%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW318+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 : n013.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 209.05s 209.33s
% Output : Proof 209.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 19 unt; 0 def)
% Number of atoms : 37 ( 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 : 8 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 35 ( 1 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_subset__insertI,axiom,
! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
file('theBenchmark.p',fact_subset__insertI) ).
fof(fact_thin,axiom,
! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ),
file('theBenchmark.p',fact_thin) ).
fof(conj_0,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
file('theBenchmark.p',conj_0) ).
fof(conj_1,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
file('theBenchmark.p',conj_1) ).
fof(f_700_1,plain,
! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_subset__insertI]) ).
fof(f_700_2,plain,
! [U_2555,U_2554,U_2553] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2553,tc_HOL_Obool)),U_2554),hAPP(hAPP(c_Set_Oinsert(U_2553),U_2555),U_2554))),
inference(variable_rename,[status(thm)],[f_700_1]) ).
fof(f_700_3,plain,
! [U_2553,U_2554,U_2555] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2553,tc_HOL_Obool)),U_2554),hAPP(hAPP(c_Set_Oinsert(U_2553),U_2555),U_2554))),
inference(definitional_conversion,[status(esa)],[f_700_2]) ).
cnf(f_700_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2553,tc_HOL_Obool)),U_2554),hAPP(hAPP(c_Set_Oinsert(U_2553),U_2555),U_2554))),
inference(clausify,[status(thm)],[f_700_3]) ).
fof(f_738_1,plain,
! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) ),
inference(fof_nnf,[status(thm)],[fact_thin]) ).
fof(f_738_2,plain,
! [U_2688,U_2687,U_2686,U_2685] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_2685,U_2688,U_2687)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_2685),tc_HOL_Obool)),U_2686),U_2688))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_2685,U_2686,U_2687) ),
inference(variable_rename,[status(thm)],[f_738_1]) ).
fof(f_738_3,plain,
! [U_2685,U_2686,U_2687,U_2688] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_2685,U_2688,U_2687)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_2685),tc_HOL_Obool)),U_2686),U_2688))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_2685,U_2686,U_2687) ),
inference(definitional_conversion,[status(esa)],[f_738_2]) ).
cnf(f_738_4,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_2685,U_2688,U_2687)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_2685),tc_HOL_Obool)),U_2686),U_2688))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_2685,U_2686,U_2687) ),
inference(clausify,[status(thm)],[f_738_3]) ).
fof(f_5225_1,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[conj_0]) ).
fof(f_5225_2,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_5225_1]) ).
cnf(f_5225_3,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_5225_2]) ).
fof(f_5226_1,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(negate,[status(cth)],[conj_1]) ).
fof(f_5226_2,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_5226_1]) ).
cnf(f_5226_3,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_5226_2]) ).
cnf(t1,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(start,[status(thm),parent(0:0)],[f_5226_3]) ).
cnf(t2,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
inference(extension,[status(thm),parent(t1:1)],[f_738_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_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(extension,[status(thm),parent(t2:2)],[f_5225_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G))),
inference(extension,[status(thm),parent(t2:3)],[f_700_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW318+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 This is a FOF_CAX_RFO_SEQ problem
% 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 05:21:22 UTC 2026
% 0.11/0.38 % CPUTime :
% 209.05/209.33 % SZS status Theorem for theBenchmark
% 209.05/209.33 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------