%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWW473+5 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n018.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 : Wed Apr 9 09:52:46 PM UTC 2025
% Result : Theorem 55.97s 38.69s
% Output : CNFRefutation 56.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 4 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 45 ( 45 usr; 15 con; 0-5 aty)
% Number of variables : 18 ( 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ preorder > order > hBOOL > finite_finite_1 > hAPP > combs > combc > combb > ti > image > fun > #nlpp > undefined > ord_less_eq > minus_minus > member > insert > finite_finite > finite_card > fequal > combi > collect > x_a > u > suc > pname > pn > p > nat > na > mgt_call > g > fimplies > fdisj > fconj > fNot > bool > #skF_6 > #skF_5 > #skF_12 > #skF_11 > #skF_7 > #skF_2 > #skF_10 > #skF_9 > #skF_4 > #skF_1 > #skF_13 > #skF_3 > #skF_8
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(fconj,type,
fconj: $i ).
tff(hAPP,type,
hAPP: ( $i * $i * $i * $i ) > $i ).
tff(ord_less_eq,type,
ord_less_eq: $i > $i ).
tff(suc,type,
suc: $i ).
tff(combs,type,
combs: ( $i * $i * $i ) > $i ).
tff(member,type,
member: $i > $i ).
tff(combb,type,
combb: ( $i * $i * $i ) > $i ).
tff(fimplies,type,
fimplies: $i ).
tff(fNot,type,
fNot: $i ).
tff(u,type,
u: $i ).
tff(bool,type,
bool: $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i * $i * $i ) > $i ).
tff(collect,type,
collect: $i > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i * $i * $i ) > $i ).
tff(nat,type,
nat: $i ).
tff(fun,type,
fun: ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i * $i ) > $i ).
tff(fequal,type,
fequal: $i > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff(undefined,type,
undefined: $i > $i ).
tff(combi,type,
combi: $i > $i ).
tff(insert,type,
insert: $i > $i ).
tff(pn,type,
pn: $i ).
tff(fdisj,type,
fdisj: $i ).
tff(finite_finite,type,
finite_finite: $i > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i * $i ) > $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(g,type,
g: $i ).
tff(mgt_call,type,
mgt_call: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff(minus_minus,type,
minus_minus: $i > $i ).
tff(ti,type,
ti: ( $i * $i ) > $i ).
tff(pname,type,
pname: $i ).
tff(x_a,type,
x_a: $i ).
tff(na,type,
na: $i ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(preorder,type,
preorder: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff(p,type,
p: $i ).
tff(finite_finite_1,type,
finite_finite_1: $i > $o ).
tff(order,type,
order: $i > $o ).
tff(combc,type,
combc: ( $i * $i * $i ) > $i ).
tff(finite_card,type,
finite_card: $i > $i ).
tff(f_683,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
tff(f_472,axiom,
! [X_c,X_b,F,X_2,A_1] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
=> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_imageI) ).
tff(f_680,hypothesis,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f_492,axiom,
! [X_b,X_2,A_1,B] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_1)),B))
<=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B))
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_insert__subset) ).
tff(f_687,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
tff(c_398,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(cnfTransformation,[status(thm)],[f_683]) ).
tff(c_274,plain,
! [F_277,X_c_275,X_b_276,A_1_279,X_2_278] :
( hBOOL(hAPP(fun(X_c_275,bool),bool,hAPP(X_c_275,fun(fun(X_c_275,bool),bool),member(X_c_275),hAPP(X_b_276,X_c_275,F_277,X_2_278)),hAPP(fun(X_b_276,bool),fun(X_c_275,bool),hAPP(fun(X_b_276,X_c_275),fun(fun(X_b_276,bool),fun(X_c_275,bool)),image(X_b_276,X_c_275),F_277),A_1_279)))
| ~ hBOOL(hAPP(fun(X_b_276,bool),bool,hAPP(X_b_276,fun(fun(X_b_276,bool),bool),member(X_b_276),X_2_278),A_1_279)) ),
inference(cnfTransformation,[status(thm)],[f_472]) ).
tff(c_392,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(cnfTransformation,[status(thm)],[f_680]) ).
tff(c_165931,plain,
! [X_b_1331,X_2_1332,A_1_1333,B_1334] :
( hBOOL(hAPP(fun(X_b_1331,bool),bool,hAPP(fun(X_b_1331,bool),fun(fun(X_b_1331,bool),bool),ord_less_eq(fun(X_b_1331,bool)),hAPP(fun(X_b_1331,bool),fun(X_b_1331,bool),hAPP(X_b_1331,fun(fun(X_b_1331,bool),fun(X_b_1331,bool)),insert(X_b_1331),X_2_1332),A_1_1333)),B_1334))
| ~ hBOOL(hAPP(fun(X_b_1331,bool),bool,hAPP(fun(X_b_1331,bool),fun(fun(X_b_1331,bool),bool),ord_less_eq(fun(X_b_1331,bool)),A_1_1333),B_1334))
| ~ hBOOL(hAPP(fun(X_b_1331,bool),bool,hAPP(X_b_1331,fun(fun(X_b_1331,bool),bool),member(X_b_1331),X_2_1332),B_1334)) ),
inference(cnfTransformation,[status(thm)],[f_492]) ).
tff(c_402,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(cnfTransformation,[status(thm)],[f_687]) ).
tff(c_165968,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
inference(resolution,[status(thm)],[c_165931,c_402]) ).
tff(c_166010,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(demodulation,[status(thm),theory(equality)],[c_392,c_165968]) ).
tff(c_170664,plain,
~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(resolution,[status(thm)],[c_274,c_166010]) ).
tff(c_170671,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_398,c_170664]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWW473+5 : TPTP v9.0.0. Released v5.3.0.
% 0.08/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Apr 9 05:58:47 EDT 2025
% 0.14/0.34 % CPUTime :
% 55.97/38.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 55.97/38.69
% 55.97/38.69 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------