%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW326+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:31:46 PM UTC 2026
% Result : Theorem 34.91s 21.37s
% Output : CNFRefutation 35.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 17 unt; 0 def)
% Number of atoms : 120 ( 11 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 137 ( 59 ~; 50 |; 11 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 92 ( 14 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__mem__eq,axiom,
! [X150,X6] : hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X150)) = X150,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).
fof(fact_Collect__def,axiom,
! [X26,X6] : hAPP(c_Set_OCollect(X6),X26) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(conj_1,hypothesis,
! [X28,X29] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X28,v_n,X29)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X3) )
=> ! [X27] :
( v_P(X27,X28)
=> ( v_P(X27,X29)
& ~ hBOOL(hAPP(v_b,X29)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(conj_2,conjecture,
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X3) )
=> ! [X27,X28] :
( v_P(X27,X28)
=> ! [X29] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X28,v_n,X29)
=> ( v_P(X27,X29)
& ~ hBOOL(hAPP(v_b,X29)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(help_c__COMBC__1,axiom,
! [X190,X25,X26,X6,X117,X51] : hAPP(hAPP(hAPP(c_COMBC(X51,X117,X6),X26),X25),X190) = hAPP(hAPP(X26,X190),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(fact_mem__def,axiom,
! [X150,X103,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X103),X150))
<=> hBOOL(hAPP(X150,X103)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(c_0_6,plain,
! [X29130,X29131] : hAPP(c_Set_OCollect(X29131),hAPP(hAPP(c_COMBC(X29131,tc_fun(X29131,tc_HOL_Obool),tc_HOL_Obool),c_member(X29131)),X29130)) = X29130,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(c_0_7,plain,
! [X29162,X29163] : hAPP(c_Set_OCollect(X29163),X29162) = X29162,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_8,hypothesis,
! [X28,X29] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X28,v_n,X29)
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X3) )
=> ! [X27] :
( v_P(X27,X28)
=> ( v_P(X27,X29)
& ~ hBOOL(hAPP(v_b,X29)) ) ) ) ),
inference(fof_simplification,[status(thm)],[conj_1]) ).
fof(c_0_9,negated_conjecture,
~ ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X3) )
=> ! [X27,X28] :
( v_P(X27,X28)
=> ! [X29] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X28,v_n,X29)
=> ( v_P(X27,X29)
& ~ hBOOL(hAPP(v_b,X29)) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_2])]) ).
fof(c_0_10,plain,
! [X34440,X34441,X34442,X34443,X34444,X34445] : hAPP(hAPP(hAPP(c_COMBC(X34445,X34444,X34443),X34442),X34441),X34440) = hAPP(hAPP(X34442,X34440),X34441),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_0_11,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,hypothesis,
! [X34481,X34482,X34484] :
( ( v_P(X34484,X34482)
| ~ v_P(X34484,X34481)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk496_2(X34481,X34482)),v_G))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X34481,v_n,X34482) )
& ( ~ hBOOL(hAPP(v_b,X34482))
| ~ v_P(X34484,X34481)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk496_2(X34481,X34482)),v_G))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X34481,v_n,X34482) )
& ( v_P(X34484,X34482)
| ~ v_P(X34484,X34481)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,esk496_2(X34481,X34482))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X34481,v_n,X34482) )
& ( ~ hBOOL(hAPP(v_b,X34482))
| ~ v_P(X34484,X34481)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,esk496_2(X34481,X34482))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X34481,v_n,X34482) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
fof(c_0_14,negated_conjecture,
! [X34485] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X34485),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X34485) )
& v_P(esk497_0,esk498_0)
& c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),esk498_0,v_n,esk499_0)
& ( ~ v_P(esk497_0,esk499_0)
| hBOOL(hAPP(v_b,esk499_0)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_15,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,hypothesis,
( v_P(X1,X2)
| ~ v_P(X1,X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,esk496_2(X3,X2))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X3,v_n,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),esk498_0,v_n,esk499_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,hypothesis,
( ~ hBOOL(hAPP(v_b,X1))
| ~ v_P(X2,X3)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,esk496_2(X3,X1))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X3,v_n,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,hypothesis,
( v_P(X1,X2)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk496_2(X3,X2)),v_G))
| ~ v_P(X1,X3)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X3,v_n,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,negated_conjecture,
( v_P(X1,esk499_0)
| ~ v_P(X1,esk498_0)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,esk496_2(esk498_0,esk499_0)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X1)
| ~ hBOOL(hAPP(v_G,X1)) ),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( ~ v_P(X1,esk498_0)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,esk496_2(esk498_0,esk499_0))
| ~ hBOOL(hAPP(v_b,esk499_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
fof(c_0_26,plain,
! [X25089,X25090,X25091] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X25091),X25090),X25089))
| hBOOL(hAPP(X25089,X25090)) )
& ( ~ hBOOL(hAPP(X25089,X25090))
| hBOOL(hAPP(hAPP(c_member(X25091),X25090),X25089)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
cnf(c_0_27,hypothesis,
( v_P(X1,X2)
| hBOOL(hAPP(v_G,esk496_2(X3,X2)))
| ~ v_P(X1,X3)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X3,v_n,X2) ),
inference(rw,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( v_P(X1,esk499_0)
| ~ v_P(X1,esk498_0)
| ~ hBOOL(hAPP(v_G,esk496_2(esk498_0,esk499_0))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,hypothesis,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk496_2(X3,X1)),v_G))
| ~ hBOOL(hAPP(v_b,X1))
| ~ v_P(X2,X3)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X3,v_n,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_30,negated_conjecture,
( ~ v_P(X1,esk498_0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk496_2(esk498_0,esk499_0)),v_G))
| ~ hBOOL(hAPP(v_b,esk499_0)) ),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_31,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( v_P(X1,esk499_0)
| ~ v_P(X1,esk498_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_18]),c_0_28]) ).
cnf(c_0_33,negated_conjecture,
v_P(esk497_0,esk498_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_34,hypothesis,
( hBOOL(hAPP(v_G,esk496_2(X1,X2)))
| ~ v_P(X3,X1)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(v_b,v_c),X1,v_n,X2)
| ~ hBOOL(hAPP(v_b,X2)) ),
inference(rw,[status(thm)],[c_0_29,c_0_20]) ).
cnf(c_0_35,negated_conjecture,
( ~ v_P(X1,esk498_0)
| ~ hBOOL(hAPP(v_G,esk496_2(esk498_0,esk499_0)))
| ~ hBOOL(hAPP(v_b,esk499_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( hBOOL(hAPP(v_b,esk499_0))
| ~ v_P(esk497_0,esk499_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_37,negated_conjecture,
v_P(esk497_0,esk499_0),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( ~ v_P(X1,esk498_0)
| ~ hBOOL(hAPP(v_b,esk499_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_18]),c_0_35]) ).
cnf(c_0_39,negated_conjecture,
hBOOL(hAPP(v_b,esk499_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_40,negated_conjecture,
~ v_P(X1,esk498_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_33,c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW326+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n013.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 06:37:11 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 34.91/21.37 % Version : CSE_E---1.7
% 34.91/21.37 % Problem : theBenchmark.p
% 34.91/21.37 % SZS status Theorem for theBenchmark.p
% 34.91/21.37 % SZS output start CNFRefutation
% See solution above
% 35.01/21.48 % Total time : 16.990s
%------------------------------------------------------------------------------