%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL798-1 : 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 : n012.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 11:12:46 AM UTC 2026
% Result : Unsatisfiable 4.11s 1.80s
% Output : CNFRefutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 13 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 12 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 13 con; 0-4 aty)
% Number of variables : 9 ( 9 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Type_Otyping > 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_Type_Oshift > c_List_Olist_OCons > 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_ua______ > v_u____ > v_rs____ > v_n____ > v_i____ > v_e____ > v_as____ > v_a____ > v_T____ > v_T_H_H____ > tc_nat > tc_Type_Otype > tc_Lambda_OdB
%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(tc_Type_Otype,type,
tc_Type_Otype: $i ).
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(v_rs____,type,
v_rs____: $i ).
tff(c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: ( $i * $i ) > $i ).
tff(v_ua______,type,
v_ua______: $i ).
tff(c_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(c_Type_Oshift,type,
c_Type_Oshift: ( $i * $i * $i * $i ) > $i ).
tff(v_n____,type,
v_n____: $i ).
tff(c_Type_Otyping,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(v_e____,type,
v_e____: $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(class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_List_Olist_OCons,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(c_Lambda_Osko__Lambda__Xbeta__cases__2__1,type,
c_Lambda_Osko__Lambda__Xbeta__cases__2__1: ( $i * $i ) > $i ).
tff(v_T____,type,
v_T____: $i ).
tff(v_i____,type,
v_i____: $i ).
tff(v_as____,type,
v_as____: $i ).
tff(v_a____,type,
v_a____: $i ).
tff(v_u____,type,
v_u____: $i ).
tff(v_T_H_H____,type,
v_T_H_H____: $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_385,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file(unknown,unknown) ).
tff(f_386,axiom,
c_InductTermi_OIT(v_u____),
file(unknown,unknown) ).
tff(f_387,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
file(unknown,unknown) ).
tff(f_384,axiom,
! [V_u,V_i,V_e,V_T_H] :
( c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_u,V_i))
| ~ c_Type_Otyping(V_e,V_u,v_T____)
| ~ c_InductTermi_OIT(V_u)
| ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),v_a____,V_T_H) ),
file(unknown,unknown) ).
tff(f_389,axiom,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),
file(unknown,unknown) ).
tff(c_142,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_144,plain,
c_InductTermi_OIT(v_u____),
inference(cnfTransformation,[status(thm)],[f_386]) ).
tff(c_146,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
inference(cnfTransformation,[status(thm)],[f_387]) ).
tff(c_1641,plain,
! [V_e_420,V_i_421,V_T_H_422,V_u_423] :
( ~ c_Type_Otyping(c_Type_Oshift(V_e_420,V_i_421,v_T____,tc_Type_Otype),v_a____,V_T_H_422)
| ~ c_InductTermi_OIT(V_u_423)
| ~ c_Type_Otyping(V_e_420,V_u_423,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_u_423,V_i_421)) ),
inference(cnfTransformation,[status(thm)],[f_384]) ).
tff(c_1670,plain,
! [V_u_442] :
( ~ c_InductTermi_OIT(V_u_442)
| ~ c_Type_Otyping(v_e____,V_u_442,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_a____,V_u_442,v_i____)) ),
inference(resolution,[status(thm)],[c_146,c_1641]) ).
tff(c_148,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_a____,v_u____,v_i____)),
inference(cnfTransformation,[status(thm)],[f_389]) ).
tff(c_1673,plain,
( ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____) ),
inference(resolution,[status(thm)],[c_1670,c_148]) ).
tff(c_1677,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_142,c_144,c_1673]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL798-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % 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
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Sat Sep 5 20:42:12 UTC 2026
% 0.02/0.30 % CPUTime :
% 4.11/1.80 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.11/1.81
% 4.11/1.81 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------