%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWX219+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n002.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 : Timeout 292.53s 275.36s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 30 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 74 ( 43 ~; 26 |; 1 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 6 ( 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 : 94 ( 93 !; 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/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
tff(f_85,axiom,
! [Z,Xs,N] : ( index(cons(Z,Xs),suc(N)) = index(Xs,N) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
tff(f_115,negated_conjecture,
~ ? [E] : tc(nil,E,arr(arr(b,c),arr(arr(a,b),arr(a,c)))),
file('/export/starexec/sandbox2/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_317,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(b,c),arr(arr(a,b),arr(a,c)))),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_274,plain,
! [E_159] : ~ tc(cons(arr(b,c),nil),E_159,arr(arr(a,b),arr(a,c))),
inference(resolution,[status(thm)],[c_253,c_72]) ).
tff(c_285,plain,
! [E_160] : ~ tc(cons(arr(a,b),cons(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(arr(a,b),cons(arr(b,c),nil))),E_57,c),
inference(resolution,[status(thm)],[c_64,c_285]) ).
tff(c_943,plain,
! [X2_339,Tx_340,F_341] :
( ~ tc(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X2_339,Tx_340)
| ~ tc(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),F_341,arr(Tx_340,c)) ),
inference(resolution,[status(thm)],[c_317,c_294]) ).
tff(c_3567,plain,
! [Tx_1485,X2_1484,F_1487,F_1486,Z_1483] :
( ~ tc(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),F_1486,arr(Z_1483,c))
| ~ tc(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X2_1484,Tx_1485)
| ~ tc(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),F_1487,arr(Tx_1485,Z_1483)) ),
inference(resolution,[status(thm)],[c_54,c_943]) ).
tff(c_6998,plain,
! [X2_3362,Tx_3363,X3_3365,Z_3361,F_3364] :
( ~ tc(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X2_3362,Tx_3363)
| ~ tc(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),F_3364,arr(Tx_3363,Z_3361))
| ( just(arr(Z_3361,c)) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_3365) ) ),
inference(resolution,[status(thm)],[c_68,c_3567]) ).
tff(c_13850,plain,
! [X3_7171,Z_7174,F_7173,X3_7175,Z_7172] :
( ~ tc(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),F_7173,arr(Z_7172,Z_7174))
| ( just(arr(Z_7174,c)) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_7171) )
| ( just(Z_7172) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_7175) ) ),
inference(resolution,[status(thm)],[c_68,c_6998]) ).
tff(c_28811,plain,
! [X3_16385,X3_16388,Z_16384,X3_16386,Z_16387] :
( ( just(arr(Z_16384,c)) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_16385) )
| ( just(Z_16387) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_16386) )
| ( just(arr(Z_16387,Z_16384)) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_16388) ) ),
inference(resolution,[status(thm)],[c_68,c_13850]) ).
tff(c_59391,plain,
! [X3_37216,Z_37214,N_37212,Z_37215,X3_37213] :
( ( just(arr(Z_37215,c)) != index(cons(arr(a,b),cons(arr(b,c),nil)),N_37212) )
| ( just(Z_37214) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_37213) )
| ( just(arr(Z_37214,Z_37215)) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_37216) ) ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_28811]) ).
tff(c_63067,plain,
! [Z_39497,N_39494,X3_39496,Z_39495,X3_39498] :
( ( just(arr(Z_39497,c)) != index(cons(arr(b,c),nil),N_39494) )
| ( just(Z_39495) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_39496) )
| ( just(arr(Z_39495,Z_39497)) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_39498) ) ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_59391]) ).
tff(c_63073,plain,
! [Z_39497,Z_39495,X3_39496,X3_39498] :
( ( just(arr(b,c)) != just(arr(Z_39497,c)) )
| ( just(Z_39495) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_39496) )
| ( just(arr(Z_39495,Z_39497)) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_39498) ) ),
inference(superposition,[status(thm),theory(equality)],[c_50,c_63067]) ).
tff(c_63092,plain,
! [Z_39514,X3_39515,X3_39516] :
( ( just(Z_39514) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_39515) )
| ( just(arr(Z_39514,b)) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_39516) ) ),
inference(reflexivity,[status(thm),theory(equality)],[c_63073]) ).
tff(c_63099,plain,
! [Z_39517,X3_39518] :
( ( just(a) != just(Z_39517) )
| ( just(arr(Z_39517,b)) != index(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),X3_39518) ) ),
inference(superposition,[status(thm),theory(equality)],[c_50,c_63092]) ).
tff(c_63109,plain,
! [Z_39520,N_39521] :
( ( just(a) != just(Z_39520) )
| ( just(arr(Z_39520,b)) != index(cons(arr(a,b),cons(arr(b,c),nil)),N_39521) ) ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_63099]) ).
tff(c_63117,plain,
! [Z_39520] :
( ( just(a) != just(Z_39520) )
| ( just(arr(a,b)) != just(arr(Z_39520,b)) ) ),
inference(superposition,[status(thm),theory(equality)],[c_50,c_63109]) ).
tff(c_63130,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_63117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWX219+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.16/0.35 % Computer : n002.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue May 5 12:22:46 EDT 2026
% 0.16/0.35 % CPUTime :
% 292.53/275.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 292.53/275.37
% 292.53/275.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------