TSTP Solution File: SET837-2 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET837-2 : 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 : 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 : Tue Aug 22 10:57:08 EDT 2023
% Result : Unsatisfiable 9.40s 3.28s
% Output : CNFRefutation 9.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 130 ( 54 unt; 10 typ; 0 def)
% Number of atoms : 219 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 190 ( 91 ~; 99 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 129 (; 129 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_union > 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_union,type,
c_union: ( $i * $i * $i ) > $i ).
tff(v_Y,type,
v_Y: $i ).
tff(v_Z,type,
v_Z: $i ).
tff(f_101,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_77,axiom,
! [V_c,V_B,T_a,V_A] :
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_106,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_89,axiom,
! [V_c,V_A,V_B,T_a] :
( ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a) ),
file(unknown,unknown) ).
tff(f_114,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_31,axiom,
( ( v_X = c_union(v_Y,v_Z,t_a) )
| c_lessequals(v_Z,v_X,tc_set(t_a)) ),
file(unknown,unknown) ).
tff(f_62,axiom,
( ~ c_lessequals(v_X,v_x,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ( v_X != c_union(v_Y,v_Z,t_a) ) ),
file(unknown,unknown) ).
tff(f_41,axiom,
( c_lessequals(v_Y,v_x,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ( v_X != c_union(v_Y,v_Z,t_a) ) ),
file(unknown,unknown) ).
tff(f_82,axiom,
! [V_c,V_A,T_a,V_B] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_51,axiom,
( c_lessequals(v_Z,v_x,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ( v_X != c_union(v_Y,v_Z,t_a) ) ),
file(unknown,unknown) ).
tff(f_97,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_72,axiom,
! [V_U] :
( ( v_X = c_union(v_Y,v_Z,t_a) )
| c_lessequals(v_X,V_U,tc_set(t_a))
| ~ c_lessequals(v_Z,V_U,tc_set(t_a))
| ~ c_lessequals(v_Y,V_U,tc_set(t_a)) ),
file(unknown,unknown) ).
tff(f_28,axiom,
( ( v_X = c_union(v_Y,v_Z,t_a) )
| c_lessequals(v_Y,v_X,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_101]) ).
tff(c_14,plain,
! [V_c_2,V_A_5,V_B_3,T_a_4] :
( c_in(V_c_2,c_union(V_A_5,V_B_3,T_a_4),T_a_4)
| ~ c_in(V_c_2,V_B_3,T_a_4) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_447,plain,
! [V_A_84,V_B_85,T_a_86] :
( c_lessequals(V_A_84,V_B_85,tc_set(T_a_86))
| ~ c_in(c_Main_OsubsetI__1(V_A_84,V_B_85,T_a_86),V_B_85,T_a_86) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_833,plain,
! [V_A_131,V_A_132,V_B_133,T_a_134] :
( c_lessequals(V_A_131,c_union(V_A_132,V_B_133,T_a_134),tc_set(T_a_134))
| ~ c_in(c_Main_OsubsetI__1(V_A_131,c_union(V_A_132,V_B_133,T_a_134),T_a_134),V_B_133,T_a_134) ),
inference(resolution,[status(thm)],[c_14,c_447]) ).
tff(c_859,plain,
! [V_A_18,V_A_132,T_a_20] : c_lessequals(V_A_18,c_union(V_A_132,V_A_18,T_a_20),tc_set(T_a_20)),
inference(resolution,[status(thm)],[c_22,c_833]) ).
tff(c_504,plain,
! [V_c_100,V_A_101,T_a_102,V_B_103] :
( c_in(V_c_100,V_A_101,T_a_102)
| c_in(V_c_100,V_B_103,T_a_102)
| ~ c_in(V_c_100,c_union(V_A_101,V_B_103,T_a_102),T_a_102) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_1236,plain,
! [V_A_160,V_B_161,T_a_162,V_B_163] :
( c_in(c_Main_OsubsetI__1(c_union(V_A_160,V_B_161,T_a_162),V_B_163,T_a_162),V_A_160,T_a_162)
| c_in(c_Main_OsubsetI__1(c_union(V_A_160,V_B_161,T_a_162),V_B_163,T_a_162),V_B_161,T_a_162)
| c_lessequals(c_union(V_A_160,V_B_161,T_a_162),V_B_163,tc_set(T_a_162)) ),
inference(resolution,[status(thm)],[c_22,c_504]) ).
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_106]) ).
tff(c_1349,plain,
! [V_A_166,V_B_167,T_a_168] :
( c_in(c_Main_OsubsetI__1(c_union(V_A_166,V_B_167,T_a_168),V_B_167,T_a_168),V_A_166,T_a_168)
| c_lessequals(c_union(V_A_166,V_B_167,T_a_168),V_B_167,tc_set(T_a_168)) ),
inference(resolution,[status(thm)],[c_1236,c_24]) ).
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_114]) ).
tff(c_1381,plain,
! [V_A_166,V_B_167,T_a_168] :
( ( c_union(V_A_166,V_B_167,T_a_168) = V_B_167 )
| ~ c_lessequals(V_B_167,c_union(V_A_166,V_B_167,T_a_168),tc_set(T_a_168))
| c_in(c_Main_OsubsetI__1(c_union(V_A_166,V_B_167,T_a_168),V_B_167,T_a_168),V_A_166,T_a_168) ),
inference(resolution,[status(thm)],[c_1349,c_26]) ).
tff(c_2138,plain,
! [V_A_203,V_B_204,T_a_205] :
( ( c_union(V_A_203,V_B_204,T_a_205) = V_B_204 )
| c_in(c_Main_OsubsetI__1(c_union(V_A_203,V_B_204,T_a_205),V_B_204,T_a_205),V_A_203,T_a_205) ),
inference(demodulation,[status(thm),theory(equality)],[c_859,c_1381]) ).
tff(c_4,plain,
( c_lessequals(v_Z,v_X,tc_set(t_a))
| ( c_union(v_Y,v_Z,t_a) = v_X ) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_27,plain,
c_union(v_Y,v_Z,t_a) = v_X,
inference(splitLeft,[status(thm)],[c_4]) ).
tff(c_10,plain,
( ( c_union(v_Y,v_Z,t_a) != v_X )
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_114,plain,
( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_27,c_10]) ).
tff(c_115,plain,
~ c_lessequals(v_X,v_x,tc_set(t_a)),
inference(splitLeft,[status(thm)],[c_114]) ).
tff(c_119,plain,
c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_X,t_a),
inference(resolution,[status(thm)],[c_22,c_115]) ).
tff(c_87,plain,
! [V_c_55,V_A_56,T_a_57,V_B_58] :
( c_in(V_c_55,V_A_56,T_a_57)
| c_in(V_c_55,V_B_58,T_a_57)
| ~ c_in(V_c_55,c_union(V_A_56,V_B_58,T_a_57),T_a_57) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_100,plain,
! [V_c_55] :
( c_in(V_c_55,v_Y,t_a)
| c_in(V_c_55,v_Z,t_a)
| ~ c_in(V_c_55,v_X,t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_27,c_87]) ).
tff(c_6,plain,
( ( c_union(v_Y,v_Z,t_a) != v_X )
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_x,tc_set(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_137,plain,
( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_x,tc_set(t_a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_27,c_6]) ).
tff(c_138,plain,
~ c_lessequals(v_Z,v_X,tc_set(t_a)),
inference(splitLeft,[status(thm)],[c_137]) ).
tff(c_142,plain,
c_in(c_Main_OsubsetI__1(v_Z,v_X,t_a),v_Z,t_a),
inference(resolution,[status(thm)],[c_22,c_138]) ).
tff(c_38,plain,
! [V_c_32,V_A_33,V_B_34,T_a_35] :
( c_in(V_c_32,c_union(V_A_33,V_B_34,T_a_35),T_a_35)
| ~ c_in(V_c_32,V_B_34,T_a_35) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_41,plain,
! [V_c_32] :
( c_in(V_c_32,v_X,t_a)
| ~ c_in(V_c_32,v_Z,t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_27,c_38]) ).
tff(c_149,plain,
c_in(c_Main_OsubsetI__1(v_Z,v_X,t_a),v_X,t_a),
inference(resolution,[status(thm)],[c_142,c_41]) ).
tff(c_153,plain,
c_lessequals(v_Z,v_X,tc_set(t_a)),
inference(resolution,[status(thm)],[c_149,c_24]) ).
tff(c_158,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_138,c_153]) ).
tff(c_160,plain,
c_lessequals(v_Z,v_X,tc_set(t_a)),
inference(splitRight,[status(thm)],[c_137]) ).
tff(c_159,plain,
( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_x,tc_set(t_a)) ),
inference(splitRight,[status(thm)],[c_137]) ).
tff(c_171,plain,
~ c_lessequals(v_Y,v_X,tc_set(t_a)),
inference(splitLeft,[status(thm)],[c_159]) ).
tff(c_175,plain,
c_in(c_Main_OsubsetI__1(v_Y,v_X,t_a),v_Y,t_a),
inference(resolution,[status(thm)],[c_22,c_171]) ).
tff(c_33,plain,
! [V_c_27,V_A_28,V_B_29,T_a_30] :
( c_in(V_c_27,c_union(V_A_28,V_B_29,T_a_30),T_a_30)
| ~ c_in(V_c_27,V_A_28,T_a_30) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_36,plain,
! [V_c_27] :
( c_in(V_c_27,v_X,t_a)
| ~ c_in(V_c_27,v_Y,t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_27,c_33]) ).
tff(c_186,plain,
c_in(c_Main_OsubsetI__1(v_Y,v_X,t_a),v_X,t_a),
inference(resolution,[status(thm)],[c_175,c_36]) ).
tff(c_194,plain,
c_lessequals(v_Y,v_X,tc_set(t_a)),
inference(resolution,[status(thm)],[c_186,c_24]) ).
tff(c_199,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_171,c_194]) ).
tff(c_201,plain,
c_lessequals(v_Y,v_X,tc_set(t_a)),
inference(splitRight,[status(thm)],[c_159]) ).
tff(c_8,plain,
( ( c_union(v_Y,v_Z,t_a) != v_X )
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Z,v_x,tc_set(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_232,plain,
c_lessequals(v_Z,v_x,tc_set(t_a)),
inference(demodulation,[status(thm),theory(equality)],[c_160,c_201,c_27,c_8]) ).
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_97]) ).
tff(c_257,plain,
! [V_c_64] :
( c_in(V_c_64,v_x,t_a)
| ~ c_in(V_c_64,v_Z,t_a) ),
inference(resolution,[status(thm)],[c_232,c_20]) ).
tff(c_279,plain,
! [V_A_66] :
( c_lessequals(V_A_66,v_x,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(V_A_66,v_x,t_a),v_Z,t_a) ),
inference(resolution,[status(thm)],[c_257,c_24]) ).
tff(c_289,plain,
~ c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_Z,t_a),
inference(resolution,[status(thm)],[c_279,c_115]) ).
tff(c_295,plain,
( c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_Y,t_a)
| ~ c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_X,t_a) ),
inference(resolution,[status(thm)],[c_100,c_289]) ).
tff(c_298,plain,
c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_Y,t_a),
inference(demodulation,[status(thm),theory(equality)],[c_119,c_295]) ).
tff(c_200,plain,
c_lessequals(v_Y,v_x,tc_set(t_a)),
inference(splitRight,[status(thm)],[c_159]) ).
tff(c_271,plain,
! [V_c_65] :
( c_in(V_c_65,v_x,t_a)
| ~ c_in(V_c_65,v_Y,t_a) ),
inference(resolution,[status(thm)],[c_200,c_20]) ).
tff(c_353,plain,
! [V_A_74] :
( c_lessequals(V_A_74,v_x,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(V_A_74,v_x,t_a),v_Y,t_a) ),
inference(resolution,[status(thm)],[c_271,c_24]) ).
tff(c_356,plain,
~ c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_Y,t_a),
inference(resolution,[status(thm)],[c_353,c_115]) ).
tff(c_366,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_298,c_356]) ).
tff(c_367,plain,
( ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_Y,v_X,tc_set(t_a)) ),
inference(splitRight,[status(thm)],[c_114]) ).
tff(c_389,plain,
~ c_lessequals(v_Y,v_X,tc_set(t_a)),
inference(splitLeft,[status(thm)],[c_367]) ).
tff(c_393,plain,
c_in(c_Main_OsubsetI__1(v_Y,v_X,t_a),v_Y,t_a),
inference(resolution,[status(thm)],[c_22,c_389]) ).
tff(c_397,plain,
c_in(c_Main_OsubsetI__1(v_Y,v_X,t_a),v_X,t_a),
inference(resolution,[status(thm)],[c_393,c_36]) ).
tff(c_399,plain,
c_lessequals(v_Y,v_X,tc_set(t_a)),
inference(resolution,[status(thm)],[c_397,c_24]) ).
tff(c_403,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_389,c_399]) ).
tff(c_404,plain,
~ c_lessequals(v_Z,v_X,tc_set(t_a)),
inference(splitRight,[status(thm)],[c_367]) ).
tff(c_412,plain,
c_in(c_Main_OsubsetI__1(v_Z,v_X,t_a),v_Z,t_a),
inference(resolution,[status(thm)],[c_22,c_404]) ).
tff(c_425,plain,
c_in(c_Main_OsubsetI__1(v_Z,v_X,t_a),v_X,t_a),
inference(resolution,[status(thm)],[c_412,c_41]) ).
tff(c_434,plain,
c_lessequals(v_Z,v_X,tc_set(t_a)),
inference(resolution,[status(thm)],[c_425,c_24]) ).
tff(c_438,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_404,c_434]) ).
tff(c_439,plain,
c_lessequals(v_Z,v_X,tc_set(t_a)),
inference(splitRight,[status(thm)],[c_4]) ).
tff(c_488,plain,
! [V_c_95,V_B_96,T_a_97,V_A_98] :
( c_in(V_c_95,V_B_96,T_a_97)
| ~ c_lessequals(V_A_98,V_B_96,tc_set(T_a_97))
| ~ c_in(V_c_95,V_A_98,T_a_97) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_500,plain,
! [V_c_95] :
( c_in(V_c_95,v_X,t_a)
| ~ c_in(V_c_95,v_Z,t_a) ),
inference(resolution,[status(thm)],[c_439,c_488]) ).
tff(c_2851,plain,
! [V_B_223] :
( c_in(c_Main_OsubsetI__1(c_union(v_Z,V_B_223,t_a),V_B_223,t_a),v_X,t_a)
| ( c_union(v_Z,V_B_223,t_a) = V_B_223 ) ),
inference(resolution,[status(thm)],[c_2138,c_500]) ).
tff(c_2878,plain,
( c_lessequals(c_union(v_Z,v_X,t_a),v_X,tc_set(t_a))
| ( c_union(v_Z,v_X,t_a) = v_X ) ),
inference(resolution,[status(thm)],[c_2851,c_24]) ).
tff(c_2882,plain,
c_union(v_Z,v_X,t_a) = v_X,
inference(splitLeft,[status(thm)],[c_2878]) ).
tff(c_16,plain,
! [V_c_6,V_A_7,V_B_9,T_a_8] :
( c_in(V_c_6,c_union(V_A_7,V_B_9,T_a_8),T_a_8)
| ~ c_in(V_c_6,V_A_7,T_a_8) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_454,plain,
! [V_A_84,V_A_7,V_B_9,T_a_8] :
( c_lessequals(V_A_84,c_union(V_A_7,V_B_9,T_a_8),tc_set(T_a_8))
| ~ c_in(c_Main_OsubsetI__1(V_A_84,c_union(V_A_7,V_B_9,T_a_8),T_a_8),V_A_7,T_a_8) ),
inference(resolution,[status(thm)],[c_16,c_447]) ).
tff(c_2931,plain,
! [V_A_84] :
( c_lessequals(V_A_84,c_union(v_Z,v_X,t_a),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(V_A_84,v_X,t_a),v_Z,t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_2882,c_454]) ).
tff(c_3203,plain,
! [V_A_229] :
( c_lessequals(V_A_229,v_X,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(V_A_229,v_X,t_a),v_Z,t_a) ),
inference(demodulation,[status(thm),theory(equality)],[c_2882,c_2931]) ).
tff(c_440,plain,
c_union(v_Y,v_Z,t_a) != v_X,
inference(splitRight,[status(thm)],[c_4]) ).
tff(c_877,plain,
! [V_A_141,V_A_142,V_B_143,T_a_144] :
( c_lessequals(V_A_141,c_union(V_A_142,V_B_143,T_a_144),tc_set(T_a_144))
| ~ c_in(c_Main_OsubsetI__1(V_A_141,c_union(V_A_142,V_B_143,T_a_144),T_a_144),V_A_142,T_a_144) ),
inference(resolution,[status(thm)],[c_16,c_447]) ).
tff(c_903,plain,
! [V_A_18,V_B_143,T_a_20] : c_lessequals(V_A_18,c_union(V_A_18,V_B_143,T_a_20),tc_set(T_a_20)),
inference(resolution,[status(thm)],[c_22,c_877]) ).
tff(c_12,plain,
! [V_U_1] :
( ~ c_lessequals(v_Y,V_U_1,tc_set(t_a))
| ~ c_lessequals(v_Z,V_U_1,tc_set(t_a))
| c_lessequals(v_X,V_U_1,tc_set(t_a))
| ( c_union(v_Y,v_Z,t_a) = v_X ) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_907,plain,
! [V_U_145] :
( ~ c_lessequals(v_Y,V_U_145,tc_set(t_a))
| ~ c_lessequals(v_Z,V_U_145,tc_set(t_a))
| c_lessequals(v_X,V_U_145,tc_set(t_a)) ),
inference(negUnitSimplification,[status(thm)],[c_440,c_12]) ).
tff(c_1199,plain,
! [V_A_159] :
( ~ c_lessequals(v_Y,c_union(V_A_159,v_Z,t_a),tc_set(t_a))
| c_lessequals(v_X,c_union(V_A_159,v_Z,t_a),tc_set(t_a)) ),
inference(resolution,[status(thm)],[c_859,c_907]) ).
tff(c_1207,plain,
c_lessequals(v_X,c_union(v_Y,v_Z,t_a),tc_set(t_a)),
inference(resolution,[status(thm)],[c_903,c_1199]) ).
tff(c_1214,plain,
( ( c_union(v_Y,v_Z,t_a) = v_X )
| ~ c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c_1207,c_26]) ).
tff(c_1221,plain,
~ c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a)),
inference(negUnitSimplification,[status(thm)],[c_440,c_1214]) ).
tff(c_3241,plain,
~ c_in(c_Main_OsubsetI__1(c_union(v_Y,v_Z,t_a),v_X,t_a),v_Z,t_a),
inference(resolution,[status(thm)],[c_3203,c_1221]) ).
tff(c_2,plain,
( c_lessequals(v_Y,v_X,tc_set(t_a))
| ( c_union(v_Y,v_Z,t_a) = v_X ) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_441,plain,
c_union(v_Y,v_Z,t_a) = v_X,
inference(splitLeft,[status(thm)],[c_2]) ).
tff(c_442,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_440,c_441]) ).
tff(c_443,plain,
c_lessequals(v_Y,v_X,tc_set(t_a)),
inference(splitRight,[status(thm)],[c_2]) ).
tff(c_499,plain,
! [V_c_95] :
( c_in(V_c_95,v_X,t_a)
| ~ c_in(V_c_95,v_Y,t_a) ),
inference(resolution,[status(thm)],[c_443,c_488]) ).
tff(c_2194,plain,
! [V_B_206] :
( c_in(c_Main_OsubsetI__1(c_union(v_Y,V_B_206,t_a),V_B_206,t_a),v_X,t_a)
| ( c_union(v_Y,V_B_206,t_a) = V_B_206 ) ),
inference(resolution,[status(thm)],[c_2138,c_499]) ).
tff(c_2221,plain,
( c_lessequals(c_union(v_Y,v_X,t_a),v_X,tc_set(t_a))
| ( c_union(v_Y,v_X,t_a) = v_X ) ),
inference(resolution,[status(thm)],[c_2194,c_24]) ).
tff(c_2225,plain,
c_union(v_Y,v_X,t_a) = v_X,
inference(splitLeft,[status(thm)],[c_2221]) ).
tff(c_2269,plain,
! [V_A_84] :
( c_lessequals(V_A_84,c_union(v_Y,v_X,t_a),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(V_A_84,v_X,t_a),v_Y,t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_2225,c_454]) ).
tff(c_2385,plain,
! [V_A_207] :
( c_lessequals(V_A_207,v_X,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(V_A_207,v_X,t_a),v_Y,t_a) ),
inference(demodulation,[status(thm),theory(equality)],[c_2225,c_2269]) ).
tff(c_2411,plain,
~ c_in(c_Main_OsubsetI__1(c_union(v_Y,v_Z,t_a),v_X,t_a),v_Y,t_a),
inference(resolution,[status(thm)],[c_2385,c_1221]) ).
tff(c_9911,plain,
! [V_A_363,V_B_364,T_a_365,V_B_366] :
( ( c_union(V_A_363,V_B_364,T_a_365) = V_B_366 )
| ~ c_lessequals(V_B_366,c_union(V_A_363,V_B_364,T_a_365),tc_set(T_a_365))
| c_in(c_Main_OsubsetI__1(c_union(V_A_363,V_B_364,T_a_365),V_B_366,T_a_365),V_A_363,T_a_365)
| c_in(c_Main_OsubsetI__1(c_union(V_A_363,V_B_364,T_a_365),V_B_366,T_a_365),V_B_364,T_a_365) ),
inference(resolution,[status(thm)],[c_1236,c_26]) ).
tff(c_9991,plain,
( ( c_union(v_Y,v_Z,t_a) = v_X )
| c_in(c_Main_OsubsetI__1(c_union(v_Y,v_Z,t_a),v_X,t_a),v_Y,t_a)
| c_in(c_Main_OsubsetI__1(c_union(v_Y,v_Z,t_a),v_X,t_a),v_Z,t_a) ),
inference(resolution,[status(thm)],[c_1207,c_9911]) ).
tff(c_10043,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3241,c_2411,c_440,c_9991]) ).
tff(c_10045,plain,
c_union(v_Z,v_X,t_a) != v_X,
inference(splitRight,[status(thm)],[c_2878]) ).
tff(c_10044,plain,
c_lessequals(c_union(v_Z,v_X,t_a),v_X,tc_set(t_a)),
inference(splitRight,[status(thm)],[c_2878]) ).
tff(c_864,plain,
! [V_A_135,V_A_136,T_a_137] : c_lessequals(V_A_135,c_union(V_A_136,V_A_135,T_a_137),tc_set(T_a_137)),
inference(resolution,[status(thm)],[c_22,c_833]) ).
tff(c_873,plain,
! [V_A_136,V_A_135,T_a_137] :
( ( c_union(V_A_136,V_A_135,T_a_137) = V_A_135 )
| ~ c_lessequals(c_union(V_A_136,V_A_135,T_a_137),V_A_135,tc_set(T_a_137)) ),
inference(resolution,[status(thm)],[c_864,c_26]) ).
tff(c_10048,plain,
c_union(v_Z,v_X,t_a) = v_X,
inference(resolution,[status(thm)],[c_10044,c_873]) ).
tff(c_10058,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10045,c_10048]) ).
tff(c_10060,plain,
c_union(v_Y,v_X,t_a) != v_X,
inference(splitRight,[status(thm)],[c_2221]) ).
tff(c_10059,plain,
c_lessequals(c_union(v_Y,v_X,t_a),v_X,tc_set(t_a)),
inference(splitRight,[status(thm)],[c_2221]) ).
tff(c_10064,plain,
c_union(v_Y,v_X,t_a) = v_X,
inference(resolution,[status(thm)],[c_10059,c_873]) ).
tff(c_10074,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10060,c_10064]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET837-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % 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
% 0.15/0.36 % Computer : n028.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 16:20:24 EDT 2023
% 0.15/0.36 % CPUTime :
% 9.40/3.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.40/3.29
% 9.40/3.29 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.40/3.34
% 9.40/3.34 Inference rules
% 9.40/3.34 ----------------------
% 9.40/3.34 #Ref : 0
% 9.40/3.34 #Sup : 2423
% 9.40/3.34 #Fact : 6
% 9.40/3.34 #Define : 0
% 9.40/3.34 #Split : 20
% 9.40/3.34 #Chain : 0
% 9.40/3.34 #Close : 0
% 9.40/3.34
% 9.40/3.34 Ordering : KBO
% 9.40/3.34
% 9.40/3.34 Simplification rules
% 9.40/3.34 ----------------------
% 9.40/3.34 #Subsume : 470
% 9.40/3.34 #Demod : 1639
% 9.40/3.34 #Tautology : 799
% 9.40/3.34 #SimpNegUnit : 32
% 9.40/3.34 #BackRed : 19
% 9.40/3.34
% 9.40/3.34 #Partial instantiations: 0
% 9.40/3.34 #Strategies tried : 1
% 9.40/3.34
% 9.40/3.34 Timing (in seconds)
% 9.40/3.34 ----------------------
% 9.73/3.34 Preprocessing : 0.47
% 9.73/3.35 Parsing : 0.27
% 9.73/3.35 CNF conversion : 0.02
% 9.73/3.35 Main loop : 1.82
% 9.73/3.35 Inferencing : 0.61
% 9.73/3.35 Reduction : 0.65
% 9.73/3.35 Demodulation : 0.51
% 9.73/3.35 BG Simplification : 0.05
% 9.73/3.35 Subsumption : 0.38
% 9.73/3.35 Abstraction : 0.06
% 9.73/3.35 MUC search : 0.00
% 9.73/3.35 Cooper : 0.00
% 9.73/3.35 Total : 2.37
% 9.73/3.35 Index Insertion : 0.00
% 9.73/3.35 Index Deletion : 0.00
% 9.73/3.35 Index Matching : 0.00
% 9.73/3.35 BG Taut test : 0.00
%------------------------------------------------------------------------------