%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV886-1 : 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 : n012.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 2.50s 0.73s
% Output : CNFRefutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 39 ( 27 unt; 0 def)
% Number of atoms : 57 ( 35 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 21 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 34 ( 5 sgn 14 !; 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_225,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_226,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_225]) ).
fof(cls_conjecture_5,axiom,
c_Finite__Set_Ofinite(v_G,t_a),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_227,plain,
c_Finite__Set_Ofinite(v_G,t_a),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_4,axiom,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_228,plain,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_2,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_2) ).
cnf(c_230,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_2]) ).
cnf(c_231,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_230]) ).
fof(cls_conjecture_1,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_1) ).
cnf(c_232,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_1]) ).
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_256,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_Suc__diff__le_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_lessequals(VAR_1,VAR_0,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(VAR_0),VAR_1,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(VAR_0,VAR_1,tc_nat)) ),
file('theBenchmark.p',cls_Suc__diff__le_0) ).
cnf(c_263,plain,
( ~ c_lessequals(B,A,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(A),B,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(A,B,tc_nat)) ),
inference(clausify,[status(thm)],[cls_Suc__diff__le_0]) ).
fof(cls_diff__Suc__Suc_0,axiom,
! [VAR_0,VAR_1] : c_HOL_Ominus__class_Ominus(c_Suc(VAR_0),c_Suc(VAR_1),tc_nat) = c_HOL_Ominus__class_Ominus(VAR_0,VAR_1,tc_nat),
file('theBenchmark.p',cls_diff__Suc__Suc_0) ).
cnf(c_268,plain,
c_HOL_Ominus__class_Ominus(c_Suc(A),c_Suc(B),tc_nat) = c_HOL_Ominus__class_Ominus(A,B,tc_nat),
inference(clausify,[status(thm)],[cls_diff__Suc__Suc_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_291,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_301,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_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_533,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(A),
inference(clausify,[status(thm)],[cls_nat_Osimps_I2_J_0]) ).
cnf(c_534,plain,
c_Suc(A) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(copy,[status(thm)],[c_533]) ).
cnf(c_788,plain,
( c_in(A,v_G,t_a)
| c_Finite__Set_Ocard(c_Set_Oinsert(A,v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ),
inference(resolve,[status(thm)],[c_256,c_227]) ).
cnf(c_985,plain,
c_HOL_Ominus__class_Ominus(c_Suc(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_Suc(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(resolve,[status(thm)],[c_263,c_232]) ).
cnf(c_986,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_Suc(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(paramod,[status(thm)],[c_268,c_985]) ).
cnf(c_800,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_Suc(c_Finite__Set_Ocard(v_G,t_a)),
inference(paramod,[status(thm)],[c_231,c_986]) ).
cnf(c_987,plain,
c_Suc(c_Finite__Set_Ocard(v_G,t_a)) != c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a),
inference(paramod,[status(thm)],[c_800,c_226]) ).
cnf(c_802,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_Suc(c_Finite__Set_Ocard(v_G,t_a)),
inference(copy,[status(thm)],[c_987]) ).
cnf(c_988,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_Suc(c_Finite__Set_Ocard(v_G,t_a)) ),
inference(resolve,[status(thm)],[c_291,c_228]) ).
cnf(c_989,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(v_G,t_a)
| c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)) ),
inference(copy,[status(thm)],[c_988]) ).
cnf(c_854,plain,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(v_G,t_a),
inference(resolve,[status(thm)],[c_802,c_989]) ).
cnf(c_906,plain,
c_Suc(A) != c_Finite__Set_Ocard(v_G,t_a),
inference(paramod,[status(thm)],[c_854,c_534]) ).
cnf(c_990,plain,
( ~ c_in(A,v_G,t_a)
| c_Suc(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)) = c_Finite__Set_Ocard(v_G,t_a) ),
inference(resolve,[status(thm)],[c_301,c_227]) ).
cnf(c_982,plain,
~ c_in(A,v_G,t_a),
inference(resolve,[status(thm)],[c_906,c_990]) ).
cnf(c_983,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(A,v_G,t_a),t_a) = c_Suc(c_Finite__Set_Ocard(v_G,t_a)),
inference(resolve,[status(thm)],[c_982,c_788]) ).
cnf(c_984,plain,
$false,
inference(resolve,[status(thm)],[c_983,c_802]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV886-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n012.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 15:06:34 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 886654 was started by sandbox on n012,
% 0.07/0.34 % Sat Sep 26 15:06:34 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 2.50/0.73
% 2.50/0.73 % SZS status Unsatisfiable for theBenchmark
% 2.50/0.73
% 2.50/0.73 % Proof 1 at 0.33 (+ 0.03) seconds.
% 2.50/0.73 % Length of proof is 22.
% 2.50/0.73 % Level of proof is 8.
% 2.50/0.73 % Maximum clause weight is 61.000.
% 2.50/0.73 % Given clauses 125.
% 2.50/0.73
% 2.50/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------