%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET849-2 : 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 : n005.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 08:39:25 PM UTC 2025
% Result : Unsatisfiable 2.62s 1.86s
% Output : CNFRefutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 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 : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 18 ( 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_Zorn_Osucc > c_Zorn_OTFin > c_Union > #nlpp > tc_set > 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(t_a,type,
t_a: $i ).
tff(c_Zorn_OTFin,type,
c_Zorn_OTFin: ( $i * $i ) > $i ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(c_Union,type,
c_Union: ( $i * $i ) > $i ).
tff(f_27,axiom,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
file(unknown,unknown) ).
tff(f_32,axiom,
! [V_Y,V_S,T_a] :
( ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a))))
| c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file(unknown,unknown) ).
tff(f_37,axiom,
! [V_S,T_a] :
( ~ c_in(c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ( c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)) = c_Zorn_Osucc(V_S,c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),T_a) ) ),
file(unknown,unknown) ).
tff(f_39,axiom,
c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
file(unknown,unknown) ).
tff(c_2,plain,
! [V_A_1,T_a_2] : c_lessequals(V_A_1,V_A_1,tc_set(T_a_2)),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_4,plain,
! [V_Y_3,T_a_5,V_S_4] :
( c_in(c_Union(V_Y_3,tc_set(T_a_5)),c_Zorn_OTFin(V_S_4,T_a_5),tc_set(tc_set(T_a_5)))
| ~ c_lessequals(V_Y_3,c_Zorn_OTFin(V_S_4,T_a_5),tc_set(tc_set(tc_set(T_a_5)))) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_11,plain,
! [V_S_13,T_a_14] :
( ( c_Zorn_Osucc(V_S_13,c_Union(c_Zorn_OTFin(V_S_13,T_a_14),tc_set(T_a_14)),T_a_14) = c_Union(c_Zorn_OTFin(V_S_13,T_a_14),tc_set(T_a_14)) )
| ~ c_in(c_Union(c_Zorn_OTFin(V_S_13,T_a_14),tc_set(T_a_14)),c_Zorn_OTFin(V_S_13,T_a_14),tc_set(tc_set(T_a_14))) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_15,plain,
! [V_S_4,T_a_5] :
( ( c_Zorn_Osucc(V_S_4,c_Union(c_Zorn_OTFin(V_S_4,T_a_5),tc_set(T_a_5)),T_a_5) = c_Union(c_Zorn_OTFin(V_S_4,T_a_5),tc_set(T_a_5)) )
| ~ c_lessequals(c_Zorn_OTFin(V_S_4,T_a_5),c_Zorn_OTFin(V_S_4,T_a_5),tc_set(tc_set(tc_set(T_a_5)))) ),
inference(resolution,[status(thm)],[c_4,c_11]) ).
tff(c_18,plain,
! [V_S_4,T_a_5] : ( c_Zorn_Osucc(V_S_4,c_Union(c_Zorn_OTFin(V_S_4,T_a_5),tc_set(T_a_5)),T_a_5) = c_Union(c_Zorn_OTFin(V_S_4,T_a_5),tc_set(T_a_5)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_15]) ).
tff(c_8,plain,
c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_22,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET849-2 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.10 % 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
% 0.10/0.30 % Computer : n005.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Apr 8 21:45:12 EDT 2025
% 0.10/0.30 % CPUTime :
% 2.62/1.86 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.62/1.86
% 2.62/1.86 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------