%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT161+1 : TPTP v9.3.1. Released v5.2.0.
% 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 08:28:35 AM UTC 2026
% Result : Theorem 29.06s 4.72s
% Output : CNFRefutation 29.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 87 ( 26 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 85 ( 29 ~; 31 |; 14 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 98 ( 8 sgn 55 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [B_h] :
( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
=> c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_inj__on__def,axiom,
! [V_A_2,V_f_2,T_b,T_a] :
( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
=> ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
=> B_x = B_xa ) ) ) ),
file('theBenchmark.p',fact_inj__on__def) ).
fof(fact_inj__eq,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
=> ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_inj__eq) ).
fof(fact_finite__subset,axiom,
! [V_B_2,V_A_2,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
=> ( c_Finite__Set_Ofinite(T_a,V_B_2)
=> c_Finite__Set_Ofinite(T_a,V_A_2) ) ),
file('theBenchmark.p',fact_finite__subset) ).
fof(fact_subset__UNIV,axiom,
! [V_A_2,T_a] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))),
file('theBenchmark.p',fact_subset__UNIV) ).
fof(fact_finite__imageD,axiom,
! [V_A_2,V_f_2,T_b,T_a] :
( c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)
=> c_Finite__Set_Ofinite(T_b,V_A_2) ) ),
file('theBenchmark.p',fact_finite__imageD) ).
fof(nnf_34,plain,
? [B_h] :
( c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) = c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
& c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).
fof(sk_fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,plain,
( c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) = c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,sK0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
& c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,sK0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B_h,sK0)],[nnf_34]) ).
cnf(c_849,plain,
c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,sK0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[sk_fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).
fof(nnf_52,plain,
! [V_A_2,V_f_2,T_b,T_a] :
( ( ? [B_x] :
( ? [B_xa] :
( B_xa != B_x
& hAPP(V_f_2,B_xa) = hAPP(V_f_2,B_x)
& hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) )
& hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) )
| c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) )
& ( ! [X0] :
( ! [X1] :
( X1 = X0
| hAPP(V_f_2,X1) != hAPP(V_f_2,X0)
| ~ hBOOL(hAPP(hAPP(c_member(T_a),X1),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_a),X0),V_A_2)) )
| ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__def]) ).
fof(sk_fact_inj__on__def_sk,plain,
! [V_A_2,V_f_2,T_b,T_a] :
( ( ( sK1(V_A_2,V_f_2,T_b,T_a) != sK2(V_A_2,V_f_2,T_b,T_a)
& hAPP(V_f_2,sK1(V_A_2,V_f_2,T_b,T_a)) = hAPP(V_f_2,sK2(V_A_2,V_f_2,T_b,T_a))
& hBOOL(hAPP(hAPP(c_member(T_a),sK1(V_A_2,V_f_2,T_b,T_a)),V_A_2))
& hBOOL(hAPP(hAPP(c_member(T_a),sK2(V_A_2,V_f_2,T_b,T_a)),V_A_2)) )
| c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) )
& ( ! [X0] :
( ! [X1] :
( X1 = X0
| hAPP(V_f_2,X1) != hAPP(V_f_2,X0)
| ~ hBOOL(hAPP(hAPP(c_member(T_a),X1),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_a),X0),V_A_2)) )
| ~ c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK1]),skolemize(B_x,sK2(V_A_2,V_f_2,T_b,T_a)),skolemize(B_xa,sK1(V_A_2,V_f_2,T_b,T_a))],[nnf_52]) ).
fof(sk_fact_inj__on__def,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK1(VAR_3,VAR_2,VAR_1,VAR_0) != sK2(VAR_3,VAR_2,VAR_1,VAR_0)
| c_Fun_Oinj__on(VAR_0,VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( hAPP(VAR_2,sK1(VAR_3,VAR_2,VAR_1,VAR_0)) = hAPP(VAR_2,sK2(VAR_3,VAR_2,VAR_1,VAR_0))
| c_Fun_Oinj__on(VAR_0,VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( hBOOL(hAPP(hAPP(c_member(VAR_0),sK1(VAR_3,VAR_2,VAR_1,VAR_0)),VAR_3))
| c_Fun_Oinj__on(VAR_0,VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( hBOOL(hAPP(hAPP(c_member(VAR_0),sK2(VAR_3,VAR_2,VAR_1,VAR_0)),VAR_3))
| c_Fun_Oinj__on(VAR_0,VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( VAR_5 = VAR_4
| hAPP(VAR_2,VAR_5) != hAPP(VAR_2,VAR_4)
| ~ hBOOL(hAPP(hAPP(c_member(VAR_0),VAR_5),VAR_3))
| ~ hBOOL(hAPP(hAPP(c_member(VAR_0),VAR_4),VAR_3))
| ~ c_Fun_Oinj__on(VAR_0,VAR_1,VAR_2,VAR_3) ) ),
inference(cnf_transformation,[status(thm)],[sk_fact_inj__on__def_sk]) ).
cnf(c_886,plain,
( hAPP(C,sK1(D,C,B,A)) = hAPP(C,sK2(D,C,B,A))
| c_Fun_Oinj__on(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_fact_inj__on__def]) ).
cnf(c_887,plain,
( sK1(D,C,B,A) != sK2(D,C,B,A)
| c_Fun_Oinj__on(A,B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_fact_inj__on__def]) ).
cnf(c_893,plain,
( D = E
| hAPP(C,D) != hAPP(C,E)
| ~ c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[fact_inj__eq]) ).
cnf(c_956,plain,
( c_Finite__Set_Ofinite(A,B)
| ~ c_Finite__Set_Ofinite(A,C)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool),B),C)) ),
inference(clausify,[status(thm)],[fact_finite__subset]) ).
cnf(c_982,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool),B),c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[fact_subset__UNIV]) ).
fof(fact_finite__indi,axiom,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('theBenchmark.p',fact_finite__indi) ).
cnf(c_1001,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(clausify,[status(thm)],[fact_finite__indi]) ).
cnf(c_1003,plain,
( c_Finite__Set_Ofinite(B,D)
| ~ c_Fun_Oinj__on(B,A,C,D)
| ~ c_Finite__Set_Ofinite(A,c_Set_Oimage(B,A,C,D)) ),
inference(clausify,[status(thm)],[fact_finite__imageD]) ).
fof(fact_infinite__UNIV__nat,axiom,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('theBenchmark.p',fact_infinite__UNIV__nat) ).
cnf(c_1028,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(clausify,[status(thm)],[fact_infinite__UNIV__nat]) ).
cnf(c_2342,plain,
( A = B
| hAPP(sK0,A) != hAPP(sK0,B) ),
inference(resolve,[status(thm)],[c_893,c_849]) ).
cnf(c_3781,plain,
( sK1(C,sK0,B,A) = sK2(C,sK0,B,A)
| c_Fun_Oinj__on(A,B,sK0,C) ),
inference(resolve,[status(thm)],[c_886,c_2342]) ).
cnf(c_10970,plain,
( c_Fun_Oinj__on(A,B,sK0,C)
| c_Fun_Oinj__on(A,B,sK0,C) ),
inference(resolve,[status(thm)],[c_3781,c_887]) ).
cnf(c_4244,plain,
c_Fun_Oinj__on(A,B,sK0,C),
inference(copy,[status(thm)],[c_10970]) ).
cnf(c_10971,plain,
( c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,A)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool),A),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ),
inference(resolve,[status(thm)],[c_956,c_1001]) ).
cnf(c_8321,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,A),
inference(resolve,[status(thm)],[c_982,c_10971]) ).
cnf(c_10895,plain,
( c_Finite__Set_Ofinite(B,C)
| ~ c_Finite__Set_Ofinite(A,c_Set_Oimage(B,A,sK0,C)) ),
inference(resolve,[status(thm)],[c_1003,c_4244]) ).
cnf(c_10968,plain,
c_Finite__Set_Ofinite(A,B),
inference(resolve,[status(thm)],[c_10895,c_8321]) ).
cnf(c_10969,plain,
$false,
inference(resolve,[status(thm)],[c_10968,c_1028]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT161+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 06:37:05 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 1037322 was started by sandbox on n002,
% 0.11/0.38 % Sat Sep 26 06:37:05 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.23/0.50
% 0.23/0.50 % From the command line: assign(max_seconds, 300).
% 0.23/0.50
% 0.23/0.50 % SInE: 344 to sos, 190 to usable, of 534 axioms (tolerance 2.00, depth 0 fixpoint).
% 29.06/4.72
% 29.06/4.72 % given #500 (F,wt=41): 5627 -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_COMBI(A),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fFalse))))). [para(4847(a,2),5022(a,1,2))].
% 29.06/4.72
% 29.06/4.72 % SZS status Theorem for theBenchmark
% 29.06/4.72
% 29.06/4.72 % Proof 1 at 3.75 (+ 0.37) seconds.
% 29.06/4.72 % Length of proof is 22.
% 29.06/4.72 % Level of proof is 7.
% 29.06/4.72 % Maximum clause weight is 135.000.
% 29.06/4.72 % Given clauses 671.
% 29.06/4.72
% 29.06/4.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------