%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV906-1 : TPTP v9.3.1. Released v4.1.0.
% 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 09:09:19 AM UTC 2026
% Result : Unsatisfiable 3.61s 0.91s
% Output : CNFRefutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 27 unt; 0 def)
% Number of atoms : 54 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 20 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-3 aty)
% Number of variables : 33 ( 2 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_5,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_122,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_3,axiom,
hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_124,plain,
hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_125,plain,
c_Option_Ooption_OSome(v_y,tc_Com_Ocom) = hAPP(c_Com_Obody,v_pn),
inference(copy,[status(thm)],[c_124]) ).
fof(cls_conjecture_1,axiom,
c_Com_OWT__bodies,
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_127,plain,
c_Com_OWT__bodies,
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_128,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_MGF_0,axiom,
! [VAR_0] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(VAR_0)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,VAR_0),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
file('theBenchmark.p',cls_MGF_0) ).
cnf(c_153,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(A)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,A),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(clausify,[status(thm)],[cls_MGF_0]) ).
cnf(c_2572,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(A)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,A),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(resolve,[status(thm)],[c_127,c_153]) ).
cnf(c_154,plain,
( ~ c_Com_OWT(A)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,A),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(resolve,[status(thm)],[c_128,c_2572]) ).
fof(cls_WT_OBody_0,axiom,
! [VAR_0] :
( hAPP(c_Com_Obody,VAR_0) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(hAPP(c_Com_Ocom_OBODY,VAR_0)) ),
file('theBenchmark.p',cls_WT_OBody_0) ).
cnf(c_175,plain,
( hAPP(c_Com_Obody,A) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(hAPP(c_Com_Ocom_OBODY,A)) ),
inference(clausify,[status(thm)],[cls_WT_OBody_0]) ).
fof(cls_Option_Oset_Osimps_I2_J_0,axiom,
! [VAR_0,VAR_1] : c_Option_Oset(c_Option_Ooption_OSome(VAR_0,VAR_1),VAR_1) = c_Set_Oinsert(VAR_0,c_Orderings_Obot__class_Obot(tc_fun(VAR_1,tc_bool)),VAR_1),
file('theBenchmark.p',cls_Option_Oset_Osimps_I2_J_0) ).
cnf(c_176,plain,
c_Option_Oset(c_Option_Ooption_OSome(A,B),B) = c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),
inference(clausify,[status(thm)],[cls_Option_Oset_Osimps_I2_J_0]) ).
cnf(c_177,plain,
c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B) = c_Option_Oset(c_Option_Ooption_OSome(A,B),B),
inference(copy,[status(thm)],[c_176]) ).
fof(cls_insert__is__Un_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_Set_Oinsert(VAR_0,VAR_1,VAR_2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(VAR_0,c_Orderings_Obot__class_Obot(tc_fun(VAR_2,tc_bool)),VAR_2),VAR_1,tc_fun(VAR_2,tc_bool)),
file('theBenchmark.p',cls_insert__is__Un_0) ).
cnf(c_197,plain,
c_Set_Oinsert(A,B,C) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),B,tc_fun(C,tc_bool)),
inference(clausify,[status(thm)],[cls_insert__is__Un_0]) ).
cnf(c_198,plain,
c_Set_Oinsert(A,B,C) = c_Lattices_Oupper__semilattice__class_Osup(c_Option_Oset(c_Option_Ooption_OSome(A,C),C),B,tc_fun(C,tc_bool)),
inference(paramod,[status(thm)],[c_177,c_197]) ).
fof(cls_option_Osimps_I2_J_0,axiom,
! [VAR_0,VAR_1] : c_Option_Ooption_ONone(VAR_0) != c_Option_Ooption_OSome(VAR_1,VAR_0),
file('theBenchmark.p',cls_option_Osimps_I2_J_0) ).
cnf(c_365,plain,
c_Option_Ooption_ONone(A) != c_Option_Ooption_OSome(B,A),
inference(clausify,[status(thm)],[cls_option_Osimps_I2_J_0]) ).
cnf(c_366,plain,
c_Option_Ooption_OSome(A,B) != c_Option_Ooption_ONone(B),
inference(copy,[status(thm)],[c_365]) ).
fof(cls_Un__empty__right_0,axiom,
! [VAR_0,VAR_1] : c_Lattices_Oupper__semilattice__class_Osup(VAR_0,c_Orderings_Obot__class_Obot(tc_fun(VAR_1,tc_bool)),tc_fun(VAR_1,tc_bool)) = VAR_0,
file('theBenchmark.p',cls_Un__empty__right_0) ).
cnf(c_440,plain,
c_Lattices_Oupper__semilattice__class_Osup(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),tc_fun(B,tc_bool)) = A,
inference(clausify,[status(thm)],[cls_Un__empty__right_0]) ).
cnf(c_2573,plain,
( ~ c_Com_OWT(A)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Option_Oset(c_Option_Ooption_OSome(hAPP(c_Hoare__Mirabelle_OMGT,A),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Com_Ostate) ),
inference(paramod,[status(thm)],[c_198,c_154]) ).
cnf(c_641,plain,
( ~ c_Com_OWT(A)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Option_Oset(c_Option_Ooption_OSome(hAPP(c_Hoare__Mirabelle_OMGT,A),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(paramod,[status(thm)],[c_440,c_2573]) ).
cnf(c_2574,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Option_Oset(c_Option_Ooption_OSome(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Com_Ostate),
inference(paramod,[status(thm)],[c_198,c_122]) ).
cnf(c_648,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Option_Oset(c_Option_Ooption_OSome(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(paramod,[status(thm)],[c_440,c_2574]) ).
cnf(c_2575,plain,
( c_Option_Ooption_OSome(v_y,tc_Com_Ocom) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn)) ),
inference(paramod,[status(thm)],[c_175,c_125]) ).
cnf(c_2576,plain,
( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn)) ),
inference(paramod,[status(thm)],[c_125,c_2575]) ).
cnf(c_789,plain,
( c_Option_Ooption_ONone(tc_Com_Ocom) = hAPP(c_Com_Obody,v_pn)
| c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn)) ),
inference(copy,[status(thm)],[c_2576]) ).
cnf(c_2577,plain,
hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_ONone(tc_Com_Ocom),
inference(paramod,[status(thm)],[c_125,c_366]) ).
cnf(c_1332,plain,
c_Option_Ooption_ONone(tc_Com_Ocom) != hAPP(c_Com_Obody,v_pn),
inference(copy,[status(thm)],[c_2577]) ).
cnf(c_1340,plain,
c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_pn)),
inference(resolve,[status(thm)],[c_1332,c_789]) ).
cnf(c_2578,plain,
c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Option_Oset(c_Option_Ooption_OSome(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(resolve,[status(thm)],[c_1340,c_641]) ).
cnf(c_2571,plain,
$false,
inference(resolve,[status(thm)],[c_648,c_2578]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV906-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 15:06:24 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 4032526 was started by sandbox on n007,
% 0.08/0.36 % Sat Sep 26 15:06:24 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 3.61/0.91
% 3.61/0.91 % SZS status Unsatisfiable for theBenchmark
% 3.61/0.91
% 3.61/0.91 % Proof 1 at 0.42 (+ 0.10) seconds.
% 3.61/0.91 % Length of proof is 21.
% 3.61/0.91 % Level of proof is 4.
% 3.61/0.91 % Maximum clause weight is 32.000.
% 3.61/0.91 % Given clauses 479.
% 3.61/0.91
% 3.61/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------