%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWX221+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 : n021.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 11.00s 4.09s
% Output : CNFRefutation 11.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 175 ( 86 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 252 ( 139 ~; 103 |; 3 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-3 aty)
% Number of variables : 174 ( 173 !; 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_79,axiom,
! [X,X2] : ( lam(X) != var(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
tff(f_97,axiom,
! [X4] : nf(var(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
tff(f_88,axiom,
! [Y,Z,X2] :
( ( Y != lam(proj1Lam(Y)) )
=> ( nf(app(Y,Z,X2))
<=> ( nf(Y)
& nf(Z) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
tff(f_101,axiom,
! [Z,Xs] : ( index(cons(Z,Xs),zero) = just(Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
tff(f_103,axiom,
! [Z,Xs,N] : ( index(cons(Z,Xs),suc(N)) = index(Xs,N) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_030) ).
tff(f_73,axiom,
! [X,X2,X3,X4] : ( app(X,X2,X3) != lam(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
tff(f_95,axiom,
! [E] :
( nf(lam(E))
<=> nf(E) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_035) ).
tff(f_109,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_031) ).
tff(f_119,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_033) ).
tff(f_135,negated_conjecture,
~ ? [E] :
( nf(E)
& tc(nil,E,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_036) ).
tff(c_46,plain,
! [X2_41,X_40] : ( var(X2_41) != lam(X_40) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_60,plain,
! [X4_49] : nf(var(X4_49)),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_48,plain,
! [Y_42,Z_43,X2_44] :
( nf(app(Y_42,Z_43,X2_44))
| ~ nf(Z_43)
| ~ nf(Y_42)
| ( lam(proj1Lam(Y_42)) = Y_42 ) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
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_66,plain,
! [Z_53,Xs_54,N_55] : ( index(cons(Z_53,Xs_54),suc(N_55)) = index(Xs_54,N_55) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_42,plain,
! [X4_35,X_32,X2_33,X3_34] : ( lam(X4_35) != app(X_32,X2_33,X3_34) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
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_68,plain,
! [Tx_60,Z_57,X2_59,X_56,F_58] :
( tc(X_56,app(F_58,X2_59,Tx_60),Z_57)
| ~ tc(X_56,X2_59,Tx_60)
| ~ tc(X_56,F_58,arr(Tx_60,Z_57)) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
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(arr(a,arr(b,c)),arr(b,arr(a,c))))
| ~ nf(E_75) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_328,plain,
! [E_187] :
( ~ nf(lam(E_187))
| ~ tc(cons(arr(a,arr(b,c)),nil),E_187,arr(b,arr(a,c))) ),
inference(resolution,[status(thm)],[c_299,c_86]) ).
tff(c_344,plain,
! [E_188] :
( ~ nf(lam(lam(E_188)))
| ~ tc(cons(b,cons(arr(a,arr(b,c)),nil)),E_188,arr(a,c)) ),
inference(resolution,[status(thm)],[c_78,c_328]) ).
tff(c_375,plain,
! [E_193] :
( ~ nf(lam(lam(lam(E_193))))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),E_193,c) ),
inference(resolution,[status(thm)],[c_78,c_344]) ).
tff(c_644,plain,
! [F_256,X2_257,Tx_258] :
( ~ nf(lam(lam(lam(app(F_256,X2_257,Tx_258)))))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2_257,Tx_258)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_256,arr(Tx_258,c)) ),
inference(resolution,[status(thm)],[c_68,c_375]) ).
tff(c_649,plain,
! [X2_259,Tx_260,F_261] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2_259,Tx_260)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_261,arr(Tx_260,c))
| ~ nf(lam(lam(app(F_261,X2_259,Tx_260)))) ),
inference(resolution,[status(thm)],[c_58,c_644]) ).
tff(c_808,plain,
! [F_317,Z_318,X3_319] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_317,arr(Z_318,c))
| ~ nf(lam(lam(app(F_317,var(X3_319),Z_318))))
| ( just(Z_318) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_319) ) ),
inference(resolution,[status(thm)],[c_82,c_649]) ).
tff(c_2012,plain,
! [X2_935,Tx_933,F_937,Z_934,X3_936] :
( ~ nf(lam(lam(app(app(F_937,X2_935,Tx_933),var(X3_936),Z_934))))
| ( just(Z_934) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_936) )
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2_935,Tx_933)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_937,arr(Tx_933,arr(Z_934,c))) ),
inference(resolution,[status(thm)],[c_68,c_808]) ).
tff(c_2544,plain,
! [Tx_1288,Z_1287,X2_1286,X3_1284,F_1285] :
( ( just(Z_1287) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1284) )
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2_1286,Tx_1288)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_1285,arr(Tx_1288,arr(Z_1287,c)))
| ~ nf(lam(app(app(F_1285,X2_1286,Tx_1288),var(X3_1284),Z_1287))) ),
inference(resolution,[status(thm)],[c_58,c_2012]) ).
tff(c_2551,plain,
! [Z_1289,X2_1290,Tx_1291,F_1292] :
( ( just(a) != just(Z_1289) )
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2_1290,Tx_1291)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_1292,arr(Tx_1291,arr(Z_1289,c)))
| ~ nf(lam(app(app(F_1292,X2_1290,Tx_1291),var(zero),Z_1289))) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_2544]) ).
tff(c_2564,plain,
! [Z_1293,F_1294,Z_1295,X3_1296] :
( ( just(a) != just(Z_1293) )
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_1294,arr(Z_1295,arr(Z_1293,c)))
| ~ nf(lam(app(app(F_1294,var(X3_1296),Z_1295),var(zero),Z_1293)))
| ( just(Z_1295) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1296) ) ),
inference(resolution,[status(thm)],[c_82,c_2551]) ).
tff(c_2616,plain,
! [Z_1318,X3_1319,X3_1320,Z_1321] :
( ( just(a) != just(Z_1318) )
| ~ nf(lam(app(app(var(X3_1319),var(X3_1320),Z_1321),var(zero),Z_1318)))
| ( just(Z_1321) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1320) )
| ( just(arr(Z_1321,arr(Z_1318,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1319) ) ),
inference(resolution,[status(thm)],[c_82,c_2564]) ).
tff(c_2621,plain,
! [Z_1322,Z_1323,X3_1324,X3_1325] :
( ( just(a) != just(Z_1322) )
| ( just(Z_1323) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1324) )
| ( just(arr(Z_1323,arr(Z_1322,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1325) )
| ~ nf(app(app(var(X3_1325),var(X3_1324),Z_1323),var(zero),Z_1322)) ),
inference(resolution,[status(thm)],[c_58,c_2616]) ).
tff(c_2625,plain,
! [X2_44,Z_1323,X3_1324,X3_1325] :
( ( just(a) != just(X2_44) )
| ( just(Z_1323) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1324) )
| ( just(arr(Z_1323,arr(X2_44,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1325) )
| ~ nf(var(zero))
| ~ nf(app(var(X3_1325),var(X3_1324),Z_1323))
| ( lam(proj1Lam(app(var(X3_1325),var(X3_1324),Z_1323))) = app(var(X3_1325),var(X3_1324),Z_1323) ) ),
inference(resolution,[status(thm)],[c_48,c_2621]) ).
tff(c_2628,plain,
! [X2_44,Z_1323,X3_1324,X3_1325] :
( ( just(a) != just(X2_44) )
| ( just(Z_1323) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1324) )
| ( just(arr(Z_1323,arr(X2_44,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1325) )
| ~ nf(app(var(X3_1325),var(X3_1324),Z_1323))
| ( lam(proj1Lam(app(var(X3_1325),var(X3_1324),Z_1323))) = app(var(X3_1325),var(X3_1324),Z_1323) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_2625]) ).
tff(c_2630,plain,
! [X2_1326,Z_1327,X3_1328,X3_1329] :
( ( just(a) != just(X2_1326) )
| ( just(Z_1327) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1328) )
| ( just(arr(Z_1327,arr(X2_1326,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1329) )
| ~ nf(app(var(X3_1329),var(X3_1328),Z_1327)) ),
inference(negUnitSimplification,[status(thm)],[c_42,c_2628]) ).
tff(c_2650,plain,
! [X2_1335,Z_1336,X3_1337] :
( ( just(a) != just(X2_1335) )
| ( just(a) != just(Z_1336) )
| ( just(arr(Z_1336,arr(X2_1335,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1337) )
| ~ nf(app(var(X3_1337),var(zero),Z_1336)) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_2630]) ).
tff(c_2658,plain,
! [X2_1340,Z_1341,N_1342] :
( ( just(a) != just(X2_1340) )
| ( just(a) != just(Z_1341) )
| ( just(arr(Z_1341,arr(X2_1340,c))) != index(cons(b,cons(arr(a,arr(b,c)),nil)),N_1342) )
| ~ nf(app(var(suc(N_1342)),var(zero),Z_1341)) ),
inference(superposition,[status(thm),theory(equality)],[c_66,c_2650]) ).
tff(c_2666,plain,
! [X2_1345,Z_1346,N_1347] :
( ( just(a) != just(X2_1345) )
| ( just(a) != just(Z_1346) )
| ( just(arr(Z_1346,arr(X2_1345,c))) != index(cons(arr(a,arr(b,c)),nil),N_1347) )
| ~ nf(app(var(suc(suc(N_1347))),var(zero),Z_1346)) ),
inference(superposition,[status(thm),theory(equality)],[c_66,c_2658]) ).
tff(c_2672,plain,
! [X2_1345,Z_1346] :
( ( just(a) != just(X2_1345) )
| ( just(a) != just(Z_1346) )
| ( just(arr(a,arr(b,c))) != just(arr(Z_1346,arr(X2_1345,c))) )
| ~ nf(app(var(suc(suc(zero))),var(zero),Z_1346)) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_2666]) ).
tff(c_2696,plain,
( ( just(b) != just(a) )
| ~ nf(app(var(suc(suc(zero))),var(zero),a)) ),
inference(reflexivity,[status(thm),theory(equality)],[c_2672]) ).
tff(c_2698,plain,
~ nf(app(var(suc(suc(zero))),var(zero),a)),
inference(splitLeft,[status(thm)],[c_2696]) ).
tff(c_2701,plain,
( ~ nf(var(zero))
| ~ nf(var(suc(suc(zero))))
| ( lam(proj1Lam(var(suc(suc(zero))))) = var(suc(suc(zero))) ) ),
inference(resolution,[status(thm)],[c_48,c_2698]) ).
tff(c_2704,plain,
lam(proj1Lam(var(suc(suc(zero))))) = var(suc(suc(zero))),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_60,c_2701]) ).
tff(c_2706,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_2704]) ).
tff(c_2708,plain,
nf(app(var(suc(suc(zero))),var(zero),a)),
inference(splitRight,[status(thm)],[c_2696]) ).
tff(c_3212,plain,
! [Z_1657,Tx_1658,F_1659,N_1655,X2_1656] :
( ( just(Z_1657) != index(cons(b,cons(arr(a,arr(b,c)),nil)),N_1655) )
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2_1656,Tx_1658)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_1659,arr(Tx_1658,arr(Z_1657,c)))
| ~ nf(lam(app(app(F_1659,X2_1656,Tx_1658),var(suc(N_1655)),Z_1657))) ),
inference(superposition,[status(thm),theory(equality)],[c_66,c_2544]) ).
tff(c_3627,plain,
! [F_1939,Z_1937,N_1940,X3_1936,Z_1938] :
( ( just(Z_1938) != index(cons(b,cons(arr(a,arr(b,c)),nil)),N_1940) )
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),F_1939,arr(Z_1937,arr(Z_1938,c)))
| ~ nf(lam(app(app(F_1939,var(X3_1936),Z_1937),var(suc(N_1940)),Z_1938)))
| ( just(Z_1937) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_1936) ) ),
inference(resolution,[status(thm)],[c_82,c_3212]) ).
tff(c_4411,plain,
! [X3_2521,Z_2524,N_2523,X3_2522,Z_2525] :
( ( just(Z_2525) != index(cons(b,cons(arr(a,arr(b,c)),nil)),N_2523) )
| ~ nf(lam(app(app(var(X3_2521),var(X3_2522),Z_2524),var(suc(N_2523)),Z_2525)))
| ( just(Z_2524) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_2522) )
| ( just(arr(Z_2524,arr(Z_2525,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_2521) ) ),
inference(resolution,[status(thm)],[c_82,c_3627]) ).
tff(c_4429,plain,
! [Z_2539,X3_2536,X3_2538,Z_2537,N_2535] :
( ( just(Z_2539) != index(cons(b,cons(arr(a,arr(b,c)),nil)),N_2535) )
| ( just(Z_2537) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_2538) )
| ( just(arr(Z_2537,arr(Z_2539,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_2536) )
| ~ nf(app(app(var(X3_2536),var(X3_2538),Z_2537),var(suc(N_2535)),Z_2539)) ),
inference(resolution,[status(thm)],[c_58,c_4411]) ).
tff(c_4433,plain,
! [X2_44,X3_2536,X3_2538,Z_2537,N_2535] :
( ( just(X2_44) != index(cons(b,cons(arr(a,arr(b,c)),nil)),N_2535) )
| ( just(Z_2537) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_2538) )
| ( just(arr(Z_2537,arr(X2_44,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_2536) )
| ~ nf(var(suc(N_2535)))
| ~ nf(app(var(X3_2536),var(X3_2538),Z_2537))
| ( lam(proj1Lam(app(var(X3_2536),var(X3_2538),Z_2537))) = app(var(X3_2536),var(X3_2538),Z_2537) ) ),
inference(resolution,[status(thm)],[c_48,c_4429]) ).
tff(c_4436,plain,
! [X2_44,X3_2536,X3_2538,Z_2537,N_2535] :
( ( just(X2_44) != index(cons(b,cons(arr(a,arr(b,c)),nil)),N_2535) )
| ( just(Z_2537) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_2538) )
| ( just(arr(Z_2537,arr(X2_44,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_2536) )
| ~ nf(app(var(X3_2536),var(X3_2538),Z_2537))
| ( lam(proj1Lam(app(var(X3_2536),var(X3_2538),Z_2537))) = app(var(X3_2536),var(X3_2538),Z_2537) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_4433]) ).
tff(c_4438,plain,
! [Z_2542,N_2541,X3_2540,X3_2543,X2_2544] :
( ( just(X2_2544) != index(cons(b,cons(arr(a,arr(b,c)),nil)),N_2541) )
| ( just(Z_2542) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_2540) )
| ( just(arr(Z_2542,arr(X2_2544,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_2543) )
| ~ nf(app(var(X3_2543),var(X3_2540),Z_2542)) ),
inference(negUnitSimplification,[status(thm)],[c_42,c_4436]) ).
tff(c_4445,plain,
! [X2_2545,Z_2546,X3_2547,X3_2548] :
( ( just(b) != just(X2_2545) )
| ( just(Z_2546) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_2547) )
| ( just(arr(Z_2546,arr(X2_2545,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_2548) )
| ~ nf(app(var(X3_2548),var(X3_2547),Z_2546)) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_4438]) ).
tff(c_4465,plain,
! [X2_2555,Z_2556,X3_2557] :
( ( just(b) != just(X2_2555) )
| ( just(a) != just(Z_2556) )
| ( just(arr(Z_2556,arr(X2_2555,c))) != index(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3_2557) )
| ~ nf(app(var(X3_2557),var(zero),Z_2556)) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_4445]) ).
tff(c_4473,plain,
! [X2_2560,Z_2561,N_2562] :
( ( just(b) != just(X2_2560) )
| ( just(a) != just(Z_2561) )
| ( just(arr(Z_2561,arr(X2_2560,c))) != index(cons(b,cons(arr(a,arr(b,c)),nil)),N_2562) )
| ~ nf(app(var(suc(N_2562)),var(zero),Z_2561)) ),
inference(superposition,[status(thm),theory(equality)],[c_66,c_4465]) ).
tff(c_4481,plain,
! [X2_2565,Z_2566,N_2567] :
( ( just(b) != just(X2_2565) )
| ( just(a) != just(Z_2566) )
| ( just(arr(Z_2566,arr(X2_2565,c))) != index(cons(arr(a,arr(b,c)),nil),N_2567) )
| ~ nf(app(var(suc(suc(N_2567))),var(zero),Z_2566)) ),
inference(superposition,[status(thm),theory(equality)],[c_66,c_4473]) ).
tff(c_4487,plain,
! [X2_2565,Z_2566] :
( ( just(b) != just(X2_2565) )
| ( just(a) != just(Z_2566) )
| ( just(arr(a,arr(b,c))) != just(arr(Z_2566,arr(X2_2565,c))) )
| ~ nf(app(var(suc(suc(zero))),var(zero),Z_2566)) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_4481]) ).
tff(c_4504,plain,
~ nf(app(var(suc(suc(zero))),var(zero),a)),
inference(reflexivity,[status(thm),theory(equality)],[c_4487]) ).
tff(c_4508,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2708,c_4504]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SWX221+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.15 % 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
% 0.17/0.36 % Computer : n021.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Tue May 5 12:31:25 EDT 2026
% 0.17/0.36 % CPUTime :
% 11.00/4.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.00/4.10
% 11.00/4.10 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------