%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWX222+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 : n015.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 3.76s 1.91s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 10 |; 1 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-3 aty)
% Number of variables : 35 ( 34 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ tc > nf > 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(nf,type,
nf: $i > $o ).
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_101,axiom,
! [Z,Xs] : ( index(cons(Z,Xs),zero) = just(Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
tff(f_97,axiom,
! [X4] : nf(var(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
tff(f_95,axiom,
! [E] :
( nf(lam(E))
<=> nf(E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
tff(f_130,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_035) ).
tff(f_119,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_033) ).
tff(f_135,negated_conjecture,
~ ? [E] :
( nf(E)
& tc(nil,E,arr(a,arr(b,b))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_036) ).
tff(c_64,plain,
! [Z_51,Xs_52] : ( index(cons(Z_51,Xs_52),zero) = just(Z_51) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_60,plain,
! [X4_49] : nf(var(X4_49)),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_58,plain,
! [E_48] :
( nf(lam(E_48))
| ~ nf(E_48) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_82,plain,
! [X_71,X3_73,Z_72] :
( tc(X_71,var(X3_73),Z_72)
| ( just(Z_72) != index(X_71,X3_73) ) ),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_78,plain,
! [X_64,E_65,Tx2_66,T1_67] :
( tc(X_64,lam(E_65),arr(Tx2_66,T1_67))
| ~ tc(cons(Tx2_66,X_64),E_65,T1_67) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_299,plain,
! [X_174,E_175,Tx2_176,T1_177] :
( tc(X_174,lam(E_175),arr(Tx2_176,T1_177))
| ~ tc(cons(Tx2_176,X_174),E_175,T1_177) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_86,plain,
! [E_75] :
( ~ tc(nil,E_75,arr(a,arr(b,b)))
| ~ nf(E_75) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_314,plain,
! [E_182] :
( ~ nf(lam(E_182))
| ~ tc(cons(a,nil),E_182,arr(b,b)) ),
inference(resolution,[status(thm)],[c_299,c_86]) ).
tff(c_325,plain,
! [E_183] :
( ~ nf(lam(lam(E_183)))
| ~ tc(cons(b,cons(a,nil)),E_183,b) ),
inference(resolution,[status(thm)],[c_78,c_314]) ).
tff(c_338,plain,
! [X3_185] :
( ~ nf(lam(lam(var(X3_185))))
| ( index(cons(b,cons(a,nil)),X3_185) != just(b) ) ),
inference(resolution,[status(thm)],[c_82,c_325]) ).
tff(c_353,plain,
! [X3_187] :
( ( index(cons(b,cons(a,nil)),X3_187) != just(b) )
| ~ nf(lam(var(X3_187))) ),
inference(resolution,[status(thm)],[c_58,c_338]) ).
tff(c_356,plain,
! [X3_187] :
( ( index(cons(b,cons(a,nil)),X3_187) != just(b) )
| ~ nf(var(X3_187)) ),
inference(resolution,[status(thm)],[c_58,c_353]) ).
tff(c_360,plain,
! [X3_188] : ( index(cons(b,cons(a,nil)),X3_188) != just(b) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_356]) ).
tff(c_370,plain,
$false,
inference(superposition,[status(thm),theory(equality)],[c_64,c_360]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX222+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
% 0.15/0.34 % Computer : n015.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 12:34:01 EDT 2026
% 0.15/0.34 % CPUTime :
% 3.76/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.76/1.92
% 3.76/1.92 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------