%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET864-2 : 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 : n032.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 08:39:29 PM UTC 2025
% Result : Unsatisfiable 2.39s 1.58s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 9 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 39 ( 21 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_Zorn_Omaxchain > c_Union > #nlpp > v_x > tc_set > v_c > v_S > t_a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_S,type,
v_S: $i ).
tff(v_c,type,
v_c: $i ).
tff(tc_set,type,
tc_set: $i > $i ).
tff(t_a,type,
t_a: $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(v_x,type,
v_x: $i > $i ).
tff(c_Zorn_Omaxchain,type,
c_Zorn_Omaxchain: ( $i * $i ) > $i ).
tff(f_38,axiom,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
file(unknown,unknown) ).
tff(f_54,axiom,
! [V_U] :
( ( V_U != v_x(V_U) )
| ~ c_in(V_U,v_S,tc_set(t_a)) ),
file(unknown,unknown) ).
tff(f_37,axiom,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_43,axiom,
! [V_U] :
( c_in(v_x(V_U),v_S,tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) ),
file(unknown,unknown) ).
tff(f_48,axiom,
! [V_U] :
( c_lessequals(V_U,v_x(V_U),tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) ),
file(unknown,unknown) ).
tff(f_36,axiom,
! [V_u,V_S,T_a,V_c] :
( ~ c_in(V_u,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ( c_Union(V_c,T_a) = V_u ) ),
file(unknown,unknown) ).
tff(c_6,plain,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_13,plain,
! [V_U_8] :
( ~ c_in(V_U_8,v_S,tc_set(t_a))
| ( v_x(V_U_8) != V_U_8 ) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_17,plain,
v_x(c_Union(v_c,t_a)) != c_Union(v_c,t_a),
inference(resolution,[status(thm)],[c_6,c_13]) ).
tff(c_4,plain,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_8,plain,
! [V_U_5] :
( ~ c_in(V_U_5,v_S,tc_set(t_a))
| c_in(v_x(V_U_5),v_S,tc_set(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_10,plain,
! [V_U_6] :
( ~ c_in(V_U_6,v_S,tc_set(t_a))
| c_lessequals(V_U_6,v_x(V_U_6),tc_set(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_34,plain,
! [V_c_13,T_a_14,V_u_15,V_S_16] :
( ( c_Union(V_c_13,T_a_14) = V_u_15 )
| ~ c_lessequals(c_Union(V_c_13,T_a_14),V_u_15,tc_set(T_a_14))
| ~ c_in(V_c_13,c_Zorn_Omaxchain(V_S_16,T_a_14),tc_set(tc_set(T_a_14)))
| ~ c_in(V_u_15,V_S_16,tc_set(T_a_14)) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_39,plain,
! [V_c_17,V_S_18] :
( ( v_x(c_Union(V_c_17,t_a)) = c_Union(V_c_17,t_a) )
| ~ c_in(V_c_17,c_Zorn_Omaxchain(V_S_18,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x(c_Union(V_c_17,t_a)),V_S_18,tc_set(t_a))
| ~ c_in(c_Union(V_c_17,t_a),v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c_10,c_34]) ).
tff(c_45,plain,
! [V_c_19] :
( ( v_x(c_Union(V_c_19,t_a)) = c_Union(V_c_19,t_a) )
| ~ c_in(V_c_19,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Union(V_c_19,t_a),v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c_8,c_39]) ).
tff(c_48,plain,
( ( v_x(c_Union(v_c,t_a)) = c_Union(v_c,t_a) )
| ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c_4,c_45]) ).
tff(c_51,plain,
v_x(c_Union(v_c,t_a)) = c_Union(v_c,t_a),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_48]) ).
tff(c_53,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET864-2 : TPTP v9.0.0. Released v3.2.0.
% 0.02/0.10 % 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
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Apr 8 21:47:00 EDT 2025
% 0.10/0.29 % CPUTime :
% 2.39/1.58 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.39/1.58
% 2.39/1.58 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------