%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV254-2 : TPTP v9.0.0. Released v3.2.0.
% 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 : n007.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 : Wed Apr 9 09:29:54 PM UTC 2025
% Result : Unsatisfiable 2.64s 1.64s
% Output : CNFRefutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 21 ( 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > class_Orderings_Oorder > c_insert > c_SetInterval_OatLeastLessThan > #nlpp > v_x > c_Suc > v_nat > tc_nat > c_emptyset
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_emptyset,type,
c_emptyset: $i ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(c_Suc,type,
c_Suc: $i > $i ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(v_nat,type,
v_nat: $i ).
tff(tc_nat,type,
tc_nat: $i ).
tff(c_SetInterval_OatLeastLessThan,type,
c_SetInterval_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(v_x,type,
v_x: $i > $i ).
tff(c_insert,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(f_38,axiom,
! [V_a,V_A,T_a] : ( c_emptyset != c_insert(V_a,V_A,T_a) ),
file(unknown,unknown) ).
tff(f_43,axiom,
class_Orderings_Oorder(tc_nat),
file(unknown,unknown) ).
tff(f_42,axiom,
! [V_U] : ( v_x(V_U) = v_nat ),
file(unknown,unknown) ).
tff(f_40,axiom,
! [V_U] : c_lessequals(V_U,v_x(V_U),tc_nat),
file(unknown,unknown) ).
tff(f_33,axiom,
! [T_a,V_n,V_m] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_n,V_m,T_a)
| ( c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset ) ),
file(unknown,unknown) ).
tff(f_35,axiom,
! [V_m] : ( c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) ),
file(unknown,unknown) ).
tff(c_6,plain,
! [V_a_5,V_A_6,T_a_7] : ( c_insert(V_a_5,V_A_6,T_a_7) != c_emptyset ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_12,plain,
class_Orderings_Oorder(tc_nat),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_10,plain,
! [V_U_9] : ( v_x(V_U_9) = v_nat ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_8,plain,
! [V_U_8] : c_lessequals(V_U_8,v_x(V_U_8),tc_nat),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_13,plain,
! [V_U_8] : c_lessequals(V_U_8,v_nat,tc_nat),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8]) ).
tff(c_32,plain,
! [V_m_16,V_n_17,T_a_18] :
( ( c_SetInterval_OatLeastLessThan(V_m_16,V_n_17,T_a_18) = c_emptyset )
| ~ c_lessequals(V_n_17,V_m_16,T_a_18)
| ~ class_Orderings_Oorder(T_a_18) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_35,plain,
! [V_U_8] :
( ( c_SetInterval_OatLeastLessThan(v_nat,V_U_8,tc_nat) = c_emptyset )
| ~ class_Orderings_Oorder(tc_nat) ),
inference(resolution,[status(thm)],[c_13,c_32]) ).
tff(c_39,plain,
! [V_U_19] : ( c_SetInterval_OatLeastLessThan(v_nat,V_U_19,tc_nat) = c_emptyset ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_35]) ).
tff(c_4,plain,
! [V_m_4] : ( c_SetInterval_OatLeastLessThan(V_m_4,c_Suc(V_m_4),tc_nat) = c_insert(V_m_4,c_emptyset,tc_nat) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_45,plain,
c_insert(v_nat,c_emptyset,tc_nat) = c_emptyset,
inference(superposition,[status(thm),theory(equality)],[c_39,c_4]) ).
tff(c_54,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWV254-2 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.12 % 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
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Apr 9 02:54:24 EDT 2025
% 0.13/0.33 % CPUTime :
% 2.64/1.64 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.64/1.65
% 2.64/1.65 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------