%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW339+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 : n010.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 37.86s 23.16s
% Output : CNFRefutation 37.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 19 unt; 0 def)
% Number of atoms : 85 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 27 ~; 28 |; 4 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 ( 8 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__mem__eq,axiom,
! [X10,X6] : hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X10)) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).
fof(fact_Collect__def,axiom,
! [X17,X6] : hAPP(c_Set_OCollect(X6),X17) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(conj_3,conjecture,
! [X13] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X13,X3) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X13,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
fof(help_c__COMBC__1,axiom,
! [X147,X16,X17,X6,X141,X14] : hAPP(hAPP(hAPP(c_COMBC(X14,X141,X6),X17),X16),X147) = hAPP(hAPP(X17,X147),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(fact_rev__predicate1D,axiom,
! [X16,X6,X15,X17] :
( hBOOL(hAPP(X17,X15))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool)),X17),X16))
=> hBOOL(hAPP(X16,X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_mem__def,axiom,
! [X10,X15,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X15),X10))
<=> hBOOL(hAPP(X10,X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(conj_1,hypothesis,
! [X13] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X13,X3) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_ts_H))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X13,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(conj_2,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_ts_H)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(c_0_8,plain,
! [X27697,X27698] : hAPP(c_Set_OCollect(X27698),hAPP(hAPP(c_COMBC(X27698,tc_fun(X27698,tc_HOL_Obool),tc_HOL_Obool),c_member(X27698)),X27697)) = X27697,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(c_0_9,plain,
! [X27649,X27650] : hAPP(c_Set_OCollect(X27650),X27649) = X27649,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_10,negated_conjecture,
~ ! [X13] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X13,X3) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X13,X3) ) ),
inference(assume_negation,[status(cth)],[conj_3]) ).
fof(c_0_11,plain,
! [X34215,X34216,X34217,X34218,X34219,X34220] : hAPP(hAPP(hAPP(c_COMBC(X34220,X34219,X34218),X34217),X34216),X34215) = hAPP(hAPP(X34217,X34215),X34216),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_0_12,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_8]) ).
cnf(c_0_13,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X16982,X16983,X16984,X16985] :
( ~ hBOOL(hAPP(X16985,X16984))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16983,tc_HOL_Obool)),X16985),X16982))
| hBOOL(hAPP(X16982,X16984)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(c_0_15,plain,
! [X17476,X17477,X17478] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X17478),X17477),X17476))
| hBOOL(hAPP(X17476,X17477)) )
& ( ~ hBOOL(hAPP(X17476,X17477))
| hBOOL(hAPP(hAPP(c_member(X17478),X17477),X17476)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(c_0_16,negated_conjecture,
! [X34255] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X34255),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,esk587_0,X34255) )
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk588_0),v_ts))
& ~ c_Hoare__Mirabelle_Otriple__valid(t_a,esk587_0,esk588_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_17,hypothesis,
! [X34251,X34253] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk586_1(X34251)),v_G))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X34253),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X34251,X34253) )
& ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X34251,esk586_1(X34251))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X34253),v_ts_H))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X34251,X34253) ) ),
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_18,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,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_12,c_0_13]) ).
cnf(c_0_20,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_ts_H)),
inference(split_conjunct,[status(thm)],[conj_2]) ).
cnf(c_0_22,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk588_0),v_ts)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,hypothesis,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk586_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_ts_H)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,hypothesis,
( hBOOL(hAPP(v_ts_H,X1))
| ~ hBOOL(hAPP(v_ts,X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
hBOOL(hAPP(v_ts,esk588_0)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X1,esk586_1(X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts_H)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk587_0,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_30,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_31,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| hBOOL(hAPP(v_G,esk586_1(X1)))
| ~ hBOOL(hAPP(v_ts_H,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_25]) ).
cnf(c_0_32,negated_conjecture,
hBOOL(hAPP(v_ts_H,esk588_0)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X1,esk586_1(X1))
| ~ hBOOL(hAPP(v_ts_H,X2)) ),
inference(rw,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_34,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk587_0,X1)
| ~ hBOOL(hAPP(v_G,X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,esk587_0,esk588_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_36,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,esk588_0)
| hBOOL(hAPP(v_G,esk586_1(X1))) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk587_0,X1)
| ~ hBOOL(hAPP(v_G,esk586_1(esk587_0)))
| ~ hBOOL(hAPP(v_ts_H,X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
hBOOL(hAPP(v_G,esk586_1(esk587_0))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk587_0,X1)
| ~ hBOOL(hAPP(v_ts_H,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_39]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW339+1 : TPTP v9.2.1. Released v5.2.0.
% 0.12/0.13 % 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 : n010.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 06:38:06 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 37.86/23.16 % Version : CSE_E---1.7
% 37.86/23.16 % Problem : theBenchmark.p
% 37.86/23.16 % SZS status Theorem for theBenchmark.p
% 37.86/23.16 % SZS output start CNFRefutation
% See solution above
% 37.93/23.28 % Total time : 18.308s
%------------------------------------------------------------------------------