_Oplus(VAR_0,c_HOL_Ominus__class_Ominus(VAR_1,VAR_0,tc_nat),tc_nat) = VAR_1 ),
file('theBenchmark.p',cls_le__add__diff__inverse_0) ).
cnf(c_469,plain,
( ~ c_lessequals(A,B,tc_nat)
| c_HOL_Oplus__class_Oplus(A,c_HOL_Ominus__class_Ominus(B,A,tc_nat),tc_nat) = B ),
inference(clausify,[status(thm)],[cls_le__add__diff__inverse_0]) ).
fof(cls_diff__add__inverse_0,axiom,
! [VAR_0,VAR_1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(VAR_0,VAR_1,tc_nat),VAR_0,tc_nat) = VAR_1,
file('theBenchmark.p',cls_diff__add__inverse_0) ).
cnf(c_542,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat) = B,
inference(clausify,[status(thm)],[cls_diff__add__inverse_0]) ).
fof(cls_le__add1_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(VAR_0,c_HOL_Oplus__class_Oplus(VAR_0,VAR_1,tc_nat),tc_nat),
file('theBenchmark.p',cls_le__add1_0) ).
cnf(c_599,plain,
c_lessequals(A,c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),
inference(clausify,[status(thm)],[cls_le__add1_0]) ).
fof(cls_nat_Osimps_I2_J_0,axiom,
! [VAR_0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(VAR_0),
file('theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
cnf(c_727,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(A),
inference(clausify,[status(thm)],[cls_nat_Osimps_I2_J_0]) ).
cnf(c_728,plain,
c_Suc(A) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(copy,[status(thm)],[c_727]) ).
fof(cls_Nat_Oadd__0__right_0,axiom,
! [VAR_0] : c_HOL_Oplus__class_Oplus(VAR_0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = VAR_0,
file('theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
cnf(c_828,plain,
c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A,
inference(clausify,[status(thm)],[cls_Nat_Oadd__0__right_0]) ).
fof(cls_nat__add__commute_0,axiom,
! [VAR_0,VAR_1] : c_HOL_Oplus__class_Oplus(VAR_0,VAR_1,tc_nat) = c_HOL_Oplus__class_Oplus(VAR_1,VAR_0,tc_nat),
file('theBenchmark.p',cls_nat__add__commute_0) ).
cnf(c_956,plain,
c_HOL_Oplus__class_Oplus(A,B,tc_nat) = c_HOL_Oplus__class_Oplus(B,A,tc_nat),
inference(clausify,[status(thm)],[cls_nat__add__commute_0]) ).
fof(cls_Suc__eq__plus1__left_0,axiom,
! [VAR_0] : c_Suc(VAR_0) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),VAR_0,tc_nat),
file('theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
cnf(c_992,plain,
c_Suc(A) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),
inference(clausify,[status(thm)],[cls_Suc__eq__plus1__left_0]) ).
cnf(c_1228,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(paramod,[status(thm)],[c_992,c_728]) ).
cnf(c_1249,plain,
( ~ c_Finite__Set_Ofinite(A,C)
| ~ c_in(B,A,C)
| c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),tc_fun(C,tc_bool)),C),tc_nat) = c_Finite__Set_Ocard(A,C) ),
inference(paramod,[status(thm)],[c_992,c_462]) ).
cnf(c_1253,plain,
( c_Finite__Set_Ocard(B,C) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ocard(c_Set_Oinsert(A,B,C),C) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(B,C),tc_nat)
| c_in(A,B,C) ),
inference(paramod,[status(thm)],[c_992,c_439]) ).
cnf(c_1256,plain,
( ~ c_Finite__Set_Ofinite(B,C)
| c_in(A,B,C)
| c_Finite__Set_Ocard(c_Set_Oinsert(A,B,C),C) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(B,C),tc_nat) ),
inference(paramod,[status(thm)],[c_992,c_386]) ).
cnf(c_8020,plain,
c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_na,tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
inference(paramod,[status(thm)],[c_992,c_356]) ).
cnf(c_1261,plain,
c_lessequals(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
inference(paramod,[status(thm)],[c_956,c_8020]) ).
cnf(c_8021,plain,
c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),v_na,tc_nat),tc_nat) = c_Finite__Set_Ocard(v_G,t_a),
inference(paramod,[status(thm)],[c_992,c_355]) ).
cnf(c_1262,plain,
c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(v_G,t_a),
inference(paramod,[status(thm)],[c_956,c_8021]) ).
cnf(c_8022,plain,
( ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
| c_Finite__Set_Ofinite(v_G,t_a) ),
inference(resolve,[status(thm)],[c_392,c_357]) ).
cnf(c_1533,plain,
c_Finite__Set_Ofinite(v_G,t_a),
inference(resolve,[status(thm)],[c_358,c_8022]) ).
cnf(c_8023,plain,
c_HOL_Oplus__class_Oplus(A,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,tc_nat),B,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat),B,tc_nat),
inference(resolve,[status(thm)],[c_599,c_467]) ).
cnf(c_8024,plain,
c_HOL_Oplus__class_Oplus(A,C,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat),B,tc_nat),
inference(paramod,[status(thm)],[c_542,c_8023]) ).
cnf(c_2091,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat),B,tc_nat) = c_HOL_Oplus__class_Oplus(A,C,tc_nat),
inference(copy,[status(thm)],[c_8024]) ).
cnf(c_7384,plain,
( c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
inference(resolve,[status(thm)],[c_1253,c_352]) ).
cnf(c_8025,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(resolve,[status(thm)],[c_1261,c_469]) ).
cnf(c_8026,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat) = c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(paramod,[status(thm)],[c_1262,c_8025]) ).
cnf(c_8027,plain,
c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(v_G,t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(paramod,[status(thm)],[c_956,c_8026]) ).
cnf(c_7635,plain,
c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(v_G,t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(copy,[status(thm)],[c_8027]) ).
cnf(c_8028,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(v_G,t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_na,tc_nat) != c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a),
inference(paramod,[status(thm)],[c_7635,c_351]) ).
cnf(c_8029,plain,
c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(v_G,t_a),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a),
inference(paramod,[status(thm)],[c_2091,c_8028]) ).
cnf(c_8030,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat) != c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a),
inference(paramod,[status(thm)],[c_956,c_8029]) ).
cnf(c_7650,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat),
inference(copy,[status(thm)],[c_8030]) ).
cnf(c_7651,plain,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(resolve,[status(thm)],[c_7650,c_7384]) ).
cnf(c_8031,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(paramod,[status(thm)],[c_7651,c_7650]) ).
cnf(c_7652,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Oone__class_Oone(tc_nat),
inference(paramod,[status(thm)],[c_828,c_8031]) ).
cnf(c_8032,plain,
( c_in(A,v_G,t_a)
| c_Finite__Set_Ocard(c_Set_Oinsert(A,v_G,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
inference(resolve,[status(thm)],[c_1533,c_1256]) ).
cnf(c_8033,plain,
( c_in(A,v_G,t_a)
| c_Finite__Set_Ocard(c_Set_Oinsert(A,v_G,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(paramod,[status(thm)],[c_7651,c_8032]) ).
cnf(c_7982,plain,
( c_in(A,v_G,t_a)
| c_Finite__Set_Ocard(c_Set_Oinsert(A,v_G,t_a),t_a) = c_HOL_Oone__class_Oone(tc_nat) ),
inference(paramod,[status(thm)],[c_828,c_8033]) ).
cnf(c_8034,plain,
( ~ c_in(A,v_G,t_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(v_G,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)),t_a),tc_nat) = c_Finite__Set_Ocard(v_G,t_a) ),
inference(resolve,[status(thm)],[c_1533,c_1249]) ).
cnf(c_8035,plain,
( ~ c_in(A,v_G,t_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(v_G,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),tc_fun(t_a,tc_bool)),t_a),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramod,[status(thm)],[c_7651,c_8034]) ).
cnf(c_7983,plain,
~ c_in(A,v_G,t_a),
inference(resolve,[status(thm)],[c_1228,c_8035]) ).
cnf(c_8018,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(A,v_G,t_a),t_a) = c_HOL_Oone__class_Oone(tc_nat),
inference(resolve,[status(thm)],[c_7983,c_7982]) ).
cnf(c_8019,plain,
$false,
inference(resolve,[status(thm)],[c_8018,c_7652]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV885-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 15:06:25 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 1538496 was started by sandbox2 on n006,
% 0.10/0.38 % Sat Sep 26 15:06:25 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.42
% 0.10/0.42 % From the command line: assign(max_seconds, 300).
% 23.20/3.44
% 23.20/3.44 % given #500 (I,wt=15): 1031 c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(10,a,2,a)].
% 23.20/3.44
% 23.20/3.44 % SZS status Unsatisfiable for theBenchmark
% 23.20/3.44
% 23.20/3.44 % Proof 1 at 2.52 (+ 0.35) seconds.
% 23.20/3.44 % Length of proof is 38.
% 23.20/3.44 % Level of proof is 8.
% 23.20/3.44 % Maximum clause weight is 43.000.
% 23.20/3.44 % Given clauses 703.
% 23.20/3.44
% 23.20/3.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------