%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWW470+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 03:12:25 PM UTC 2026
% Result : Theorem 161.39s 24.51s
% Output : CNFRefutation 161.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 34 unt; 0 def)
% Number of atoms : 55 ( 23 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 29 ( 13 ~; 9 |; 3 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 11 con; 0-7 aty)
% Number of variables : 90 ( 2 sgn 51 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_12_singleton__conv2,axiom,
! [X1,X26] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(X1,fun(X1,bool),fequal(X1),X26)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X26),bot_bot(fun(X1,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_singleton__conv2) ).
fof(fact_77_Collect__def,axiom,
! [X1,X16] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16) = ti(fun(X1,bool),X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def) ).
fof(tsy_c_hAPP_res,axiom,
! [X2,X3,X4,X5] : ti(X2,hAPP(X3,X2,X4,X5)) = hAPP(X3,X2,X4,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(fact_23_empty__def,axiom,
! [X1] : bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(bool,fun(X1,bool),combk(bool,X1),fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_empty__def) ).
fof(fact_62_conseq,axiom,
! [X1,X18,X6,X17,X16] :
( ! [X20,X21] :
( hBOOL(hAPP(state,bool,hAPP(X1,fun(state,bool),X16,X20),X21))
=> ? [X49,X50] :
( ! [X24] :
( ! [X25] :
( hBOOL(hAPP(state,bool,hAPP(X1,fun(state,bool),X49,X25),X21))
=> hBOOL(hAPP(state,bool,hAPP(X1,fun(state,bool),X50,X25),X24)) )
=> hBOOL(hAPP(state,bool,hAPP(X1,fun(state,bool),X18,X20),X24)) )
& hBOOL(hAPP(fun(hoare_509422987triple(X1),bool),bool,hAPP(fun(hoare_509422987triple(X1),bool),fun(fun(hoare_509422987triple(X1),bool),bool),hoare_122391849derivs(X1),X6),hAPP(fun(hoare_509422987triple(X1),bool),fun(hoare_509422987triple(X1),bool),hAPP(hoare_509422987triple(X1),fun(fun(hoare_509422987triple(X1),bool),fun(hoare_509422987triple(X1),bool)),insert(hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),hoare_509422987triple(X1),hAPP(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1))),hoare_1008221573triple(X1),X49),X17),X50)),bot_bot(fun(hoare_509422987triple(X1),bool))))) ) )
=> hBOOL(hAPP(fun(hoare_509422987triple(X1),bool),bool,hAPP(fun(hoare_509422987triple(X1),bool),fun(fun(hoare_509422987triple(X1),bool),bool),hoare_122391849derivs(X1),X6),hAPP(fun(hoare_509422987triple(X1),bool),fun(hoare_509422987triple(X1),bool),hAPP(hoare_509422987triple(X1),fun(fun(hoare_509422987triple(X1),bool),fun(hoare_509422987triple(X1),bool)),insert(hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),hoare_509422987triple(X1),hAPP(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1))),hoare_1008221573triple(X1),X16),X17),X18)),bot_bot(fun(hoare_509422987triple(X1),bool))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_conseq) ).
fof(help_COMBK_1_1_U,axiom,
! [X1,X3,X65,X66] : hAPP(X1,X3,hAPP(X3,fun(X1,X3),combk(X3,X1),X65),X66) = ti(X3,X65),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
fof(tsy_c_hAPP_arg1,axiom,
! [X3,X2,X4,X5] : hAPP(X3,X2,ti(fun(X3,X2),X4),X5) = hAPP(X3,X2,X4,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(tsy_c_fFalse_res,hypothesis,
ti(bool,fFalse) = fFalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fFalse_res) ).
fof(c_0_10,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_11,plain,
! [X254,X255] : hAPP(fun(X254,bool),fun(X254,bool),collect(X254),hAPP(X254,fun(X254,bool),fequal(X254),X255)) = hAPP(fun(X254,bool),fun(X254,bool),hAPP(X254,fun(fun(X254,bool),fun(X254,bool)),insert(X254),X255),bot_bot(fun(X254,bool))),
inference(variable_rename,[status(thm)],[fact_12_singleton__conv2]) ).
fof(c_0_12,plain,
! [X268,X269] : hAPP(fun(X268,bool),fun(X268,bool),collect(X268),X269) = ti(fun(X268,bool),X269),
inference(variable_rename,[status(thm)],[fact_77_Collect__def]) ).
fof(c_0_13,plain,
! [X80,X81,X82,X83] : ti(X80,hAPP(X81,X80,X82,X83)) = hAPP(X81,X80,X82,X83),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).
fof(c_0_14,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X71] : bot_bot(fun(X71,bool)) = hAPP(fun(X71,bool),fun(X71,bool),collect(X71),hAPP(bool,fun(X71,bool),combk(bool,X71),fFalse)),
inference(variable_rename,[status(thm)],[fact_23_empty__def]) ).
fof(c_0_16,plain,
! [X161,X162,X163,X164,X165,X168,X169,X171] :
( ( hBOOL(hAPP(fun(hoare_509422987triple(X161),bool),bool,hAPP(fun(hoare_509422987triple(X161),bool),fun(fun(hoare_509422987triple(X161),bool),bool),hoare_122391849derivs(X161),X163),hAPP(fun(hoare_509422987triple(X161),bool),fun(hoare_509422987triple(X161),bool),hAPP(hoare_509422987triple(X161),fun(fun(hoare_509422987triple(X161),bool),fun(hoare_509422987triple(X161),bool)),insert(hoare_509422987triple(X161)),hAPP(fun(X161,fun(state,bool)),hoare_509422987triple(X161),hAPP(com,fun(fun(X161,fun(state,bool)),hoare_509422987triple(X161)),hAPP(fun(X161,fun(state,bool)),fun(com,fun(fun(X161,fun(state,bool)),hoare_509422987triple(X161))),hoare_1008221573triple(X161),X165),X164),X162)),bot_bot(fun(hoare_509422987triple(X161),bool)))))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X161),bool),bool,hAPP(fun(hoare_509422987triple(X161),bool),fun(fun(hoare_509422987triple(X161),bool),bool),hoare_122391849derivs(X161),X163),hAPP(fun(hoare_509422987triple(X161),bool),fun(hoare_509422987triple(X161),bool),hAPP(hoare_509422987triple(X161),fun(fun(hoare_509422987triple(X161),bool),fun(hoare_509422987triple(X161),bool)),insert(hoare_509422987triple(X161)),hAPP(fun(X161,fun(state,bool)),hoare_509422987triple(X161),hAPP(com,fun(fun(X161,fun(state,bool)),hoare_509422987triple(X161)),hAPP(fun(X161,fun(state,bool)),fun(com,fun(fun(X161,fun(state,bool)),hoare_509422987triple(X161))),hoare_1008221573triple(X161),X168),X164),X169)),bot_bot(fun(hoare_509422987triple(X161),bool)))))
| ~ hBOOL(hAPP(state,bool,hAPP(X161,fun(state,bool),X162,esk12_5(X161,X162,X163,X164,X165)),esk14_7(X161,X162,X163,X164,X165,X168,X169))) )
& ( hBOOL(hAPP(fun(hoare_509422987triple(X161),bool),bool,hAPP(fun(hoare_509422987triple(X161),bool),fun(fun(hoare_509422987triple(X161),bool),bool),hoare_122391849derivs(X161),X163),hAPP(fun(hoare_509422987triple(X161),bool),fun(hoare_509422987triple(X161),bool),hAPP(hoare_509422987triple(X161),fun(fun(hoare_509422987triple(X161),bool),fun(hoare_509422987triple(X161),bool)),insert(hoare_509422987triple(X161)),hAPP(fun(X161,fun(state,bool)),hoare_509422987triple(X161),hAPP(com,fun(fun(X161,fun(state,bool)),hoare_509422987triple(X161)),hAPP(fun(X161,fun(state,bool)),fun(com,fun(fun(X161,fun(state,bool)),hoare_509422987triple(X161))),hoare_1008221573triple(X161),X165),X164),X162)),bot_bot(fun(hoare_509422987triple(X161),bool)))))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X161),bool),bool,hAPP(fun(hoare_509422987triple(X161),bool),fun(fun(hoare_509422987triple(X161),bool),bool),hoare_122391849derivs(X161),X163),hAPP(fun(hoare_509422987triple(X161),bool),fun(hoare_509422987triple(X161),bool),hAPP(hoare_509422987triple(X161),fun(fun(hoare_509422987triple(X161),bool),fun(hoare_509422987triple(X161),bool)),insert(hoare_509422987triple(X161)),hAPP(fun(X161,fun(state,bool)),hoare_509422987triple(X161),hAPP(com,fun(fun(X161,fun(state,bool)),hoare_509422987triple(X161)),hAPP(fun(X161,fun(state,bool)),fun(com,fun(fun(X161,fun(state,bool)),hoare_509422987triple(X161))),hoare_1008221573triple(X161),X168),X164),X169)),bot_bot(fun(hoare_509422987triple(X161),bool)))))
| hBOOL(hAPP(state,bool,hAPP(X161,fun(state,bool),X169,X171),esk14_7(X161,X162,X163,X164,X165,X168,X169)))
| ~ hBOOL(hAPP(state,bool,hAPP(X161,fun(state,bool),X168,X171),esk13_5(X161,X162,X163,X164,X165))) )
& ( hBOOL(hAPP(fun(hoare_509422987triple(X161),bool),bool,hAPP(fun(hoare_509422987triple(X161),bool),fun(fun(hoare_509422987triple(X161),bool),bool),hoare_122391849derivs(X161),X163),hAPP(fun(hoare_509422987triple(X161),bool),fun(hoare_509422987triple(X161),bool),hAPP(hoare_509422987triple(X161),fun(fun(hoare_509422987triple(X161),bool),fun(hoare_509422987triple(X161),bool)),insert(hoare_509422987triple(X161)),hAPP(fun(X161,fun(state,bool)),hoare_509422987triple(X161),hAPP(com,fun(fun(X161,fun(state,bool)),hoare_509422987triple(X161)),hAPP(fun(X161,fun(state,bool)),fun(com,fun(fun(X161,fun(state,bool)),hoare_509422987triple(X161))),hoare_1008221573triple(X161),X165),X164),X162)),bot_bot(fun(hoare_509422987triple(X161),bool)))))
| hBOOL(hAPP(state,bool,hAPP(X161,fun(state,bool),X165,esk12_5(X161,X162,X163,X164,X165)),esk13_5(X161,X162,X163,X164,X165))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_62_conseq])])])])])]) ).
cnf(c_0_17,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(X1,fun(X1,bool),fequal(X1),X2)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(bool,fun(X1,bool),combk(bool,X1),fFalse)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(X1),bool),bool,hAPP(fun(hoare_509422987triple(X1),bool),fun(fun(hoare_509422987triple(X1),bool),bool),hoare_122391849derivs(X1),X4),hAPP(fun(hoare_509422987triple(X1),bool),fun(hoare_509422987triple(X1),bool),hAPP(hoare_509422987triple(X1),fun(fun(hoare_509422987triple(X1),bool),fun(hoare_509422987triple(X1),bool)),insert(hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),hoare_509422987triple(X1),hAPP(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1))),hoare_1008221573triple(X1),X2),X5),X3)),bot_bot(fun(hoare_509422987triple(X1),bool)))))
| hBOOL(hAPP(state,bool,hAPP(X1,fun(state,bool),X2,esk12_5(X1,X3,X4,X5,X2)),esk13_5(X1,X3,X4,X5,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))) = hAPP(X1,fun(X1,bool),fequal(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
fof(c_0_24,plain,
! [X226,X227,X228,X229] : hAPP(X226,X227,hAPP(X227,fun(X226,X227),combk(X227,X226),X228),X229) = ti(X227,X228),
inference(variable_rename,[status(thm)],[help_COMBK_1_1_U]) ).
fof(c_0_25,plain,
! [X72,X73,X74,X75] : hAPP(X72,X73,ti(fun(X72,X73),X74),X75) = hAPP(X72,X73,X74,X75),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg1]) ).
fof(c_0_26,plain,
~ hBOOL(fFalse),
inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).
cnf(c_0_27,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
hAPP(bool,fun(X1,bool),combk(bool,X1),fFalse) = bot_bot(fun(X1,bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_18]),c_0_19]) ).
cnf(c_0_29,plain,
( hBOOL(hAPP(state,bool,hAPP(X1,fun(state,bool),X3,esk12_5(X1,X5,X2,X4,X3)),esk13_5(X1,X5,X2,X4,X3)))
| hBOOL(hAPP(fun(hoare_509422987triple(X1),bool),bool,hAPP(fun(hoare_509422987triple(X1),bool),fun(fun(hoare_509422987triple(X1),bool),bool),hoare_122391849derivs(X1),X2),hAPP(hoare_509422987triple(X1),fun(hoare_509422987triple(X1),bool),fequal(hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),hoare_509422987triple(X1),hAPP(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1))),hoare_1008221573triple(X1),X3),X4),X5)))) ),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = ti(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,hypothesis,
ti(bool,fFalse) = fFalse,
inference(split_conjunct,[status(thm)],[tsy_c_fFalse_res]) ).
fof(c_0_33,plain,
~ hBOOL(fFalse),
inference(fof_nnf,[status(thm)],[c_0_26]) ).
cnf(c_0_34,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_23]) ).
cnf(c_0_35,plain,
( hBOOL(hAPP(state,bool,X3,esk13_5(X1,X5,X2,X4,hAPP(fun(state,bool),fun(X1,fun(state,bool)),combk(fun(state,bool),X1),X3))))
| hBOOL(hAPP(fun(hoare_509422987triple(X1),bool),bool,hAPP(fun(hoare_509422987triple(X1),bool),fun(fun(hoare_509422987triple(X1),bool),bool),hoare_122391849derivs(X1),X2),hAPP(hoare_509422987triple(X1),fun(hoare_509422987triple(X1),bool),fequal(hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),hoare_509422987triple(X1),hAPP(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1))),hoare_1008221573triple(X1),hAPP(fun(state,bool),fun(X1,fun(state,bool)),combk(fun(state,bool),X1),X3)),X4),X5)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_36,plain,
hAPP(X1,bool,bot_bot(fun(X1,bool)),X2) = fFalse,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_32]) ).
cnf(c_0_37,plain,
~ hBOOL(fFalse),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW470+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n015.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 09:59:21 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 161.39/24.51 % Version: 3.5.1
% 161.39/24.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 161.39/24.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 161.39/24.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 161.39/24.51 % Starting new_bool_3 with 300s (1) cores
% 161.39/24.51 % Starting new_bool_1 with 300s (1) cores
% 161.39/24.51 % Starting sh5l with 300s (1) cores
% 161.39/24.51 % new_bool_1 with pid 1186703 completed with status 0
% 161.39/24.51 % Result found by new_bool_1
% 161.39/24.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 161.39/24.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 161.39/24.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 161.39/24.51 % Starting new_bool_3 with 300s (1) cores
% 161.39/24.51 % Starting new_bool_1 with 300s (1) cores
% 161.39/24.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 161.39/24.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 161.39/24.51 % Search class: FGHSM-FFLM33-DFFFFFNN
% 161.39/24.51 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 161.39/24.51 % Starting SubtermCWHack with 28s (1) cores
% 161.39/24.51 % SubtermCWHack with pid 1186705 completed with status 0
% 161.39/24.51 % Result found by SubtermCWHack
% 161.39/24.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 161.39/24.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 161.39/24.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 161.39/24.51 % Starting new_bool_3 with 300s (1) cores
% 161.39/24.51 % Starting new_bool_1 with 300s (1) cores
% 161.39/24.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 161.39/24.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 161.39/24.51 % Search class: FGHSM-FFLM33-DFFFFFNN
% 161.39/24.51 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 161.39/24.51 % Starting SubtermCWHack with 28s (1) cores
% 161.39/24.51 % Preprocessing time : 0.005 s
% 161.39/24.51
% 161.39/24.51 % Proof found!
% 161.39/24.51 % SZS status Theorem
% 161.39/24.51 % SZS output start CNFRefutation
% See solution above
% 161.39/24.51 % Parsed axioms : 163
% 161.39/24.51 % Removed by relevancy pruning/SinE : 60
% 161.39/24.51 % Initial clauses : 156
% 161.39/24.51 % Removed in clause preprocessing : 1
% 161.39/24.51 % Initial clauses in saturation : 155
% 161.39/24.51 % Processed clauses : 33231
% 161.39/24.51 % ...of these trivial : 155
% 161.39/24.51 % ...subsumed : 30585
% 161.39/24.51 % ...remaining for further processing : 2491
% 161.39/24.51 % Other redundant clauses eliminated : 253
% 161.39/24.51 % Clauses deleted for lack of memory : 0
% 161.39/24.51 % Backward-subsumed : 29
% 161.39/24.51 % Backward-rewritten : 121
% 161.39/24.51 % Generated clauses : 1013120
% 161.39/24.51 % ...of the previous two non-redundant : 955144
% 161.39/24.51 % ...aggressively subsumed : 0
% 161.39/24.51 % Contextual simplify-reflections : 24
% 161.39/24.51 % Paramodulations : 1012502
% 161.39/24.51 % Factorizations : 89
% 161.39/24.51 % NegExts : 0
% 161.39/24.51 % Equation resolutions : 529
% 161.39/24.51 % Disequality decompositions : 0
% 161.39/24.51 % Total rewrite steps : 378539
% 161.39/24.51 % ...of those cached : 364554
% 161.39/24.51 % Propositional unsat checks : 0
% 161.39/24.51 % Propositional check models : 0
% 161.39/24.51 % Propositional check unsatisfiable : 0
% 161.39/24.51 % Propositional clauses : 0
% 161.39/24.51 % Propositional clauses after purity: 0
% 161.39/24.51 % Propositional unsat core size : 0
% 161.39/24.51 % Propositional preprocessing time : 0.000
% 161.39/24.51 % Propositional encoding time : 0.000
% 161.39/24.51 % Propositional solver time : 0.000
% 161.39/24.51 % Success case prop preproc time : 0.000
% 161.39/24.51 % Success case prop encoding time : 0.000
% 161.39/24.51 % Success case prop solver time : 0.000
% 161.39/24.51 % Current number of processed clauses : 2341
% 161.39/24.51 % Positive orientable unit clauses : 153
% 161.39/24.51 % Positive unorientable unit clauses: 34
% 161.39/24.51 % Negative unit clauses : 56
% 161.39/24.51 % Non-unit-clauses : 2098
% 161.39/24.51 % Current number of unprocessed clauses: 920017
% 161.39/24.51 % ...number of literals in the above : 4404524
% 161.39/24.51 % Current number of archived formulas : 0
% 161.39/24.51 % Current number of archived clauses : 150
% 161.39/24.51 % Clause-clause subsumption calls (NU) : 1543593
% 161.39/24.51 % Rec. Clause-clause subsumption calls : 513741
% 161.39/24.51 % Non-unit clause-clause subsumptions : 23220
% 161.39/24.51 % Unit Clause-clause subsumption calls : 36007
% 161.39/24.51 % Rewrite failures with RHS unbound : 0
% 161.39/24.51 % BW rewrite match attempts : 58293
% 161.39/24.51 % BW rewrite match successes : 218
% 161.39/24.51 % Condensation attempts : 0
% 161.39/24.51 % Condensation successes : 0
% 161.39/24.51 % Termbank termtop insertions : 51687026
% 161.39/24.51 % Search garbage collected termcells : 2764
% 161.39/24.51
% 161.39/24.51 % -------------------------------------------------
% 161.39/24.51 % User time : 22.477 s
% 161.39/24.51 % System time : 0.552 s
% 161.39/24.51 % Total time : 23.029 s
% 161.39/24.51 % Maximum resident set size: 4436 pages
% 161.39/24.51
% 161.39/24.51 % -------------------------------------------------
% 161.39/24.51 % User time : 22.492 s
% 161.39/24.51 % System time : 0.557 s
% 161.39/24.51 % Total time : 23.049 s
% 161.39/24.51 % Maximum resident set size: 4864 pages
% 161.39/24.51 % E exiting
%------------------------------------------------------------------------------