%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET851-2 : 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 : n002.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 08:39:26 PM UTC 2025
% Result : Unsatisfiable 2.65s 1.62s
% Output : CNFRefutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 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; 4 con; 0-3 aty)
% Number of variables : 14 ( 14 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_Zorn_Osucc > c_Zorn_OTFin > #nlpp > tc_set > v_x > v_m > v_S > t_a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
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(v_m,type,
v_m: $i ).
tff(f_27,axiom,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
file(unknown,unknown) ).
tff(f_40,axiom,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
file(unknown,unknown) ).
tff(f_32,axiom,
! [V_x,V_y,T_a,V_S] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) ),
file(unknown,unknown) ).
tff(f_37,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_33,axiom,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_50,axiom,
! [V_U] :
( c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
file(unknown,unknown) ).
tff(f_35,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(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_12,plain,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_21,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))),
inference(splitLeft,[status(thm)],[c_12]) ).
tff(c_16,plain,
! [V_x_10,V_S_11,V_y_12,T_a_13] :
( c_lessequals(V_x_10,c_Zorn_Osucc(V_S_11,V_y_12,T_a_13),tc_set(tc_set(T_a_13)))
| ~ c_lessequals(V_x_10,V_y_12,tc_set(tc_set(T_a_13))) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_10,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_20,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[c_16,c_10]) ).
tff(c_23,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_21,c_20]) ).
tff(c_24,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(splitRight,[status(thm)],[c_12]) ).
tff(c_6,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_26,plain,
! [V_U_14] :
( ~ c_in(V_U_14,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U_14,v_m,tc_set(tc_set(t_a)))
| ( v_m = V_U_14 )
| c_lessequals(c_Zorn_Osucc(v_S,V_U_14,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_8,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_29,plain,
( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| ( v_x = v_m ) ),
inference(resolution,[status(thm)],[c_26,c_8]) ).
tff(c_32,plain,
v_x = v_m,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_6,c_29]) ).
tff(c_34,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_10]) ).
tff(c_40,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET851-2 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.13 % 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
% 0.13/0.33 % Computer : n002.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 : Tue Apr 8 21:46:17 EDT 2025
% 0.13/0.33 % CPUTime :
% 2.65/1.62 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.65/1.62
% 2.65/1.62 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------