%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET845-2 : 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/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 : n027.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 08:39:24 PM UTC 2025
% Result : Unsatisfiable 2.64s 1.67s
% Output : CNFRefutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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; 0-3 aty)
% Number of variables : 29 ( 29 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_Zorn_Osucc > c_Zorn_OTFin > c_Union > #nlpp > tc_set > 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(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(v_m,type,
v_m: $i ).
tff(f_49,axiom,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
file(unknown,unknown) ).
tff(f_46,axiom,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_45,axiom,
! [V_x,V_S,T_a] :
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file(unknown,unknown) ).
tff(f_47,axiom,
v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
file(unknown,unknown) ).
tff(f_30,axiom,
! [V_B,V_A,T_a] :
( ~ c_in(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) ),
file(unknown,unknown) ).
tff(f_40,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_38,axiom,
! [V_B,V_A,T_a] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) ),
file(unknown,unknown) ).
tff(c_14,plain,
c_Zorn_Osucc(v_S,v_m,t_a) != v_m,
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_10,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_48,plain,
! [V_S_26,V_x_27,T_a_28] :
( c_in(c_Zorn_Osucc(V_S_26,V_x_27,T_a_28),c_Zorn_OTFin(V_S_26,T_a_28),tc_set(tc_set(T_a_28)))
| ~ c_in(V_x_27,c_Zorn_OTFin(V_S_26,T_a_28),tc_set(tc_set(T_a_28))) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_12,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m,
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_20,plain,
! [V_B_16,V_A_17,T_a_18] :
( c_lessequals(V_B_16,c_Union(V_A_17,T_a_18),tc_set(T_a_18))
| ~ c_in(V_B_16,V_A_17,tc_set(T_a_18)) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_23,plain,
! [V_B_16] :
( c_lessequals(V_B_16,v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_B_16,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_20]) ).
tff(c_82,plain,
! [V_x_33] :
( c_lessequals(c_Zorn_Osucc(v_S,V_x_33,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_x_33,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_48,c_23]) ).
tff(c_6,plain,
! [V_x_7,V_S_8,T_a_9] : c_lessequals(V_x_7,c_Zorn_Osucc(V_S_8,V_x_7,T_a_9),tc_set(tc_set(T_a_9))),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_24,plain,
! [V_B_19,V_A_20,T_a_21] :
( ( V_B_19 = V_A_20 )
| ~ c_lessequals(V_A_20,V_B_19,tc_set(T_a_21))
| ~ c_lessequals(V_B_19,V_A_20,tc_set(T_a_21)) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_30,plain,
! [V_S_8,V_x_7,T_a_9] :
( ( c_Zorn_Osucc(V_S_8,V_x_7,T_a_9) = V_x_7 )
| ~ c_lessequals(c_Zorn_Osucc(V_S_8,V_x_7,T_a_9),V_x_7,tc_set(tc_set(T_a_9))) ),
inference(resolution,[status(thm)],[c_6,c_24]) ).
tff(c_86,plain,
( ( c_Zorn_Osucc(v_S,v_m,t_a) = v_m )
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_82,c_30]) ).
tff(c_91,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_86]) ).
tff(c_93,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET845-2 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 21:45:20 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.64/1.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.64/1.67
% 2.64/1.67 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------