%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW312+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 : n017.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 09:14:04 AM UTC 2026
% Result : Theorem 134.39s 19.98s
% Output : CNFRefutation 134.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 9 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_hoare__derivs_Oinsert,axiom,
! [V_tsa_2,V_t_2,V_G_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2)) ) ),
file('theBenchmark.p',fact_hoare__derivs_Oinsert) ).
fof(conj_5,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
file('theBenchmark.p',conj_5) ).
fof(conj_5_neg,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
inference(assume_negation,[status(cth)],[conj_5]) ).
cnf(c_2248,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(A,B,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(A)),C),D))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(A,B,D)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(A,B,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(A)),C),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(A),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[fact_hoare__derivs_Oinsert]) ).
fof(conj_3,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
file('theBenchmark.p',conj_3) ).
cnf(c_2738,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[conj_3]) ).
fof(conj_4,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
file('theBenchmark.p',conj_4) ).
cnf(c_2739,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
inference(clausify,[status(thm)],[conj_4]) ).
cnf(c_2740,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
inference(clausify,[status(thm)],[conj_5_neg]) ).
cnf(c_2950,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),A),v_ts))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
inference(resolve,[status(thm)],[c_2248,c_2739]) ).
cnf(c_36745,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)),
inference(resolve,[status(thm)],[c_2950,c_2738]) ).
cnf(c_36744,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2740,c_36745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW312+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.40 % Computer : n017.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sat Sep 26 15:33:50 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.40 % Process 1084691 was started by sandbox2 on n017,
% 0.11/0.40 % Sat Sep 26 15:33:50 2026
% 0.11/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 134.39/19.98
% 134.39/19.98 % SInE (scan): 770 to sos (tol 1.5x), 325 to usable (tol 2.0x), 4149 zapped, of 5244 axioms (depth 3).
% 134.39/19.98
% 134.39/19.98 % From the command line: assign(max_seconds, 300).
% 134.39/19.98
% 134.39/19.98 % given #500 (F,wt=34): 14864 c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(c_Set_OCollect(B),hAPP(c_member(C),D)). [para(11856(a,1),13564(a,1))].
% 134.39/19.98
% 134.39/19.98 % given #1000 (W,wt=24): 20012 f71(hAPP(c_fequal,c_Int_OPls)) = f62(hAPP(c_Nat_OSuc,c_Int_OPls)). [resolve(19971,b,18606,a(flip)),flip(a),unit_del(a,1463)].
% 134.39/19.98
% 134.39/19.98 % given #1500 (F,wt=37): 24315 hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A) != hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls)). [para(20272(a,1),21326(a,1,1,2))].
% 134.39/19.98
% 134.39/19.98 % given #2000 (T,wt=23): 27580 f11(hAPP(c_fequal,c_fequal),A) = c_HOL_Oequal__class_Oequal(tc_Int_Oint). [resolve(26478,a,24669,a)].
% 134.39/19.98
% 134.39/19.98 % SZS status Theorem for theBenchmark
% 134.39/19.98
% 134.39/19.98 % Proof 1 at 16.37 (+ 2.71) seconds.
% 134.39/19.98 % Length of proof is 8.
% 134.39/19.98 % Level of proof is 3.
% 134.39/19.98 % Maximum clause weight is 57.000.
% 134.39/19.98 % Given clauses 2498.
% 134.39/19.98
% 134.39/19.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------