%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW394+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 : n007.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 09:14:11 AM UTC 2026
% Result : Theorem 21.72s 3.66s
% Output : CNFRefutation 21.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 17 unt; 0 def)
% Number of atoms : 21 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 7 ~; 1 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_asm,axiom,
! [V_G_2,V_ts_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_G_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_2) ),
file('theBenchmark.p',fact_asm) ).
fof(fact_List_Oset_Osimps_I1_J,axiom,
! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).
fof(fact_subset__refl,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)),
file('theBenchmark.p',fact_subset__refl) ).
fof(fact_singleton__conv2,axiom,
! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
file('theBenchmark.p',fact_singleton__conv2) ).
fof(conj_0,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,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))),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_0) ).
fof(conj_0_neg,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,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))),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(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_970,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),B),B)),
inference(clausify,[status(thm)],[fact_subset__refl]) ).
cnf(c_1979,plain,
hAPP(c_Set_OCollect(A),hAPP(c_fequal,B)) = hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))),
inference(clausify,[status(thm)],[fact_singleton__conv2]) ).
cnf(c_1980,plain,
hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))) = hAPP(c_Set_OCollect(A),hAPP(c_fequal,B)),
inference(copy,[status(thm)],[c_1979]) ).
cnf(c_2287,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(A,C,B)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(A),tc_HOL_Obool)),B),C)) ),
inference(clausify,[status(thm)],[fact_asm]) ).
cnf(c_2591,plain,
c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(c_List_Oset(A),c_List_Olist_ONil(A)),
inference(clausify,[status(thm)],[fact_List_Oset_Osimps_I1_J]) ).
cnf(c_2604,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,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))),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_0_neg]) ).
cnf(c_8035,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),hAPP(c_List_Oset(tc_Hoare__Mirabelle_Otriple(t_a)),c_List_Olist_ONil(tc_Hoare__Mirabelle_Otriple(t_a)))),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(paramod,[status(thm)],[c_2591,c_2604]) ).
cnf(c_2605,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),hAPP(c_List_Oset(tc_Hoare__Mirabelle_Otriple(t_a)),c_List_Olist_ONil(tc_Hoare__Mirabelle_Otriple(t_a)))),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),hAPP(c_List_Oset(tc_Hoare__Mirabelle_Otriple(t_a)),c_List_Olist_ONil(tc_Hoare__Mirabelle_Otriple(t_a))))),
inference(paramod,[status(thm)],[c_2591,c_8035]) ).
cnf(c_2695,plain,
hAPP(hAPP(c_Set_Oinsert(A),B),hAPP(c_List_Oset(A),c_List_Olist_ONil(A))) = hAPP(c_Set_OCollect(A),hAPP(c_fequal,B)),
inference(paramod,[status(thm)],[c_2591,c_1980]) ).
cnf(c_8036,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,v_t)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),hAPP(c_List_Oset(tc_Hoare__Mirabelle_Otriple(t_a)),c_List_Olist_ONil(tc_Hoare__Mirabelle_Otriple(t_a))))),
inference(paramod,[status(thm)],[c_2695,c_2605]) ).
cnf(c_2811,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,v_t)),hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,v_t))),
inference(paramod,[status(thm)],[c_2695,c_8036]) ).
cnf(c_8033,plain,
c_Hoare__Mirabelle_Ohoare__derivs(A,B,B),
inference(resolve,[status(thm)],[c_2287,c_970]) ).
cnf(c_8034,plain,
$false,
inference(resolve,[status(thm)],[c_8033,c_2811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW394+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n007.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 26 15:46:24 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 4098676 was started by sandbox on n007,
% 0.09/0.38 % Sat Sep 26 15:46:24 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 21.72/3.66
% 21.72/3.66 % SInE (scan): 723 to sos (tol 1.5x), 297 to usable (tol 2.0x), 4203 zapped, of 5223 axioms (depth 3).
% 21.72/3.66
% 21.72/3.66 % From the command line: assign(max_seconds, 300).
% 21.72/3.66
% 21.72/3.66 % SZS status Theorem for theBenchmark
% 21.72/3.66
% 21.72/3.66 % Proof 1 at 2.58 (+ 0.48) seconds.
% 21.72/3.66 % Length of proof is 16.
% 21.72/3.66 % Level of proof is 5.
% 21.72/3.66 % Maximum clause weight is 125.000.
% 21.72/3.66 % Given clauses 326.
% 21.72/3.66
% 21.72/3.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------