%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWX223+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 : n011.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 5.46s 2.39s
% Output : CNFRefutation 5.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 112 ( 44 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 147 ( 79 ~; 58 |; 3 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-3 aty)
% Number of variables : 121 ( 120 !; 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/sandbox/benchmark/theBenchmark.p',axiom_023) ).
tff(f_97,axiom,
! [X4] : nf(var(X4)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_024) ).
tff(f_101,axiom,
! [Z,Xs] : ( index(cons(Z,Xs),zero) = just(Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
tff(f_103,axiom,
! [Z,Xs,N] : ( index(cons(Z,Xs),suc(N)) = index(Xs,N) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_030) ).
tff(f_73,axiom,
! [X,X2,X3,X4] : ( app(X,X2,X3) != lam(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
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_95,axiom,
! [E] :
( nf(lam(E))
<=> nf(E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_033) ).
tff(f_135,negated_conjecture,
~ ? [E] :
( nf(E)
& tc(nil,E,arr(arr(a,arr(a,b)),arr(a,b))) ),
file('/export/starexec/sandbox/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_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_58,plain,
! [E_48] :
( nf(lam(E_48))
| ~ nf(E_48) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
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_331,plain,
! [Z_185,F_188,X_186,Tx_184,X2_187] :
( tc(X_186,app(F_188,X2_187,Tx_184),Z_185)
| ~ tc(X_186,X2_187,Tx_184)
| ~ tc(X_186,F_188,arr(Tx_184,Z_185)) ),
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(a,b)),arr(a,b)))
| ~ nf(E_75) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_314,plain,
! [E_182] :
( ~ nf(lam(E_182))
| ~ tc(cons(arr(a,arr(a,b)),nil),E_182,arr(a,b)) ),
inference(resolution,[status(thm)],[c_299,c_86]) ).
tff(c_323,plain,
! [E_65] :
( ~ nf(lam(lam(E_65)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),E_65,b) ),
inference(resolution,[status(thm)],[c_78,c_314]) ).
tff(c_467,plain,
! [F_213,X2_214,Tx_215] :
( ~ nf(lam(lam(app(F_213,X2_214,Tx_215))))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X2_214,Tx_215)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),F_213,arr(Tx_215,b)) ),
inference(resolution,[status(thm)],[c_331,c_323]) ).
tff(c_472,plain,
! [X2_216,Tx_217,F_218] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X2_216,Tx_217)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),F_218,arr(Tx_217,b))
| ~ nf(lam(app(F_218,X2_216,Tx_217))) ),
inference(resolution,[status(thm)],[c_58,c_467]) ).
tff(c_535,plain,
! [F_233,Z_234,X3_235] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),F_233,arr(Z_234,b))
| ~ nf(lam(app(F_233,var(X3_235),Z_234)))
| ( just(Z_234) != index(cons(a,cons(arr(a,arr(a,b)),nil)),X3_235) ) ),
inference(resolution,[status(thm)],[c_82,c_472]) ).
tff(c_1164,plain,
! [X2_545,Z_544,F_547,X3_546,Tx_543] :
( ~ nf(lam(app(app(F_547,X2_545,Tx_543),var(X3_546),Z_544)))
| ( just(Z_544) != index(cons(a,cons(arr(a,arr(a,b)),nil)),X3_546) )
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X2_545,Tx_543)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),F_547,arr(Tx_543,arr(Z_544,b))) ),
inference(resolution,[status(thm)],[c_68,c_535]) ).
tff(c_1330,plain,
! [X3_667,Tx_669,Z_671,X2_670,F_668] :
( ( just(Z_671) != index(cons(a,cons(arr(a,arr(a,b)),nil)),X3_667) )
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X2_670,Tx_669)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),F_668,arr(Tx_669,arr(Z_671,b)))
| ~ nf(app(app(F_668,X2_670,Tx_669),var(X3_667),Z_671)) ),
inference(resolution,[status(thm)],[c_58,c_1164]) ).
tff(c_1337,plain,
! [Z_672,X2_673,Tx_674,F_675] :
( ( just(a) != just(Z_672) )
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X2_673,Tx_674)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),F_675,arr(Tx_674,arr(Z_672,b)))
| ~ nf(app(app(F_675,X2_673,Tx_674),var(zero),Z_672)) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_1330]) ).
tff(c_1350,plain,
! [Z_676,F_677,Z_678,X3_679] :
( ( just(a) != just(Z_676) )
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),F_677,arr(Z_678,arr(Z_676,b)))
| ~ nf(app(app(F_677,var(X3_679),Z_678),var(zero),Z_676))
| ( just(Z_678) != index(cons(a,cons(arr(a,arr(a,b)),nil)),X3_679) ) ),
inference(resolution,[status(thm)],[c_82,c_1337]) ).
tff(c_1371,plain,
! [Z_684,X3_685,X3_686,Z_687] :
( ( just(a) != just(Z_684) )
| ~ nf(app(app(var(X3_685),var(X3_686),Z_687),var(zero),Z_684))
| ( just(Z_687) != index(cons(a,cons(arr(a,arr(a,b)),nil)),X3_686) )
| ( just(arr(Z_687,arr(Z_684,b))) != index(cons(a,cons(arr(a,arr(a,b)),nil)),X3_685) ) ),
inference(resolution,[status(thm)],[c_82,c_1350]) ).
tff(c_1375,plain,
! [X2_44,Z_687,X3_686,X3_685] :
( ( just(a) != just(X2_44) )
| ( just(Z_687) != index(cons(a,cons(arr(a,arr(a,b)),nil)),X3_686) )
| ( just(arr(Z_687,arr(X2_44,b))) != index(cons(a,cons(arr(a,arr(a,b)),nil)),X3_685) )
| ~ nf(var(zero))
| ~ nf(app(var(X3_685),var(X3_686),Z_687))
| ( lam(proj1Lam(app(var(X3_685),var(X3_686),Z_687))) = app(var(X3_685),var(X3_686),Z_687) ) ),
inference(resolution,[status(thm)],[c_48,c_1371]) ).
tff(c_1378,plain,
! [X2_44,Z_687,X3_686,X3_685] :
( ( just(a) != just(X2_44) )
| ( just(Z_687) != index(cons(a,cons(arr(a,arr(a,b)),nil)),X3_686) )
| ( just(arr(Z_687,arr(X2_44,b))) != index(cons(a,cons(arr(a,arr(a,b)),nil)),X3_685) )
| ~ nf(app(var(X3_685),var(X3_686),Z_687))
| ( lam(proj1Lam(app(var(X3_685),var(X3_686),Z_687))) = app(var(X3_685),var(X3_686),Z_687) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_1375]) ).
tff(c_1380,plain,
! [X2_688,Z_689,X3_690,X3_691] :
( ( just(a) != just(X2_688) )
| ( just(Z_689) != index(cons(a,cons(arr(a,arr(a,b)),nil)),X3_690) )
| ( just(arr(Z_689,arr(X2_688,b))) != index(cons(a,cons(arr(a,arr(a,b)),nil)),X3_691) )
| ~ nf(app(var(X3_691),var(X3_690),Z_689)) ),
inference(negUnitSimplification,[status(thm)],[c_42,c_1378]) ).
tff(c_1395,plain,
! [X2_698,Z_699,X3_700] :
( ( just(a) != just(X2_698) )
| ( just(a) != just(Z_699) )
| ( just(arr(Z_699,arr(X2_698,b))) != index(cons(a,cons(arr(a,arr(a,b)),nil)),X3_700) )
| ~ nf(app(var(X3_700),var(zero),Z_699)) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_1380]) ).
tff(c_1403,plain,
! [X2_703,Z_704,N_705] :
( ( just(a) != just(X2_703) )
| ( just(a) != just(Z_704) )
| ( just(arr(Z_704,arr(X2_703,b))) != index(cons(arr(a,arr(a,b)),nil),N_705) )
| ~ nf(app(var(suc(N_705)),var(zero),Z_704)) ),
inference(superposition,[status(thm),theory(equality)],[c_66,c_1395]) ).
tff(c_1409,plain,
! [X2_703,Z_704] :
( ( just(a) != just(X2_703) )
| ( just(a) != just(Z_704) )
| ( just(arr(a,arr(a,b))) != just(arr(Z_704,arr(X2_703,b))) )
| ~ nf(app(var(suc(zero)),var(zero),Z_704)) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_1403]) ).
tff(c_1427,plain,
~ nf(app(var(suc(zero)),var(zero),a)),
inference(reflexivity,[status(thm),theory(equality)],[c_1409]) ).
tff(c_1431,plain,
( ~ nf(var(zero))
| ~ nf(var(suc(zero)))
| ( lam(proj1Lam(var(suc(zero)))) = var(suc(zero)) ) ),
inference(resolution,[status(thm)],[c_48,c_1427]) ).
tff(c_1434,plain,
lam(proj1Lam(var(suc(zero)))) = var(suc(zero)),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_60,c_1431]) ).
tff(c_1436,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_1434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX223+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.13 % 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
% 0.15/0.33 % Computer : n011.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 12:35:47 EDT 2026
% 0.15/0.34 % CPUTime :
% 5.46/2.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.46/2.39
% 5.46/2.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------