%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWX220+1 : TPTP v9.3.0. Released v9.3.0.
% 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 : n028.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 06:56:38 PM UTC 2026
% Result : Theorem 19.68s 11.09s
% Output : CNFRefutation 19.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 28 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 75 ( 43 ~; 27 |; 1 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 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 : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-3 aty)
% Number of variables : 88 ( 87 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ tc > app > index > cons > arr > #nlpp > var > tail > suc > proj3App > proj2Arr > proj2App > proj1Var > proj1Suc > proj1Lam > proj1Just > proj1Arr > proj1App > lam > just > head > zero > nothing > nil > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(app,type,
app: ( $i * $i * $i ) > $i ).
tff(arr,type,
arr: ( $i * $i ) > $i ).
tff(proj3App,type,
proj3App: $i > $i ).
tff(a,type,
a: $i ).
tff(proj1Suc,type,
proj1Suc: $i > $i ).
tff(proj1Lam,type,
proj1Lam: $i > $i ).
tff(b,type,
b: $i ).
tff(proj2App,type,
proj2App: $i > $i ).
tff(proj1Just,type,
proj1Just: $i > $i ).
tff(proj2Arr,type,
proj2Arr: $i > $i ).
tff(nothing,type,
nothing: $i ).
tff(var,type,
var: $i > $i ).
tff(index,type,
index: ( $i * $i ) > $i ).
tff(just,type,
just: $i > $i ).
tff(proj1Var,type,
proj1Var: $i > $i ).
tff(proj1Arr,type,
proj1Arr: $i > $i ).
tff(lam,type,
lam: $i > $i ).
tff(suc,type,
suc: $i > $i ).
tff(cons,type,
cons: ( $i * $i ) > $i ).
tff(proj1App,type,
proj1App: $i > $i ).
tff(tail,type,
tail: $i > $i ).
tff(tc,type,
tc: ( $i * $i * $i ) > $o ).
tff(head,type,
head: $i > $i ).
tff(nil,type,
nil: $i ).
tff(zero,type,
zero: $i ).
tff(c,type,
c: $i ).
tff(f_83,axiom,
! [Z,Xs] : ( index(cons(Z,Xs),zero) = just(Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
tff(f_85,axiom,
! [Z,Xs,N] : ( index(cons(Z,Xs),suc(N)) = index(Xs,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
tff(f_112,axiom,
! [X,Z,X3,Tx3] :
( ( index(X,X3) = just(Tx3) )
=> ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
tff(f_91,axiom,
! [X,Z,F,X2,Tx] :
( tc(X,app(F,X2,Tx),Z)
<=> ( tc(X,F,arr(Tx,Z))
& tc(X,X2,Tx) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
tff(f_101,axiom,
! [X,E,Tx2,T1] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
tff(f_115,negated_conjecture,
~ ? [E] : tc(nil,E,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_032) ).
tff(c_50,plain,
! [Z_43,Xs_44] : ( index(cons(Z_43,Xs_44),zero) = just(Z_43) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_52,plain,
! [Z_45,Xs_46,N_47] : ( index(cons(Z_45,Xs_46),suc(N_47)) = index(Xs_46,N_47) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_68,plain,
! [X_63,X3_65,Z_64] :
( tc(X_63,var(X3_65),Z_64)
| ( just(Z_64) != index(X_63,X3_65) ) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_54,plain,
! [Tx_52,X_48,Z_49,X2_51,F_50] :
( tc(X_48,app(F_50,X2_51,Tx_52),Z_49)
| ~ tc(X_48,X2_51,Tx_52)
| ~ tc(X_48,F_50,arr(Tx_52,Z_49)) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_321,plain,
! [X2_166,Tx_167,F_168,Z_165,X_164] :
( tc(X_164,app(F_168,X2_166,Tx_167),Z_165)
| ~ tc(X_164,X2_166,Tx_167)
| ~ tc(X_164,F_168,arr(Tx_167,Z_165)) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_64,plain,
! [X_56,E_57,Tx2_58,T1_59] :
( tc(X_56,lam(E_57),arr(Tx2_58,T1_59))
| ~ tc(cons(Tx2_58,X_56),E_57,T1_59) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_253,plain,
! [X_144,E_145,Tx2_146,T1_147] :
( tc(X_144,lam(E_145),arr(Tx2_146,T1_147))
| ~ tc(cons(Tx2_146,X_144),E_145,T1_147) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_72,plain,
! [E_67] : ~ tc(nil,E_67,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_274,plain,
! [E_159] : ~ tc(cons(arr(a,arr(b,c)),nil),E_159,arr(b,arr(a,c))),
inference(resolution,[status(thm)],[c_253,c_72]) ).
tff(c_285,plain,
! [E_160] : ~ tc(cons(b,cons(arr(a,arr(b,c)),nil)),E_160,arr(a,c)),
inference(resolution,[status(thm)],[c_64,c_274]) ).
tff(c_294,plain,
! [E_57] : ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),E_57,c),
inference(resolution,[status(thm)],[c_64,c_285]) ).
tff(c_1036,plain,
! [X2_362,Tx_363,F_364] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2_362,Tx_363)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_364,arr(Tx_363,c)) ),
inference(resolution,[status(thm)],[c_321,c_294]) ).
tff(c_1619,plain,
! [F_617,Z_618,X3_619] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_617,arr(Z_618,c))
| ( just(Z_618) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_619) ) ),
inference(resolution,[status(thm)],[c_68,c_1036]) ).
tff(c_6547,plain,
! [X3_3179,Tx_3177,X2_3176,F_3178,Z_3175] :
( ( just(Z_3175) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_3179) )
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2_3176,Tx_3177)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_3178,arr(Tx_3177,arr(Z_3175,c))) ),
inference(resolution,[status(thm)],[c_54,c_1619]) ).
tff(c_11475,plain,
! [Z_5948,Tx_5950,N_5949,X2_5951,F_5952] :
( ( just(Z_5948) != index(cons(b,cons(arr(a,arr(b,c)),nil)),N_5949) )
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2_5951,Tx_5950)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_5952,arr(Tx_5950,arr(Z_5948,c))) ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_6547]) ).
tff(c_11683,plain,
! [Z_6050,X2_6051,Tx_6052,F_6053] :
( ( just(b) != just(Z_6050) )
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2_6051,Tx_6052)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_6053,arr(Tx_6052,arr(Z_6050,c))) ),
inference(superposition,[status(thm),theory(equality)],[c_50,c_11475]) ).
tff(c_11697,plain,
! [Z_6058,F_6059,Z_6060,X3_6061] :
( ( just(b) != just(Z_6058) )
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_6059,arr(Z_6060,arr(Z_6058,c)))
| ( just(Z_6060) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_6061) ) ),
inference(resolution,[status(thm)],[c_68,c_11683]) ).
tff(c_11954,plain,
! [Z_6165,Z_6166,X3_6167,X3_6168] :
( ( just(b) != just(Z_6165) )
| ( just(Z_6166) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_6167) )
| ( just(arr(Z_6166,arr(Z_6165,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_6168) ) ),
inference(resolution,[status(thm)],[c_68,c_11697]) ).
tff(c_11969,plain,
! [Z_6178,Z_6179,X3_6180] :
( ( just(b) != just(Z_6178) )
| ( just(a) != just(Z_6179) )
| ( just(arr(Z_6179,arr(Z_6178,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_6180) ) ),
inference(superposition,[status(thm),theory(equality)],[c_50,c_11954]) ).
tff(c_11979,plain,
! [Z_6183,Z_6184,N_6185] :
( ( just(b) != just(Z_6183) )
| ( just(a) != just(Z_6184) )
| ( just(arr(Z_6184,arr(Z_6183,c))) != index(cons(b,cons(arr(a,arr(b,c)),nil)),N_6185) ) ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_11969]) ).
tff(c_12002,plain,
! [Z_6198,Z_6199,N_6200] :
( ( just(b) != just(Z_6198) )
| ( just(a) != just(Z_6199) )
| ( just(arr(Z_6199,arr(Z_6198,c))) != index(cons(arr(a,arr(b,c)),nil),N_6200) ) ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_11979]) ).
tff(c_12010,plain,
! [Z_6198,Z_6199] :
( ( just(b) != just(Z_6198) )
| ( just(a) != just(Z_6199) )
| ( just(arr(a,arr(b,c))) != just(arr(Z_6199,arr(Z_6198,c))) ) ),
inference(superposition,[status(thm),theory(equality)],[c_50,c_12002]) ).
tff(c_12016,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_12010]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX220+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % 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
% 0.17/0.34 % Computer : n028.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 12:27:15 EDT 2026
% 0.17/0.34 % CPUTime :
% 19.68/11.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.68/11.09
% 19.68/11.09 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------