%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET859-2 : 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 : n010.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 08:39:28 PM UTC 2025
% Result : Unsatisfiable 2.49s 1.60s
% Output : CNFRefutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 18 ( 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_Zorn_Osucc > #nlpp > tc_set > v_n > v_m > v_S > t_a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_S,type,
v_S: $i ).
tff(tc_set,type,
tc_set: $i > $i ).
tff(c_Zorn_Osucc,type,
c_Zorn_Osucc: ( $i * $i * $i ) > $i ).
tff(v_n,type,
v_n: $i ).
tff(t_a,type,
t_a: $i ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(v_m,type,
v_m: $i ).
tff(f_38,axiom,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_36,axiom,
c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_35,axiom,
! [V_x,V_S,T_a] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
file(unknown,unknown) ).
tff(f_33,axiom,
! [V_B,V_C,T_a,V_A] :
( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) ),
file(unknown,unknown) ).
tff(c_8,plain,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_6,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_4,plain,
! [V_x_5,V_S_6,T_a_7] : c_lessequals(V_x_5,c_Zorn_Osucc(V_S_6,V_x_5,T_a_7),tc_set(tc_set(T_a_7))),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_10,plain,
! [V_A_11,V_C_12,T_a_13,V_B_14] :
( c_lessequals(V_A_11,V_C_12,tc_set(T_a_13))
| ~ c_lessequals(V_A_11,V_B_14,tc_set(T_a_13))
| ~ c_lessequals(V_B_14,V_C_12,tc_set(T_a_13)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_17,plain,
! [V_x_15,V_C_16,T_a_17,V_S_18] :
( c_lessequals(V_x_15,V_C_16,tc_set(tc_set(T_a_17)))
| ~ c_lessequals(c_Zorn_Osucc(V_S_18,V_x_15,T_a_17),V_C_16,tc_set(tc_set(T_a_17))) ),
inference(resolution,[status(thm)],[c_4,c_10]) ).
tff(c_24,plain,
c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[c_6,c_17]) ).
tff(c_29,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET859-2 : TPTP v9.0.0. Released v3.2.0.
% 0.10/0.13 % 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
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 21:47:18 EDT 2025
% 0.14/0.34 % CPUTime :
% 2.49/1.60 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.49/1.60
% 2.49/1.60 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------