%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL853-1 : 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 3.30s 2.18s
% Output : CNFRefutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 2
% Syntax : Number of formulae : 5 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 5 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_HOL_Oord__class_Oless > class_Ring__and__Field_Oordered__idom > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > c_InductTermi_OIT > c_Lambda_Osubst > c_Lambda_Olift > c_Lambda_OdB_OApp > #nlpp > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > v_ta____ > v_s____ > 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(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(v_s____,type,
v_s____: $i ).
tff(f_254,axiom,
~ c_InductTermi_OIT(v_s____),
file(unknown,unknown) ).
tff(f_239,axiom,
c_InductTermi_OIT(v_s____),
file(unknown,unknown) ).
tff(c_88,plain,
~ c_InductTermi_OIT(v_s____),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_78,plain,
c_InductTermi_OIT(v_s____),
inference(cnfTransformation,[status(thm)],[f_239]) ).
tff(c_95,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_88,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL853-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % 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
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 00:35:09 UTC 2026
% 0.11/0.38 % CPUTime :
% 3.30/2.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.30/2.18
% 3.30/2.18 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------