%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET840-2 : 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 : n028.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 08:39:23 PM UTC 2025
% Result : Unsatisfiable 4.47s 2.11s
% Output : CNFRefutation 4.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 19 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 85 ( 37 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 4 ( 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 : 118 ( 118 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_insert > c_Main_OsubsetI__1 > c_Union > #nlpp > tc_set > v_S > t_b > c_emptyset
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_S,type,
v_S: $i ).
tff(tc_set,type,
tc_set: $i > $i ).
tff(c_emptyset,type,
c_emptyset: $i ).
tff(c_Main_OsubsetI__1,type,
c_Main_OsubsetI__1: ( $i * $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(t_b,type,
t_b: $i ).
tff(c_insert,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(f_48,axiom,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file(unknown,unknown) ).
tff(f_28,axiom,
! [V_U] : ~ c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
file(unknown,unknown) ).
tff(f_59,axiom,
! [V_A,V_B,T_a] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
file(unknown,unknown) ).
tff(f_46,axiom,
! [V_a,V_B,T_a,V_b] :
( ~ c_in(V_a,V_B,T_a)
| c_in(V_a,c_insert(V_b,V_B,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_64,axiom,
! [V_A,V_B,T_a] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
file(unknown,unknown) ).
tff(f_55,axiom,
! [V_a,V_b,V_A,T_a] :
( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| c_in(V_a,V_A,T_a)
| ( V_a = V_b ) ),
file(unknown,unknown) ).
tff(f_72,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(f_41,axiom,
! [V_A,V_X,T_a,V_C] :
( ~ c_in(V_A,V_X,T_a)
| ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_33,axiom,
! [V_U] :
( c_lessequals(c_Union(v_S,t_b),V_U,tc_set(t_b))
| ~ c_in(V_U,v_S,tc_set(t_b)) ),
file(unknown,unknown) ).
tff(c_10,plain,
! [V_x_11,V_B_12,T_a_13] : c_in(V_x_11,c_insert(V_x_11,V_B_12,T_a_13),T_a_13),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_2,plain,
! [V_U_1] : ~ c_lessequals(v_S,c_insert(V_U_1,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_14,plain,
! [V_A_18,V_B_19,T_a_20] :
( c_lessequals(V_A_18,V_B_19,tc_set(T_a_20))
| c_in(c_Main_OsubsetI__1(V_A_18,V_B_19,T_a_20),V_A_18,T_a_20) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_8,plain,
! [V_a_7,V_b_10,V_B_8,T_a_9] :
( c_in(V_a_7,c_insert(V_b_10,V_B_8,T_a_9),T_a_9)
| ~ c_in(V_a_7,V_B_8,T_a_9) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_27,plain,
! [V_A_39,V_B_40,T_a_41] :
( c_lessequals(V_A_39,V_B_40,tc_set(T_a_41))
| ~ c_in(c_Main_OsubsetI__1(V_A_39,V_B_40,T_a_41),V_B_40,T_a_41) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_151,plain,
! [V_A_66,V_b_67,V_B_68,T_a_69] :
( c_lessequals(V_A_66,c_insert(V_b_67,V_B_68,T_a_69),tc_set(T_a_69))
| ~ c_in(c_Main_OsubsetI__1(V_A_66,c_insert(V_b_67,V_B_68,T_a_69),T_a_69),V_B_68,T_a_69) ),
inference(resolution,[status(thm)],[c_8,c_27]) ).
tff(c_164,plain,
! [V_A_18,V_b_67,T_a_20] : c_lessequals(V_A_18,c_insert(V_b_67,V_A_18,T_a_20),tc_set(T_a_20)),
inference(resolution,[status(thm)],[c_14,c_151]) ).
tff(c_48,plain,
! [V_b_47,V_a_48,V_A_49,T_a_50] :
( ( V_b_47 = V_a_48 )
| c_in(V_a_48,V_A_49,T_a_50)
| ~ c_in(V_a_48,c_insert(V_b_47,V_A_49,T_a_50),T_a_50) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_281,plain,
! [V_b_105,V_A_106,T_a_107,V_B_108] :
( ( c_Main_OsubsetI__1(c_insert(V_b_105,V_A_106,T_a_107),V_B_108,T_a_107) = V_b_105 )
| c_in(c_Main_OsubsetI__1(c_insert(V_b_105,V_A_106,T_a_107),V_B_108,T_a_107),V_A_106,T_a_107)
| c_lessequals(c_insert(V_b_105,V_A_106,T_a_107),V_B_108,tc_set(T_a_107)) ),
inference(resolution,[status(thm)],[c_14,c_48]) ).
tff(c_16,plain,
! [V_A_21,V_B_22,T_a_23] :
( c_lessequals(V_A_21,V_B_22,tc_set(T_a_23))
| ~ c_in(c_Main_OsubsetI__1(V_A_21,V_B_22,T_a_23),V_B_22,T_a_23) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_322,plain,
! [V_b_109,V_A_110,T_a_111] :
( ( c_Main_OsubsetI__1(c_insert(V_b_109,V_A_110,T_a_111),V_A_110,T_a_111) = V_b_109 )
| c_lessequals(c_insert(V_b_109,V_A_110,T_a_111),V_A_110,tc_set(T_a_111)) ),
inference(resolution,[status(thm)],[c_281,c_16]) ).
tff(c_18,plain,
! [V_B_24,V_A_25,T_a_26] :
( ( V_B_24 = V_A_25 )
| ~ c_lessequals(V_A_25,V_B_24,tc_set(T_a_26))
| ~ c_lessequals(V_B_24,V_A_25,tc_set(T_a_26)) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_333,plain,
! [V_b_109,V_A_110,T_a_111] :
( ( c_insert(V_b_109,V_A_110,T_a_111) = V_A_110 )
| ~ c_lessequals(V_A_110,c_insert(V_b_109,V_A_110,T_a_111),tc_set(T_a_111))
| ( c_Main_OsubsetI__1(c_insert(V_b_109,V_A_110,T_a_111),V_A_110,T_a_111) = V_b_109 ) ),
inference(resolution,[status(thm)],[c_322,c_18]) ).
tff(c_341,plain,
! [V_b_112,V_A_113,T_a_114] :
( ( c_insert(V_b_112,V_A_113,T_a_114) = V_A_113 )
| ( c_Main_OsubsetI__1(c_insert(V_b_112,V_A_113,T_a_114),V_A_113,T_a_114) = V_b_112 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_164,c_333]) ).
tff(c_382,plain,
! [V_b_115,V_A_116,T_a_117] :
( c_lessequals(c_insert(V_b_115,V_A_116,T_a_117),V_A_116,tc_set(T_a_117))
| ~ c_in(V_b_115,V_A_116,T_a_117)
| ( c_insert(V_b_115,V_A_116,T_a_117) = V_A_116 ) ),
inference(superposition,[status(thm),theory(equality)],[c_341,c_16]) ).
tff(c_185,plain,
! [V_A_75,V_b_76,T_a_77] : c_lessequals(V_A_75,c_insert(V_b_76,V_A_75,T_a_77),tc_set(T_a_77)),
inference(resolution,[status(thm)],[c_14,c_151]) ).
tff(c_191,plain,
! [V_b_76,V_A_75,T_a_77] :
( ( c_insert(V_b_76,V_A_75,T_a_77) = V_A_75 )
| ~ c_lessequals(c_insert(V_b_76,V_A_75,T_a_77),V_A_75,tc_set(T_a_77)) ),
inference(resolution,[status(thm)],[c_185,c_18]) ).
tff(c_400,plain,
! [V_b_118,V_A_119,T_a_120] :
( ~ c_in(V_b_118,V_A_119,T_a_120)
| ( c_insert(V_b_118,V_A_119,T_a_120) = V_A_119 ) ),
inference(resolution,[status(thm)],[c_382,c_191]) ).
tff(c_438,plain,
! [V_A_18,V_B_19,T_a_20] :
( ( c_insert(c_Main_OsubsetI__1(V_A_18,V_B_19,T_a_20),V_A_18,T_a_20) = V_A_18 )
| c_lessequals(V_A_18,V_B_19,tc_set(T_a_20)) ),
inference(resolution,[status(thm)],[c_14,c_400]) ).
tff(c_63,plain,
! [V_A_51,V_C_52,T_a_53,V_X_54] :
( c_in(V_A_51,c_Union(V_C_52,T_a_53),T_a_53)
| ~ c_in(V_X_54,V_C_52,tc_set(T_a_53))
| ~ c_in(V_A_51,V_X_54,T_a_53) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_166,plain,
! [V_B_73,T_a_70,V_A_74,V_b_71,V_a_72] :
( c_in(V_A_74,c_Union(c_insert(V_b_71,V_B_73,tc_set(T_a_70)),T_a_70),T_a_70)
| ~ c_in(V_A_74,V_a_72,T_a_70)
| ~ c_in(V_a_72,V_B_73,tc_set(T_a_70)) ),
inference(resolution,[status(thm)],[c_8,c_63]) ).
tff(c_995,plain,
! [V_B_153,V_B_150,V_b_152,T_a_151,V_A_154] :
( c_in(c_Main_OsubsetI__1(V_A_154,V_B_150,T_a_151),c_Union(c_insert(V_b_152,V_B_153,tc_set(T_a_151)),T_a_151),T_a_151)
| ~ c_in(V_A_154,V_B_153,tc_set(T_a_151))
| c_lessequals(V_A_154,V_B_150,tc_set(T_a_151)) ),
inference(resolution,[status(thm)],[c_14,c_166]) ).
tff(c_1034,plain,
! [V_A_155,V_B_156,T_a_157,V_b_158] :
( ~ c_in(V_A_155,V_B_156,tc_set(T_a_157))
| c_lessequals(V_A_155,c_Union(c_insert(V_b_158,V_B_156,tc_set(T_a_157)),T_a_157),tc_set(T_a_157)) ),
inference(resolution,[status(thm)],[c_995,c_16]) ).
tff(c_1352,plain,
! [V_A_162,V_A_163,T_a_164,V_B_165] :
( ~ c_in(V_A_162,V_A_163,tc_set(T_a_164))
| c_lessequals(V_A_162,c_Union(V_A_163,T_a_164),tc_set(T_a_164))
| c_lessequals(V_A_163,V_B_165,tc_set(tc_set(T_a_164))) ),
inference(superposition,[status(thm),theory(equality)],[c_438,c_1034]) ).
tff(c_1394,plain,
! [V_A_166] :
( ~ c_in(V_A_166,v_S,tc_set(t_b))
| c_lessequals(V_A_166,c_Union(v_S,t_b),tc_set(t_b)) ),
inference(resolution,[status(thm)],[c_1352,c_2]) ).
tff(c_4,plain,
! [V_U_2] :
( ~ c_in(V_U_2,v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),V_U_2,tc_set(t_b)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_23,plain,
! [V_B_36,V_A_37,T_a_38] :
( ( V_B_36 = V_A_37 )
| ~ c_lessequals(V_A_37,V_B_36,tc_set(T_a_38))
| ~ c_lessequals(V_B_36,V_A_37,tc_set(T_a_38)) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_26,plain,
! [V_U_2] :
( ( c_Union(v_S,t_b) = V_U_2 )
| ~ c_lessequals(V_U_2,c_Union(v_S,t_b),tc_set(t_b))
| ~ c_in(V_U_2,v_S,tc_set(t_b)) ),
inference(resolution,[status(thm)],[c_4,c_23]) ).
tff(c_1413,plain,
! [V_A_167] :
( ( c_Union(v_S,t_b) = V_A_167 )
| ~ c_in(V_A_167,v_S,tc_set(t_b)) ),
inference(resolution,[status(thm)],[c_1394,c_26]) ).
tff(c_1439,plain,
! [V_B_168] :
( ( c_Main_OsubsetI__1(v_S,V_B_168,tc_set(t_b)) = c_Union(v_S,t_b) )
| c_lessequals(v_S,V_B_168,tc_set(tc_set(t_b))) ),
inference(resolution,[status(thm)],[c_14,c_1413]) ).
tff(c_1639,plain,
! [V_U_174] : ( c_Main_OsubsetI__1(v_S,c_insert(V_U_174,c_emptyset,tc_set(t_b)),tc_set(t_b)) = c_Union(v_S,t_b) ),
inference(resolution,[status(thm)],[c_1439,c_2]) ).
tff(c_1662,plain,
! [V_U_174] :
( c_lessequals(v_S,c_insert(V_U_174,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b)))
| ~ c_in(c_Union(v_S,t_b),c_insert(V_U_174,c_emptyset,tc_set(t_b)),tc_set(t_b)) ),
inference(superposition,[status(thm),theory(equality)],[c_1639,c_16]) ).
tff(c_1692,plain,
! [V_U_175] : ~ c_in(c_Union(v_S,t_b),c_insert(V_U_175,c_emptyset,tc_set(t_b)),tc_set(t_b)),
inference(negUnitSimplification,[status(thm)],[c_2,c_1662]) ).
tff(c_1716,plain,
$false,
inference(resolution,[status(thm)],[c_10,c_1692]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET840-2 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.13 % 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
% 0.14/0.34 % Computer : n028.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 21:44:34 EDT 2025
% 0.14/0.34 % CPUTime :
% 4.47/2.11 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.69/2.12
% 4.69/2.12 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------