%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW338+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 : n005.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 05:31:47 PM UTC 2026
% Result : Theorem 36.76s 24.92s
% Output : CNFRefutation 36.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 17 unt; 0 def)
% Number of atoms : 99 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 88 ( 32 ~; 38 |; 5 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 85 ( 6 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__mem__eq,axiom,
! [X23,X7] : hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X23)) = X23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).
fof(fact_Collect__def,axiom,
! [X16,X7] : hAPP(c_Set_OCollect(X7),X16) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(help_c__COMBC__1,axiom,
! [X17,X15,X16,X7,X182,X30] : hAPP(hAPP(hAPP(c_COMBC(X30,X182,X7),X16),X15),X17) = hAPP(hAPP(X16,X17),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(conj_4,conjecture,
! [X8] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X8,X3) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X8,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
fof(conj_1,hypothesis,
! [X8] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G_H))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X8,X3) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X8,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(fact_mem__def,axiom,
! [X23,X37,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X37),X23))
<=> hBOOL(hAPP(X23,X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(conj_3,hypothesis,
! [X8] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X8,X3) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G_H))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X8,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
fof(c_0_7,plain,
! [X28051,X28052] : hAPP(c_Set_OCollect(X28052),hAPP(hAPP(c_COMBC(X28052,tc_fun(X28052,tc_HOL_Obool),tc_HOL_Obool),c_member(X28052)),X28051)) = X28051,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(c_0_8,plain,
! [X28078,X28079] : hAPP(c_Set_OCollect(X28079),X28078) = X28078,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_9,plain,
! [X34351,X34352,X34353,X34354,X34355,X34356] : hAPP(hAPP(hAPP(c_COMBC(X34356,X34355,X34354),X34353),X34352),X34351) = hAPP(hAPP(X34353,X34351),X34352),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_0_10,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_7]) ).
cnf(c_0_11,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,negated_conjecture,
~ ! [X8] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X8,X3) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X8,X3) ) ),
inference(assume_negation,[status(cth)],[conj_4]) ).
fof(c_0_13,hypothesis,
! [X34387,X34389] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk577_1(X34387)),v_G_H))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X34389),v_ts))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X34387,X34389) )
& ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X34387,esk577_1(X34387))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X34389),v_ts))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X34387,X34389) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_1])])])])]) ).
cnf(c_0_14,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,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_10,c_0_11]) ).
fof(c_0_16,plain,
! [X17424,X17425,X17426] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X17426),X17425),X17424))
| hBOOL(hAPP(X17424,X17425)) )
& ( ~ hBOOL(hAPP(X17424,X17425))
| hBOOL(hAPP(hAPP(c_member(X17426),X17425),X17424)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(c_0_17,negated_conjecture,
! [X34394] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X34394),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,esk579_0,X34394) )
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk580_0),v_ts))
& ~ c_Hoare__Mirabelle_Otriple__valid(t_a,esk579_0,esk580_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_18,hypothesis,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk577_1(X1)),v_G_H))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk580_0),v_ts)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,hypothesis,
! [X34390,X34392] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk578_1(X34390)),v_G))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X34392),v_G_H))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X34390,X34392) )
& ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X34390,esk578_1(X34390))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X34392),v_G_H))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X34390,X34392) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_3])])])])]) ).
cnf(c_0_23,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| hBOOL(hAPP(v_G_H,esk577_1(X1)))
| ~ hBOOL(hAPP(v_ts,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).
cnf(c_0_24,negated_conjecture,
hBOOL(hAPP(v_ts,esk580_0)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,hypothesis,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk578_1(X1)),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G_H)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,esk579_0,esk580_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,esk580_0)
| hBOOL(hAPP(v_G_H,esk577_1(X1))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X1,esk577_1(X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_29,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| hBOOL(hAPP(v_G,esk578_1(X1)))
| ~ hBOOL(hAPP(v_G_H,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_19]),c_0_19]) ).
cnf(c_0_30,negated_conjecture,
hBOOL(hAPP(v_G_H,esk577_1(esk579_0))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X1,esk578_1(X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G_H)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk579_0,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X1,esk577_1(X1))
| ~ hBOOL(hAPP(v_ts,X2)) ),
inference(rw,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_34,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,esk577_1(esk579_0))
| hBOOL(hAPP(v_G,esk578_1(X1))) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X1,esk578_1(X1))
| ~ hBOOL(hAPP(v_G_H,X2)) ),
inference(rw,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_36,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk579_0,X1)
| ~ hBOOL(hAPP(v_G,X1)) ),
inference(rw,[status(thm)],[c_0_32,c_0_19]) ).
cnf(c_0_37,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk579_0,X1)
| hBOOL(hAPP(v_G,esk578_1(esk579_0)))
| ~ hBOOL(hAPP(v_ts,X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk579_0,X1)
| ~ hBOOL(hAPP(v_G,esk578_1(esk579_0)))
| ~ hBOOL(hAPP(v_G_H,X1)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
hBOOL(hAPP(v_G,esk578_1(esk579_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_24]),c_0_26]) ).
cnf(c_0_40,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk579_0,X1)
| ~ hBOOL(hAPP(v_G_H,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_41,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk579_0,X1)
| ~ hBOOL(hAPP(v_ts,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_40]),c_0_30])]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_41]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW338+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % 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
% 0.16/0.34 % Computer : n005.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 06:38:15 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 36.76/24.92 % Version : CSE_E---1.7
% 36.76/24.92 % Problem : theBenchmark.p
% 36.76/24.92 % SZS status Theorem for theBenchmark.p
% 36.76/24.92 % SZS output start CNFRefutation
% See solution above
% 36.76/25.01 % Total time : 21.116s
%------------------------------------------------------------------------------