%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW312+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 : Thu Sep 24 09:06:14 AM UTC 2026
% Result : Theorem 31.43s 42.03s
% Output : Proof 31.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 18 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 10 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 20 ( 0 sgn 16 !; 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_3,hypothesis,
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) ).
fof(conj_4,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
file('theBenchmark.p',conj_4) ).
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(f_7_1,plain,
! [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),V_tsa_2))
| ~ 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),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oinsert]) ).
fof(f_7_2,plain,
! [U_21,U_20,U_19,U_18] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_18,U_19,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_18)),U_20),U_21))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_18,U_19,U_21)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_18,U_19,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_18)),U_20),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_18),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_18,U_20,U_21,U_19] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_18,U_19,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_18)),U_20),U_21))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_18,U_19,U_21)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_18,U_19,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_18)),U_20),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_18),tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_18,U_19,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_18)),U_20),U_21))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_18,U_19,U_21)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_18,U_19,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_18)),U_20),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_18),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_5243_1,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(fof_nnf,[status(thm)],[conj_3]) ).
fof(f_5243_2,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(definitional_conversion,[status(esa)],[f_5243_1]) ).
cnf(f_5243_3,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)],[f_5243_2]) ).
fof(f_5244_1,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
inference(fof_nnf,[status(thm)],[conj_4]) ).
fof(f_5244_2,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
inference(definitional_conversion,[status(esa)],[f_5244_1]) ).
cnf(f_5244_3,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
inference(clausify,[status(thm)],[f_5244_2]) ).
fof(f_5245_1,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(negate,[status(cth)],[conj_5]) ).
fof(f_5245_2,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(definitional_conversion,[status(esa)],[f_5245_1]) ).
cnf(f_5245_3,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)],[f_5245_2]) ).
cnf(t1,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(start,[status(thm),parent(0:0)],[f_5245_3]) ).
cnf(t2,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)
| ~ 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))))
| 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(extension,[status(thm),parent(t1:1)],[f_7_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,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(extension,[status(thm),parent(t2:2)],[f_5243_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
inference(extension,[status(thm),parent(t2:3)],[f_5244_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW312+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 This is a FOF_CAX_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.60 % Computer : n006.cluster.edu
% 0.09/10.60 % Model : x86_64 x86_64
% 0.09/10.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.60 % Memory : 8046.5625MB
% 0.09/10.60 % OS : Linux 6.8.0-71-generic
% 0.09/10.60 % CPULimit : 300
% 0.09/10.60 % WCLimit : 300
% 0.09/10.60 % DateTime : Sun Sep 20 05:21:09 UTC 2026
% 0.09/10.60 % CPUTime :
% 31.43/42.03 % SZS status Theorem for theBenchmark
% 31.43/42.03 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------