%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW298+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 : n003.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 09:14:03 AM UTC 2026
% Result : Theorem 251.28s 37.24s
% Output : CNFRefutation 251.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 6 ~; 2 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 6 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_triple__valid__Suc,axiom,
! [V_t,V_n,T_a] :
( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
=> c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ),
file('theBenchmark.p',fact_triple__valid__Suc) ).
fof(conj_0,axiom,
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),B_x) ),
file('theBenchmark.p',conj_0) ).
fof(conj_1,conjecture,
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x) ),
file('theBenchmark.p',conj_1) ).
fof(conj_1_neg,negated_conjecture,
~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x) ),
inference(assume_negation,[status(cth)],[conj_1]) ).
cnf(c_2824,plain,
( c_Hoare__Mirabelle_Otriple__valid(A,B,C)
| ~ c_Hoare__Mirabelle_Otriple__valid(A,hAPP(c_Nat_OSuc,B),C) ),
inference(clausify,[status(thm)],[fact_triple__valid__Suc]) ).
cnf(c_3798,plain,
( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),A)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),A),v_ts)) ),
inference(clausify,[status(thm)],[conj_0]) ).
fof(nnf_1366,plain,
? [B_x] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts)) ),
inference(fof_nnf,[status(thm)],[conj_1_neg]) ).
fof(sk_conj_1_neg,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK0)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0),v_ts)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B_x,sK0)],[nnf_1366]) ).
cnf(c_3799,negated_conjecture,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK0),v_ts)),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_3800,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK0),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_65778,plain,
c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),sK0),
inference(resolve,[status(thm)],[c_3799,c_3798]) ).
cnf(c_65975,plain,
c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK0),
inference(resolve,[status(thm)],[c_65778,c_2824]) ).
cnf(c_65974,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_3800,c_65975]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW298+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 15:39:11 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 3216973 was started by sandbox on n003,
% 0.12/0.37 % Sat Sep 26 15:39:11 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 251.28/37.24
% 251.28/37.24 % SInE (scan): 1142 to sos (tol 1.5x), 285 to usable (tol 2.0x), 3797 zapped, of 5224 axioms (depth 3).
% 251.28/37.24
% 251.28/37.24 % From the command line: assign(max_seconds, 300).
% 251.28/37.24
% 251.28/37.24 % given #500 (F,wt=35): 6728 hAPP(c_Set_OCollect(A),hAPP(c_Set_OCollect(B),c_Set_OCollect(C))) != hAPP(c_Nat_OSuc,c_Set_OCollect(D)). [para(6588(a,1),6329(a,2))].
% 251.28/37.24
% 251.28/37.24 % given #1000 (W,wt=28): 23536 hBOOL(hAPP(c_Int_Onat,c_Int_OBit1(c_Int_OPls))) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),f10(c_Int_OPls,c_Nat_OSuc)) = c_Int_OPls. [para(22974(a,1),3010(a,1)),unit_del(c,3467)].
% 251.28/37.24
% 251.28/37.24 % given #1500 (F,wt=30): 27824 f50(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != f3(c_Groups_Oone__class_Oone(tc_Nat_Onat)). [para(22627(a,1),27821(a,2))].
% 251.28/37.24
% 251.28/37.24 % given #2000 (T,wt=29): 32226 -hBOOL(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_Set_OCollect(A),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,B))). [para(29427(a,1),32156(a,1))].
% 251.28/37.24
% 251.28/37.24 % given #2500 (F,wt=25): 43719 c_Int_OBit0(c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,A)) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [para(3449(a,1),42799(a,2,2))].
% 251.28/37.24
% 251.28/37.24 % given #3000 (T,wt=24): 62859 hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Int_OPls) = f3(hAPP(c_Nat_OSuc,c_Int_OPls)). [para(49300(a,1),37479(a,1))].
% 251.28/37.24
% 251.28/37.24 % SZS status Theorem for theBenchmark
% 251.28/37.24
% 251.28/37.24 % Proof 1 at 30.36 (+ 5.17) seconds.
% 251.28/37.24 % Length of proof is 9.
% 251.28/37.24 % Level of proof is 3.
% 251.28/37.24 % Maximum clause weight is 41.000.
% 251.28/37.24 % Given clauses 3038.
% 251.28/37.24
% 251.28/37.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------