%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL844-1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:12:53 AM UTC 2026
% Result : Unsatisfiable 4.38s 2.42s
% Output : CNFRefutation 4.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 2 ( 2 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_HOL_Oord__class_Oless > c_Lambda_Obeta > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__idom > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_Nat_Osemiring__char__0 > c_InductTermi_OIT > c_Lambda_Osubst > c_Nat_Osemiring__1__class_Oof__nat > c_Lambda_Osko__Lambda__Xbeta__cases__2__1 > c_Lambda_Olift > c_Lambda_OdB_OApp > #nlpp > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > v_ta______ > tc_nat
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_Lambda_Olift,type,
c_Lambda_Olift: ( $i * $i ) > $i ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_InductTermi_OIT,type,
c_InductTermi_OIT: $i > $o ).
tff(c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(c_Lambda_Obeta,type,
c_Lambda_Obeta: ( $i * $i ) > $o ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(c_Lambda_Osubst,type,
c_Lambda_Osubst: ( $i * $i * $i ) > $i ).
tff(c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: ( $i * $i ) > $i ).
tff(c_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(c_Lambda_OdB_OAbs,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(tc_nat,type,
tc_nat: $i ).
tff(v_ta______,type,
v_ta______: $i ).
tff(class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_Lambda_Osko__Lambda__Xbeta__cases__2__1,type,
c_Lambda_Osko__Lambda__Xbeta__cases__2__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(f_329,axiom,
c_InductTermi_OIT(v_ta______),
file(unknown,unknown) ).
tff(f_349,axiom,
! [V_r] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ),
file(unknown,unknown) ).
tff(f_356,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(v_ta______)),
file(unknown,unknown) ).
tff(c_112,plain,
c_InductTermi_OIT(v_ta______),
inference(cnfTransformation,[status(thm)],[f_329]) ).
tff(c_146,plain,
! [V_r_156] :
( ~ c_InductTermi_OIT(V_r_156)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r_156)) ),
inference(cnfTransformation,[status(thm)],[f_349]) ).
tff(c_126,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(v_ta______)),
inference(cnfTransformation,[status(thm)],[f_356]) ).
tff(c_149,plain,
~ c_InductTermi_OIT(v_ta______),
inference(resolution,[status(thm)],[c_146,c_126]) ).
tff(c_153,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_112,c_149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL844-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % 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
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 08:34:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 4.38/2.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.38/2.42
% 4.38/2.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------