TSTP Solution File: SET831-2 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET831-2 : TPTP v8.1.2. 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 : n006.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 : Tue Aug 22 10:57:06 EDT 2023
% Result : Unsatisfiable 6.57s 2.67s
% Output : CNFRefutation 6.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 23
% Syntax : Number of formulae : 149 ( 55 unt; 10 typ; 0 def)
% Number of atoms : 258 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 224 ( 105 ~; 119 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 5 >; 8 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 163 (; 163 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_inter > c_Main_OsubsetI__1 > #nlpp > tc_set > v_x > v_Z > v_Y > v_X > t_a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(v_X,type,
v_X: $i ).
tff(tc_set,type,
tc_set: $i > $i ).
tff(t_a,type,
t_a: $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_inter,type,
c_inter: ( $i * $i * $i ) > $i ).
tff(v_Y,type,
v_Y: $i ).
tff(v_Z,type,
v_Z: $i ).
tff(f_102,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_31,axiom,
( ( v_X = c_inter(v_Y,v_Z,t_a) )
| c_lessequals(v_X,v_Z,tc_set(t_a)) ),
file(unknown,unknown) ).
tff(f_41,axiom,
( c_lessequals(v_x,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ( v_X != c_inter(v_Y,v_Z,t_a) ) ),
file(unknown,unknown) ).
tff(f_77,axiom,
! [V_c,V_A,V_B,T_a] :
( ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
| c_in(V_c,V_B,T_a) ),
file(unknown,unknown) ).
tff(f_107,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_82,axiom,
! [V_c,V_A,V_B,T_a] :
( ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
| c_in(V_c,V_A,T_a) ),
file(unknown,unknown) ).
tff(f_62,axiom,
( ~ c_lessequals(v_x,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ( v_X != c_inter(v_Y,v_Z,t_a) ) ),
file(unknown,unknown) ).
tff(f_98,axiom,
! [V_c,V_A,T_a,V_B] :
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) ),
file(unknown,unknown) ).
tff(f_51,axiom,
( c_lessequals(v_x,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ( v_X != c_inter(v_Y,v_Z,t_a) ) ),
file(unknown,unknown) ).
tff(f_90,axiom,
! [V_c,V_B,T_a,V_A] :
( ~ c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_72,axiom,
! [V_U] :
( ( v_X = c_inter(v_Y,v_Z,t_a) )
| c_lessequals(V_U,v_X,tc_set(t_a))
| ~ c_lessequals(V_U,v_Z,tc_set(t_a))
| ~ c_lessequals(V_U,v_Y,tc_set(t_a)) ),
file(unknown,unknown) ).
tff(f_115,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_28,axiom,
( ( v_X = c_inter(v_Y,v_Z,t_a) )
| c_lessequals(v_X,v_Y,tc_set(t_a)) ),
file(unknown,unknown) ).
tff(c_22,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_102]) ).
tff(c_4,plain,
( c_lessequals(v_X,v_Z,tc_set(t_a))
| ( c_inter(v_Y,v_Z,t_a) = v_X ) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_27,plain,
c_inter(v_Y,v_Z,t_a) = v_X,
inference(splitLeft,[status(thm)],[c_4]) ).
tff(c_6,plain,
( ( c_inter(v_Y,v_Z,t_a) != v_X )
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Y,tc_set(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_183,plain,
( ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Y,tc_set(t_a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_27,c_6]) ).
tff(c_184,plain,
~ c_lessequals(v_X,v_Z,tc_set(t_a)),
inference(splitLeft,[status(thm)],[c_183]) ).
tff(c_192,plain,
c_in(c_Main_OsubsetI__1(v_X,v_Z,t_a),v_X,t_a),
inference(resolution,[status(thm)],[c_22,c_184]) ).
tff(c_38,plain,
! [V_c_32,V_B_33,T_a_34,V_A_35] :
( c_in(V_c_32,V_B_33,T_a_34)
| ~ c_in(V_c_32,c_inter(V_A_35,V_B_33,T_a_34),T_a_34) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_41,plain,
! [V_c_32] :
( c_in(V_c_32,v_Z,t_a)
| ~ c_in(V_c_32,v_X,t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_27,c_38]) ).
tff(c_54,plain,
! [V_A_40,V_B_41,T_a_42] :
( c_lessequals(V_A_40,V_B_41,tc_set(T_a_42))
| ~ c_in(c_Main_OsubsetI__1(V_A_40,V_B_41,T_a_42),V_B_41,T_a_42) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_65,plain,
! [V_A_40] :
( c_lessequals(V_A_40,v_Z,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(V_A_40,v_Z,t_a),v_X,t_a) ),
inference(resolution,[status(thm)],[c_41,c_54]) ).
tff(c_191,plain,
~ c_in(c_Main_OsubsetI__1(v_X,v_Z,t_a),v_X,t_a),
inference(resolution,[status(thm)],[c_65,c_184]) ).
tff(c_194,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_192,c_191]) ).
tff(c_196,plain,
c_lessequals(v_X,v_Z,tc_set(t_a)),
inference(splitRight,[status(thm)],[c_183]) ).
tff(c_195,plain,
( ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| c_lessequals(v_x,v_Y,tc_set(t_a)) ),
inference(splitRight,[status(thm)],[c_183]) ).
tff(c_207,plain,
~ c_lessequals(v_X,v_Y,tc_set(t_a)),
inference(splitLeft,[status(thm)],[c_195]) ).
tff(c_215,plain,
c_in(c_Main_OsubsetI__1(v_X,v_Y,t_a),v_X,t_a),
inference(resolution,[status(thm)],[c_22,c_207]) ).
tff(c_33,plain,
! [V_c_27,V_A_28,T_a_29,V_B_30] :
( c_in(V_c_27,V_A_28,T_a_29)
| ~ c_in(V_c_27,c_inter(V_A_28,V_B_30,T_a_29),T_a_29) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_36,plain,
! [V_c_27] :
( c_in(V_c_27,v_Y,t_a)
| ~ c_in(V_c_27,v_X,t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_27,c_33]) ).
tff(c_66,plain,
! [V_A_40] :
( c_lessequals(V_A_40,v_Y,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(V_A_40,v_Y,t_a),v_X,t_a) ),
inference(resolution,[status(thm)],[c_36,c_54]) ).
tff(c_214,plain,
~ c_in(c_Main_OsubsetI__1(v_X,v_Y,t_a),v_X,t_a),
inference(resolution,[status(thm)],[c_66,c_207]) ).
tff(c_227,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_215,c_214]) ).
tff(c_229,plain,
c_lessequals(v_X,v_Y,tc_set(t_a)),
inference(splitRight,[status(thm)],[c_195]) ).
tff(c_10,plain,
( ( c_inter(v_Y,v_Z,t_a) != v_X )
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_x,v_X,tc_set(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_260,plain,
~ c_lessequals(v_x,v_X,tc_set(t_a)),
inference(demodulation,[status(thm),theory(equality)],[c_196,c_229,c_27,c_10]) ).
tff(c_264,plain,
c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_x,t_a),
inference(resolution,[status(thm)],[c_22,c_260]) ).
tff(c_228,plain,
c_lessequals(v_x,v_Y,tc_set(t_a)),
inference(splitRight,[status(thm)],[c_195]) ).
tff(c_20,plain,
! [V_c_14,V_B_17,T_a_16,V_A_15] :
( c_in(V_c_14,V_B_17,T_a_16)
| ~ c_lessequals(V_A_15,V_B_17,tc_set(T_a_16))
| ~ c_in(V_c_14,V_A_15,T_a_16) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_293,plain,
! [V_c_64] :
( c_in(V_c_64,v_Y,t_a)
| ~ c_in(V_c_64,v_x,t_a) ),
inference(resolution,[status(thm)],[c_228,c_20]) ).
tff(c_299,plain,
c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_Y,t_a),
inference(resolution,[status(thm)],[c_264,c_293]) ).
tff(c_8,plain,
( ( c_inter(v_Y,v_Z,t_a) != v_X )
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Z,tc_set(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_274,plain,
c_lessequals(v_x,v_Z,tc_set(t_a)),
inference(demodulation,[status(thm),theory(equality)],[c_196,c_229,c_27,c_8]) ).
tff(c_300,plain,
! [V_c_65] :
( c_in(V_c_65,v_Z,t_a)
| ~ c_in(V_c_65,v_x,t_a) ),
inference(resolution,[status(thm)],[c_274,c_20]) ).
tff(c_306,plain,
c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_Z,t_a),
inference(resolution,[status(thm)],[c_264,c_300]) ).
tff(c_113,plain,
! [V_c_57,V_A_58,V_B_59,T_a_60] :
( c_in(V_c_57,c_inter(V_A_58,V_B_59,T_a_60),T_a_60)
| ~ c_in(V_c_57,V_A_58,T_a_60)
| ~ c_in(V_c_57,V_B_59,T_a_60) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_125,plain,
! [V_c_57] :
( c_in(V_c_57,v_X,t_a)
| ~ c_in(V_c_57,v_Y,t_a)
| ~ c_in(V_c_57,v_Z,t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_27,c_113]) ).
tff(c_309,plain,
( c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_X,t_a)
| ~ c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_Y,t_a) ),
inference(resolution,[status(thm)],[c_306,c_125]) ).
tff(c_312,plain,
c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_X,t_a),
inference(demodulation,[status(thm),theory(equality)],[c_299,c_309]) ).
tff(c_24,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_107]) ).
tff(c_314,plain,
c_lessequals(v_x,v_X,tc_set(t_a)),
inference(resolution,[status(thm)],[c_312,c_24]) ).
tff(c_318,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_260,c_314]) ).
tff(c_320,plain,
c_inter(v_Y,v_Z,t_a) != v_X,
inference(splitRight,[status(thm)],[c_4]) ).
tff(c_324,plain,
! [V_A_74,V_B_75,T_a_76] :
( c_lessequals(V_A_74,V_B_75,tc_set(T_a_76))
| c_in(c_Main_OsubsetI__1(V_A_74,V_B_75,T_a_76),V_A_74,T_a_76) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_16,plain,
! [V_c_6,V_A_7,T_a_9,V_B_8] :
( c_in(V_c_6,V_A_7,T_a_9)
| ~ c_in(V_c_6,c_inter(V_A_7,V_B_8,T_a_9),T_a_9) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_899,plain,
! [V_A_126,V_B_127,T_a_128,V_B_129] :
( c_in(c_Main_OsubsetI__1(c_inter(V_A_126,V_B_127,T_a_128),V_B_129,T_a_128),V_A_126,T_a_128)
| c_lessequals(c_inter(V_A_126,V_B_127,T_a_128),V_B_129,tc_set(T_a_128)) ),
inference(resolution,[status(thm)],[c_324,c_16]) ).
tff(c_943,plain,
! [V_A_126,V_B_127,T_a_128] : c_lessequals(c_inter(V_A_126,V_B_127,T_a_128),V_A_126,tc_set(T_a_128)),
inference(resolution,[status(thm)],[c_899,c_24]) ).
tff(c_14,plain,
! [V_c_2,V_B_4,T_a_5,V_A_3] :
( c_in(V_c_2,V_B_4,T_a_5)
| ~ c_in(V_c_2,c_inter(V_A_3,V_B_4,T_a_5),T_a_5) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_952,plain,
! [V_A_130,V_B_131,T_a_132,V_B_133] :
( c_in(c_Main_OsubsetI__1(c_inter(V_A_130,V_B_131,T_a_132),V_B_133,T_a_132),V_B_131,T_a_132)
| c_lessequals(c_inter(V_A_130,V_B_131,T_a_132),V_B_133,tc_set(T_a_132)) ),
inference(resolution,[status(thm)],[c_324,c_14]) ).
tff(c_1029,plain,
! [V_A_137,V_B_138,T_a_139] : c_lessequals(c_inter(V_A_137,V_B_138,T_a_139),V_B_138,tc_set(T_a_139)),
inference(resolution,[status(thm)],[c_952,c_24]) ).
tff(c_12,plain,
! [V_U_1] :
( ~ c_lessequals(V_U_1,v_Y,tc_set(t_a))
| ~ c_lessequals(V_U_1,v_Z,tc_set(t_a))
| c_lessequals(V_U_1,v_X,tc_set(t_a))
| ( c_inter(v_Y,v_Z,t_a) = v_X ) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_417,plain,
! [V_U_1] :
( ~ c_lessequals(V_U_1,v_Y,tc_set(t_a))
| ~ c_lessequals(V_U_1,v_Z,tc_set(t_a))
| c_lessequals(V_U_1,v_X,tc_set(t_a)) ),
inference(negUnitSimplification,[status(thm)],[c_320,c_12]) ).
tff(c_1145,plain,
! [V_A_152] :
( ~ c_lessequals(c_inter(V_A_152,v_Z,t_a),v_Y,tc_set(t_a))
| c_lessequals(c_inter(V_A_152,v_Z,t_a),v_X,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c_1029,c_417]) ).
tff(c_1162,plain,
c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(t_a)),
inference(resolution,[status(thm)],[c_943,c_1145]) ).
tff(c_26,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_115]) ).
tff(c_1221,plain,
( ( c_inter(v_Y,v_Z,t_a) = v_X )
| ~ c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)) ),
inference(resolution,[status(thm)],[c_1162,c_26]) ).
tff(c_1228,plain,
~ c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)),
inference(negUnitSimplification,[status(thm)],[c_320,c_1221]) ).
tff(c_996,plain,
! [V_A_130,V_B_131,T_a_132] : c_lessequals(c_inter(V_A_130,V_B_131,T_a_132),V_B_131,tc_set(T_a_132)),
inference(resolution,[status(thm)],[c_952,c_24]) ).
tff(c_1005,plain,
! [V_A_134,V_B_135,T_a_136] : c_lessequals(c_inter(V_A_134,V_B_135,T_a_136),V_A_134,tc_set(T_a_136)),
inference(resolution,[status(thm)],[c_899,c_24]) ).
tff(c_2176,plain,
! [V_B_193] :
( ~ c_lessequals(c_inter(v_Z,V_B_193,t_a),v_Y,tc_set(t_a))
| c_lessequals(c_inter(v_Z,V_B_193,t_a),v_X,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c_1005,c_417]) ).
tff(c_2200,plain,
c_lessequals(c_inter(v_Z,v_Y,t_a),v_X,tc_set(t_a)),
inference(resolution,[status(thm)],[c_996,c_2176]) ).
tff(c_2213,plain,
( ( c_inter(v_Z,v_Y,t_a) = v_X )
| ~ c_lessequals(v_X,c_inter(v_Z,v_Y,t_a),tc_set(t_a)) ),
inference(resolution,[status(thm)],[c_2200,c_26]) ).
tff(c_2284,plain,
~ c_lessequals(v_X,c_inter(v_Z,v_Y,t_a),tc_set(t_a)),
inference(splitLeft,[status(thm)],[c_2213]) ).
tff(c_2292,plain,
c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Z,v_Y,t_a),t_a),v_X,t_a),
inference(resolution,[status(thm)],[c_22,c_2284]) ).
tff(c_2,plain,
( c_lessequals(v_X,v_Y,tc_set(t_a))
| ( c_inter(v_Y,v_Z,t_a) = v_X ) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_321,plain,
c_lessequals(v_X,v_Y,tc_set(t_a)),
inference(negUnitSimplification,[status(thm)],[c_320,c_2]) ).
tff(c_362,plain,
! [V_c_85,V_B_86,T_a_87,V_A_88] :
( c_in(V_c_85,V_B_86,T_a_87)
| ~ c_lessequals(V_A_88,V_B_86,tc_set(T_a_87))
| ~ c_in(V_c_85,V_A_88,T_a_87) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_373,plain,
! [V_c_85] :
( c_in(V_c_85,v_Y,t_a)
| ~ c_in(V_c_85,v_X,t_a) ),
inference(resolution,[status(thm)],[c_321,c_362]) ).
tff(c_519,plain,
! [V_c_103,V_B_104,T_a_105,V_A_106] :
( c_in(V_c_103,V_B_104,T_a_105)
| ~ c_in(V_c_103,V_A_106,T_a_105)
| c_in(c_Main_OsubsetI__1(V_A_106,V_B_104,T_a_105),V_A_106,T_a_105) ),
inference(resolution,[status(thm)],[c_22,c_362]) ).
tff(c_1573,plain,
! [V_A_169,V_B_170,T_a_171,V_B_172] :
( c_in(c_Main_OsubsetI__1(V_A_169,V_B_170,T_a_171),V_B_172,T_a_171)
| c_in(c_Main_OsubsetI__1(V_A_169,V_B_172,T_a_171),V_A_169,T_a_171)
| c_lessequals(V_A_169,V_B_170,tc_set(T_a_171)) ),
inference(resolution,[status(thm)],[c_22,c_519]) ).
tff(c_380,plain,
! [V_c_89,V_A_90,V_B_91,T_a_92] :
( c_in(V_c_89,c_inter(V_A_90,V_B_91,T_a_92),T_a_92)
| ~ c_in(V_c_89,V_A_90,T_a_92)
| ~ c_in(V_c_89,V_B_91,T_a_92) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_1166,plain,
! [V_A_153,V_A_154,V_B_155,T_a_156] :
( c_lessequals(V_A_153,c_inter(V_A_154,V_B_155,T_a_156),tc_set(T_a_156))
| ~ c_in(c_Main_OsubsetI__1(V_A_153,c_inter(V_A_154,V_B_155,T_a_156),T_a_156),V_A_154,T_a_156)
| ~ c_in(c_Main_OsubsetI__1(V_A_153,c_inter(V_A_154,V_B_155,T_a_156),T_a_156),V_B_155,T_a_156) ),
inference(resolution,[status(thm)],[c_380,c_24]) ).
tff(c_1215,plain,
! [V_A_18,V_B_155,T_a_20] :
( ~ c_in(c_Main_OsubsetI__1(V_A_18,c_inter(V_A_18,V_B_155,T_a_20),T_a_20),V_B_155,T_a_20)
| c_lessequals(V_A_18,c_inter(V_A_18,V_B_155,T_a_20),tc_set(T_a_20)) ),
inference(resolution,[status(thm)],[c_22,c_1166]) ).
tff(c_2003,plain,
! [V_A_186,V_B_187,T_a_188] :
( c_in(c_Main_OsubsetI__1(V_A_186,V_B_187,T_a_188),V_A_186,T_a_188)
| c_lessequals(V_A_186,c_inter(V_A_186,V_B_187,T_a_188),tc_set(T_a_188)) ),
inference(resolution,[status(thm)],[c_1573,c_1215]) ).
tff(c_1028,plain,
! [V_A_134,V_B_135,T_a_136] :
( ( c_inter(V_A_134,V_B_135,T_a_136) = V_A_134 )
| ~ c_lessequals(V_A_134,c_inter(V_A_134,V_B_135,T_a_136),tc_set(T_a_136)) ),
inference(resolution,[status(thm)],[c_1005,c_26]) ).
tff(c_2036,plain,
! [V_A_186,V_B_187,T_a_188] :
( ( c_inter(V_A_186,V_B_187,T_a_188) = V_A_186 )
| c_in(c_Main_OsubsetI__1(V_A_186,V_B_187,T_a_188),V_A_186,T_a_188) ),
inference(resolution,[status(thm)],[c_2003,c_1028]) ).
tff(c_341,plain,
! [V_B_82,V_A_83,T_a_84] :
( ( V_B_82 = V_A_83 )
| ~ c_lessequals(V_A_83,V_B_82,tc_set(T_a_84))
| ~ c_lessequals(V_B_82,V_A_83,tc_set(T_a_84)) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_354,plain,
! [V_B_19,V_A_18,T_a_20] :
( ( V_B_19 = V_A_18 )
| ~ c_lessequals(V_B_19,V_A_18,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(resolution,[status(thm)],[c_22,c_341]) ).
tff(c_1217,plain,
( ( c_inter(v_Y,v_Z,t_a) = v_X )
| c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_X,t_a) ),
inference(resolution,[status(thm)],[c_1162,c_354]) ).
tff(c_1224,plain,
c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_X,t_a),
inference(negUnitSimplification,[status(thm)],[c_320,c_1217]) ).
tff(c_319,plain,
c_lessequals(v_X,v_Z,tc_set(t_a)),
inference(splitRight,[status(thm)],[c_4]) ).
tff(c_393,plain,
! [V_c_93] :
( c_in(V_c_93,v_Z,t_a)
| ~ c_in(V_c_93,v_X,t_a) ),
inference(resolution,[status(thm)],[c_319,c_362]) ).
tff(c_403,plain,
! [V_A_95] :
( c_lessequals(V_A_95,v_Z,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(V_A_95,v_Z,t_a),v_X,t_a) ),
inference(resolution,[status(thm)],[c_393,c_24]) ).
tff(c_408,plain,
! [V_c_14,V_A_95] :
( c_in(V_c_14,v_Z,t_a)
| ~ c_in(V_c_14,V_A_95,t_a)
| ~ c_in(c_Main_OsubsetI__1(V_A_95,v_Z,t_a),v_X,t_a) ),
inference(resolution,[status(thm)],[c_403,c_20]) ).
tff(c_1244,plain,
( c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Z,t_a)
| ~ c_in(c_Main_OsubsetI__1(v_X,v_Z,t_a),v_X,t_a) ),
inference(resolution,[status(thm)],[c_1224,c_408]) ).
tff(c_2560,plain,
~ c_in(c_Main_OsubsetI__1(v_X,v_Z,t_a),v_X,t_a),
inference(splitLeft,[status(thm)],[c_1244]) ).
tff(c_2574,plain,
c_inter(v_X,v_Z,t_a) = v_X,
inference(resolution,[status(thm)],[c_2036,c_2560]) ).
tff(c_334,plain,
! [V_A_3,V_B_4,T_a_76,V_B_75] :
( c_in(c_Main_OsubsetI__1(c_inter(V_A_3,V_B_4,T_a_76),V_B_75,T_a_76),V_B_4,T_a_76)
| c_lessequals(c_inter(V_A_3,V_B_4,T_a_76),V_B_75,tc_set(T_a_76)) ),
inference(resolution,[status(thm)],[c_324,c_14]) ).
tff(c_2618,plain,
! [V_B_75] :
( c_in(c_Main_OsubsetI__1(c_inter(v_X,v_Z,t_a),V_B_75,t_a),v_Z,t_a)
| c_lessequals(v_X,V_B_75,tc_set(t_a)) ),
inference(superposition,[status(thm),theory(equality)],[c_2574,c_334]) ).
tff(c_2655,plain,
! [V_B_205] :
( c_in(c_Main_OsubsetI__1(v_X,V_B_205,t_a),v_Z,t_a)
| c_lessequals(v_X,V_B_205,tc_set(t_a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2574,c_2618]) ).
tff(c_2687,plain,
c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Z,v_Y,t_a),t_a),v_Z,t_a),
inference(resolution,[status(thm)],[c_2655,c_2284]) ).
tff(c_390,plain,
! [V_A_21,V_A_90,V_B_91,T_a_92] :
( c_lessequals(V_A_21,c_inter(V_A_90,V_B_91,T_a_92),tc_set(T_a_92))
| ~ c_in(c_Main_OsubsetI__1(V_A_21,c_inter(V_A_90,V_B_91,T_a_92),T_a_92),V_A_90,T_a_92)
| ~ c_in(c_Main_OsubsetI__1(V_A_21,c_inter(V_A_90,V_B_91,T_a_92),T_a_92),V_B_91,T_a_92) ),
inference(resolution,[status(thm)],[c_380,c_24]) ).
tff(c_2796,plain,
( c_lessequals(v_X,c_inter(v_Z,v_Y,t_a),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Z,v_Y,t_a),t_a),v_Y,t_a) ),
inference(resolution,[status(thm)],[c_2687,c_390]) ).
tff(c_2807,plain,
~ c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Z,v_Y,t_a),t_a),v_Y,t_a),
inference(negUnitSimplification,[status(thm)],[c_2284,c_2796]) ).
tff(c_2815,plain,
~ c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Z,v_Y,t_a),t_a),v_X,t_a),
inference(resolution,[status(thm)],[c_373,c_2807]) ).
tff(c_2819,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2292,c_2815]) ).
tff(c_2820,plain,
c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Z,t_a),
inference(splitRight,[status(thm)],[c_1244]) ).
tff(c_2821,plain,
c_in(c_Main_OsubsetI__1(v_X,v_Z,t_a),v_X,t_a),
inference(splitRight,[status(thm)],[c_1244]) ).
tff(c_398,plain,
! [V_c_94] :
( c_in(V_c_94,v_Y,t_a)
| ~ c_in(V_c_94,v_X,t_a) ),
inference(resolution,[status(thm)],[c_321,c_362]) ).
tff(c_410,plain,
! [V_A_96] :
( c_lessequals(V_A_96,v_Y,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(V_A_96,v_Y,t_a),v_X,t_a) ),
inference(resolution,[status(thm)],[c_398,c_24]) ).
tff(c_415,plain,
! [V_c_14,V_A_96] :
( c_in(V_c_14,v_Y,t_a)
| ~ c_in(V_c_14,V_A_96,t_a)
| ~ c_in(c_Main_OsubsetI__1(V_A_96,v_Y,t_a),v_X,t_a) ),
inference(resolution,[status(thm)],[c_410,c_20]) ).
tff(c_2880,plain,
( c_in(c_Main_OsubsetI__1(v_X,v_Z,t_a),v_Y,t_a)
| ~ c_in(c_Main_OsubsetI__1(v_X,v_Y,t_a),v_X,t_a) ),
inference(resolution,[status(thm)],[c_2821,c_415]) ).
tff(c_2921,plain,
~ c_in(c_Main_OsubsetI__1(v_X,v_Y,t_a),v_X,t_a),
inference(splitLeft,[status(thm)],[c_2880]) ).
tff(c_2934,plain,
c_inter(v_X,v_Y,t_a) = v_X,
inference(resolution,[status(thm)],[c_2036,c_2921]) ).
tff(c_3049,plain,
! [V_B_75] :
( c_in(c_Main_OsubsetI__1(c_inter(v_X,v_Y,t_a),V_B_75,t_a),v_Y,t_a)
| c_lessequals(v_X,V_B_75,tc_set(t_a)) ),
inference(superposition,[status(thm),theory(equality)],[c_2934,c_334]) ).
tff(c_3085,plain,
! [V_B_217] :
( c_in(c_Main_OsubsetI__1(v_X,V_B_217,t_a),v_Y,t_a)
| c_lessequals(v_X,V_B_217,tc_set(t_a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2934,c_3049]) ).
tff(c_3118,plain,
c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Y,t_a),
inference(resolution,[status(thm)],[c_3085,c_1228]) ).
tff(c_3197,plain,
( c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Z,t_a) ),
inference(resolution,[status(thm)],[c_3118,c_390]) ).
tff(c_3206,plain,
c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)),
inference(demodulation,[status(thm),theory(equality)],[c_2820,c_3197]) ).
tff(c_3208,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1228,c_3206]) ).
tff(c_3210,plain,
c_in(c_Main_OsubsetI__1(v_X,v_Y,t_a),v_X,t_a),
inference(splitRight,[status(thm)],[c_2880]) ).
tff(c_1243,plain,
( c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Y,t_a)
| ~ c_in(c_Main_OsubsetI__1(v_X,v_Y,t_a),v_X,t_a) ),
inference(resolution,[status(thm)],[c_1224,c_415]) ).
tff(c_4057,plain,
c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Y,t_a),
inference(demodulation,[status(thm),theory(equality)],[c_3210,c_1243]) ).
tff(c_4059,plain,
( c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Z,t_a) ),
inference(resolution,[status(thm)],[c_4057,c_390]) ).
tff(c_4068,plain,
c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)),
inference(demodulation,[status(thm),theory(equality)],[c_2820,c_4059]) ).
tff(c_4070,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1228,c_4068]) ).
tff(c_4071,plain,
c_inter(v_Z,v_Y,t_a) = v_X,
inference(splitRight,[status(thm)],[c_2213]) ).
tff(c_333,plain,
! [V_A_7,V_B_8,T_a_76,V_B_75] :
( c_in(c_Main_OsubsetI__1(c_inter(V_A_7,V_B_8,T_a_76),V_B_75,T_a_76),V_A_7,T_a_76)
| c_lessequals(c_inter(V_A_7,V_B_8,T_a_76),V_B_75,tc_set(T_a_76)) ),
inference(resolution,[status(thm)],[c_324,c_16]) ).
tff(c_4118,plain,
! [V_B_75] :
( c_in(c_Main_OsubsetI__1(c_inter(v_Z,v_Y,t_a),V_B_75,t_a),v_Z,t_a)
| c_lessequals(v_X,V_B_75,tc_set(t_a)) ),
inference(superposition,[status(thm),theory(equality)],[c_4071,c_333]) ).
tff(c_4483,plain,
! [V_B_249] :
( c_in(c_Main_OsubsetI__1(v_X,V_B_249,t_a),v_Z,t_a)
| c_lessequals(v_X,V_B_249,tc_set(t_a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4071,c_4118]) ).
tff(c_4512,plain,
c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Z,t_a),
inference(resolution,[status(thm)],[c_4483,c_1228]) ).
tff(c_4114,plain,
! [V_B_75] :
( c_in(c_Main_OsubsetI__1(c_inter(v_Z,v_Y,t_a),V_B_75,t_a),v_Y,t_a)
| c_lessequals(v_X,V_B_75,tc_set(t_a)) ),
inference(superposition,[status(thm),theory(equality)],[c_4071,c_334]) ).
tff(c_4540,plain,
! [V_B_250] :
( c_in(c_Main_OsubsetI__1(v_X,V_B_250,t_a),v_Y,t_a)
| c_lessequals(v_X,V_B_250,tc_set(t_a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4071,c_4114]) ).
tff(c_4569,plain,
c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Y,t_a),
inference(resolution,[status(thm)],[c_4540,c_1228]) ).
tff(c_4583,plain,
( c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Z,t_a) ),
inference(resolution,[status(thm)],[c_4569,c_390]) ).
tff(c_4592,plain,
c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)),
inference(demodulation,[status(thm),theory(equality)],[c_4512,c_4583]) ).
tff(c_4594,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1228,c_4592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET831-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % 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
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 16:49:43 EDT 2023
% 0.14/0.36 % CPUTime :
% 6.57/2.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.57/2.69
% 6.57/2.69 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.57/2.74
% 6.57/2.74 Inference rules
% 6.57/2.74 ----------------------
% 6.57/2.74 #Ref : 0
% 6.57/2.74 #Sup : 1018
% 6.57/2.74 #Fact : 8
% 6.57/2.74 #Define : 0
% 6.57/2.74 #Split : 14
% 6.57/2.74 #Chain : 0
% 6.57/2.74 #Close : 0
% 6.57/2.74
% 6.57/2.74 Ordering : KBO
% 6.57/2.74
% 6.57/2.74 Simplification rules
% 6.57/2.74 ----------------------
% 6.57/2.74 #Subsume : 165
% 6.57/2.74 #Demod : 493
% 6.57/2.74 #Tautology : 309
% 6.57/2.74 #SimpNegUnit : 27
% 6.57/2.74 #BackRed : 4
% 6.57/2.74
% 6.57/2.74 #Partial instantiations: 0
% 6.57/2.74 #Strategies tried : 1
% 6.57/2.74
% 6.57/2.74 Timing (in seconds)
% 6.57/2.74 ----------------------
% 6.57/2.74 Preprocessing : 0.46
% 6.57/2.74 Parsing : 0.26
% 6.57/2.74 CNF conversion : 0.02
% 6.57/2.74 Main loop : 1.16
% 6.57/2.74 Inferencing : 0.44
% 6.57/2.74 Reduction : 0.33
% 6.57/2.74 Demodulation : 0.24
% 6.57/2.74 BG Simplification : 0.04
% 6.57/2.74 Subsumption : 0.27
% 6.57/2.74 Abstraction : 0.04
% 6.57/2.74 MUC search : 0.00
% 6.57/2.74 Cooper : 0.00
% 6.57/2.74 Total : 1.70
% 6.57/2.74 Index Insertion : 0.00
% 6.57/2.74 Index Deletion : 0.00
% 6.57/2.74 Index Matching : 0.00
% 6.57/2.74 BG Taut test : 0.00
%------------------------------------------------------------------------------