%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW337+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 09:14:06 AM UTC 2026
% Result : Theorem 80.42s 12.28s
% Output : CNFRefutation 80.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 33 ( 12 ~; 8 |; 4 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 4 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_rev__predicate1D,axiom,
! [V_Q_2,T_b,V_x_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
=> hBOOL(hAPP(V_Q_2,V_x_2)) ) ),
file('theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_mem__def,axiom,
! [V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
<=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_mem__def) ).
fof(conj_1,conjecture,
! [B_n] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) )
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) ),
file('theBenchmark.p',conj_1) ).
fof(conj_1_neg,negated_conjecture,
~ ! [B_n] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) )
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) ),
inference(assume_negation,[status(cth)],[conj_1]) ).
cnf(c_2227,plain,
( hBOOL(hAPP(D,B))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(C,tc_HOL_Obool)),A),D))
| ~ hBOOL(hAPP(A,B)) ),
inference(clausify,[status(thm)],[fact_rev__predicate1D]) ).
cnf(c_2371,plain,
( hBOOL(hAPP(C,B))
| ~ hBOOL(hAPP(hAPP(c_member(A),B),C)) ),
inference(clausify,[status(thm)],[fact_mem__def]) ).
cnf(c_2372,plain,
( ~ hBOOL(hAPP(C,B))
| hBOOL(hAPP(hAPP(c_member(A),B),C)) ),
inference(clausify,[status(thm)],[fact_mem__def]) ).
fof(conj_0,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)),
file('theBenchmark.p',conj_0) ).
cnf(c_2572,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)),
inference(clausify,[status(thm)],[conj_0]) ).
fof(nnf_917,plain,
? [B_n] :
( ? [B_x] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts)) )
& ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) ) ),
inference(fof_nnf,[status(thm)],[conj_1_neg]) ).
fof(sk_conj_1_neg,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK0,sK1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK1),v_ts))
& ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK0,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B_n,sK0),skolemize(B_x,sK1)],[nnf_917]) ).
cnf(c_2573,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,sK0,A)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),A),v_G)) ),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_2574,negated_conjecture,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK1),v_ts)),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_2575,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_27258,plain,
( hBOOL(hAPP(v_G,A))
| ~ hBOOL(hAPP(v_ts,A)) ),
inference(resolve,[status(thm)],[c_2572,c_2227]) ).
cnf(c_27287,plain,
hBOOL(hAPP(v_ts,sK1)),
inference(resolve,[status(thm)],[c_2574,c_2371]) ).
cnf(c_27334,plain,
hBOOL(hAPP(v_G,sK1)),
inference(resolve,[status(thm)],[c_27287,c_27258]) ).
cnf(c_27349,plain,
hBOOL(hAPP(hAPP(c_member(A),sK1),v_G)),
inference(resolve,[status(thm)],[c_27334,c_2372]) ).
cnf(c_27544,negated_conjecture,
c_Hoare__Mirabelle_Otriple__valid(t_a,sK0,sK1),
inference(resolve,[status(thm)],[c_27349,c_2573]) ).
cnf(c_27543,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2575,c_27544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW337+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n009.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sat Sep 26 15:41:14 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.47 % Process 536053 was started by sandbox2 on n009,
% 0.20/0.47 % Sat Sep 26 15:41:14 2026
% 0.20/0.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 80.42/12.28
% 80.42/12.28 % SInE (scan): 726 to sos (tol 1.5x), 245 to usable (tol 2.0x), 4254 zapped, of 5225 axioms (depth 3).
% 80.42/12.28
% 80.42/12.28 % From the command line: assign(max_seconds, 300).
% 80.42/12.28
% 80.42/12.28 % given #500 (F,wt=25): 18827 hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls)) != hAPP(c_Int_Onat,c_Int_OBit0(c_Int_OPls)). [para(14627(a,1),18811(a,1)),flip(a)].
% 80.42/12.28
% 80.42/12.28 % given #1000 (W,wt=26): 24232 hAPP(c_Nat_OSuc,f29(A,A)) != f29(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [para(23857(a,1),23677(a,1)),flip(a)].
% 80.42/12.28
% 80.42/12.28 % SZS status Theorem for theBenchmark
% 80.42/12.28
% 80.42/12.28 % Proof 1 at 10.20 (+ 1.21) seconds.
% 80.42/12.28 % Length of proof is 15.
% 80.42/12.28 % Level of proof is 5.
% 80.42/12.28 % Maximum clause weight is 42.000.
% 80.42/12.28 % Given clauses 1337.
% 80.42/12.28
% 80.42/12.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------