%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW390+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 : n001.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 09:14:10 AM UTC 2026
% Result : Theorem 2.81s 0.95s
% Output : CNFRefutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 14 unt; 0 def)
% Number of atoms : 18 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 40 ( 15 sgn 7 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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_falseE,axiom,
! [V_Q_2,V_ca_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
file('theBenchmark.p',fact_falseE) ).
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,
( ? [B_Z,B_x1] : v_P(B_Z,B_x1)
=> ? [B_P_H,B_Q_H] : 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),B_P_H),v_c),B_Q_H)),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,
~ ( ? [B_Z,B_x1] : v_P(B_Z,B_x1)
=> ? [B_P_H,B_Q_H] : 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),B_P_H),v_c),B_Q_H)),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_1798,plain,
c_Hoare__Mirabelle_Ohoare__derivs(A,B,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(A)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(A),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),A),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),C),D)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(A),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[fact_falseE]) ).
cnf(c_2053,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_2054,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_2053]) ).
cnf(c_2675,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_2692,negated_conjecture,
~ 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),A),v_c),B)),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_2693,negated_conjecture,
~ 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),A),v_c),B)),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_2675,c_2692]) ).
cnf(c_2798,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_2675,c_2054]) ).
cnf(c_2940,plain,
c_Hoare__Mirabelle_Ohoare__derivs(A,B,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(A)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(A),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),A),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),C),D)),hAPP(c_List_Oset(tc_Hoare__Mirabelle_Otriple(A)),c_List_Olist_ONil(tc_Hoare__Mirabelle_Otriple(A))))),
inference(paramod,[status(thm)],[c_2675,c_1798]) ).
cnf(c_2846,plain,
c_Hoare__Mirabelle_Ohoare__derivs(A,B,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(A)),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(A),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),A),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),C),D)))),
inference(paramod,[status(thm)],[c_2798,c_2940]) ).
cnf(c_2938,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),A),v_c),B)))),
inference(paramod,[status(thm)],[c_2798,c_2693]) ).
cnf(c_2939,plain,
$false,
inference(resolve,[status(thm)],[c_2938,c_2846]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW390+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.41 % Computer : n001.cluster.edu
% 0.10/0.41 % Model : x86_64 x86_64
% 0.10/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.41 % Memory : 8046.5625MB
% 0.10/0.41 % OS : Linux 6.8.0-71-generic
% 0.10/0.41 % CPULimit : 300
% 0.10/0.41 % WCLimit : 300
% 0.10/0.41 % DateTime : Sat Sep 26 15:53:28 UTC 2026
% 0.10/0.42 % CPUTime :
% 0.10/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.42 % Process 2134441 was started by sandbox on n001,
% 0.10/0.42 % Sat Sep 26 15:53:28 2026
% 0.10/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 2.81/0.95
% 2.81/0.95 % SInE (scan): 749 to sos (tol 1.5x), 309 to usable (tol 2.0x), 4169 zapped, of 5227 axioms (depth 3).
% 2.81/0.95
% 2.81/0.95 % From the command line: assign(max_seconds, 300).
% 2.81/0.95
% 2.81/0.95 % SZS status Theorem for theBenchmark
% 2.81/0.95
% 2.81/0.95 % Proof 1 at 0.22 (+ 0.10) seconds.
% 2.81/0.95 % Length of proof is 14.
% 2.81/0.95 % Level of proof is 5.
% 2.81/0.95 % Maximum clause weight is 110.000.
% 2.81/0.95 % Given clauses 0.
% 2.81/0.95
% 2.81/0.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------