TSTP Solution File: SET858-2 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET858-2 : 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 : n007.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 10:57:14 EDT 2023
% Result : Unsatisfiable 272.97s 167.69s
% Output : CNFRefutation 273.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of formulae : 76 ( 19 unt; 10 typ; 0 def)
% Number of atoms : 225 ( 24 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 263 ( 104 ~; 159 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 6 >; 9 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 131 (; 131 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_Zorn_Osucc > c_Zorn_OTFin__linear__lemma1__1 > c_Zorn_OTFin > #nlpp > tc_set > v_n > v_m > v_S > t_a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_S,type,
v_S: $i ).
tff(c_Zorn_OTFin__linear__lemma1__1,type,
c_Zorn_OTFin__linear__lemma1__1: ( $i * $i * $i ) > $i ).
tff(tc_set,type,
tc_set: $i > $i ).
tff(c_Zorn_Osucc,type,
c_Zorn_Osucc: ( $i * $i * $i ) > $i ).
tff(v_n,type,
v_n: $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_31,axiom,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_29,axiom,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_27,axiom,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_26,axiom,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_65,axiom,
! [V_m,V_S,T_a,V_n] :
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ),
file(unknown,unknown) ).
tff(f_41,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_39,axiom,
! [V_B,V_C,T_a,V_A] :
( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [V_m,V_S,T_a,V_n] :
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ),
file(unknown,unknown) ).
tff(f_78,axiom,
! [V_m,V_S,T_a,V_n] :
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a) != V_m )
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ),
file(unknown,unknown) ).
tff(f_104,axiom,
! [V_U,V_S,T_a,V_m] :
( ~ c_in(V_U,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_U,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_U,T_a),V_m,tc_set(tc_set(T_a)))
| ( V_U = V_m ) ),
file(unknown,unknown) ).
tff(f_91,axiom,
! [V_m,V_S,T_a,V_n] :
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Osucc(V_S,c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),T_a),V_m,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ),
file(unknown,unknown) ).
tff(c_8,plain,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_6,plain,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_4,plain,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_2,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_184,plain,
! [V_S_88,V_m_89,T_a_90,V_n_91] :
( c_lessequals(c_Zorn_Osucc(V_S_88,V_m_89,T_a_90),V_n_91,tc_set(tc_set(T_a_90)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S_88,V_m_89,T_a_90),V_m_89,tc_set(tc_set(T_a_90)))
| c_lessequals(V_n_91,V_m_89,tc_set(tc_set(T_a_90)))
| ~ c_in(V_n_91,c_Zorn_OTFin(V_S_88,T_a_90),tc_set(tc_set(T_a_90)))
| ~ c_in(V_m_89,c_Zorn_OTFin(V_S_88,T_a_90),tc_set(tc_set(T_a_90))) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_12,plain,
! [V_x_5,V_S_6,T_a_7] : c_lessequals(V_x_5,c_Zorn_Osucc(V_S_6,V_x_5,T_a_7),tc_set(tc_set(T_a_7))),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_24,plain,
! [V_A_31,V_C_32,T_a_33,V_B_34] :
( c_lessequals(V_A_31,V_C_32,tc_set(T_a_33))
| ~ c_lessequals(V_A_31,V_B_34,tc_set(T_a_33))
| ~ c_lessequals(V_B_34,V_C_32,tc_set(T_a_33)) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_27,plain,
! [V_x_5,V_C_32,T_a_7,V_S_6] :
( c_lessequals(V_x_5,V_C_32,tc_set(tc_set(T_a_7)))
| ~ c_lessequals(c_Zorn_Osucc(V_S_6,V_x_5,T_a_7),V_C_32,tc_set(tc_set(T_a_7))) ),
inference(resolution,[status(thm)],[c_12,c_24]) ).
tff(c_1937,plain,
! [V_m_276,V_n_277,T_a_278,V_S_279] :
( c_lessequals(V_m_276,V_n_277,tc_set(tc_set(T_a_278)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S_279,V_m_276,T_a_278),V_m_276,tc_set(tc_set(T_a_278)))
| c_lessequals(V_n_277,V_m_276,tc_set(tc_set(T_a_278)))
| ~ c_in(V_n_277,c_Zorn_OTFin(V_S_279,T_a_278),tc_set(tc_set(T_a_278)))
| ~ c_in(V_m_276,c_Zorn_OTFin(V_S_279,T_a_278),tc_set(tc_set(T_a_278))) ),
inference(resolution,[status(thm)],[c_184,c_27]) ).
tff(c_1946,plain,
! [V_m_276] :
( c_lessequals(V_m_276,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,V_m_276,t_a),V_m_276,tc_set(tc_set(t_a)))
| c_lessequals(v_m,V_m_276,tc_set(tc_set(t_a)))
| ~ c_in(V_m_276,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_2,c_1937]) ).
tff(c_332,plain,
! [V_S_116,V_m_117,T_a_118,V_n_119] :
( c_lessequals(c_Zorn_Osucc(V_S_116,V_m_117,T_a_118),V_n_119,tc_set(tc_set(T_a_118)))
| c_lessequals(V_n_119,V_m_117,tc_set(tc_set(T_a_118)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(V_S_116,V_m_117,T_a_118),c_Zorn_OTFin(V_S_116,T_a_118),tc_set(tc_set(T_a_118)))
| ~ c_in(V_n_119,c_Zorn_OTFin(V_S_116,T_a_118),tc_set(tc_set(T_a_118)))
| ~ c_in(V_m_117,c_Zorn_OTFin(V_S_116,T_a_118),tc_set(tc_set(T_a_118))) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_4058,plain,
! [V_m_380,V_n_381,T_a_382,V_S_383] :
( c_lessequals(V_m_380,V_n_381,tc_set(tc_set(T_a_382)))
| c_lessequals(V_n_381,V_m_380,tc_set(tc_set(T_a_382)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(V_S_383,V_m_380,T_a_382),c_Zorn_OTFin(V_S_383,T_a_382),tc_set(tc_set(T_a_382)))
| ~ c_in(V_n_381,c_Zorn_OTFin(V_S_383,T_a_382),tc_set(tc_set(T_a_382)))
| ~ c_in(V_m_380,c_Zorn_OTFin(V_S_383,T_a_382),tc_set(tc_set(T_a_382))) ),
inference(resolution,[status(thm)],[c_332,c_27]) ).
tff(c_4070,plain,
! [V_m_380] :
( c_lessequals(V_m_380,v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,V_m_380,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,V_m_380,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(V_m_380,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_2,c_4058]) ).
tff(c_144,plain,
! [V_S_76,V_m_77,T_a_78,V_n_79] :
( c_lessequals(c_Zorn_Osucc(V_S_76,V_m_77,T_a_78),V_n_79,tc_set(tc_set(T_a_78)))
| c_lessequals(V_n_79,V_m_77,tc_set(tc_set(T_a_78)))
| ( c_Zorn_OTFin__linear__lemma1__1(V_S_76,V_m_77,T_a_78) != V_m_77 )
| ~ c_in(V_n_79,c_Zorn_OTFin(V_S_76,T_a_78),tc_set(tc_set(T_a_78)))
| ~ c_in(V_m_77,c_Zorn_OTFin(V_S_76,T_a_78),tc_set(tc_set(T_a_78))) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_512,plain,
! [V_m_148,V_n_149,T_a_150,V_S_151] :
( c_lessequals(V_m_148,V_n_149,tc_set(tc_set(T_a_150)))
| c_lessequals(V_n_149,V_m_148,tc_set(tc_set(T_a_150)))
| ( c_Zorn_OTFin__linear__lemma1__1(V_S_151,V_m_148,T_a_150) != V_m_148 )
| ~ c_in(V_n_149,c_Zorn_OTFin(V_S_151,T_a_150),tc_set(tc_set(T_a_150)))
| ~ c_in(V_m_148,c_Zorn_OTFin(V_S_151,T_a_150),tc_set(tc_set(T_a_150))) ),
inference(resolution,[status(thm)],[c_144,c_27]) ).
tff(c_522,plain,
! [V_m_152] :
( c_lessequals(V_m_152,v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,V_m_152,tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(v_S,V_m_152,t_a) != V_m_152 )
| ~ c_in(V_m_152,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_4,c_512]) ).
tff(c_534,plain,
( c_lessequals(v_n,v_n,tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) != v_n ) ),
inference(resolution,[status(thm)],[c_4,c_522]) ).
tff(c_538,plain,
c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) != v_n,
inference(splitLeft,[status(thm)],[c_534]) ).
tff(c_10,plain,
! [V_A_4,V_C_2,T_a_3,V_B_1] :
( c_lessequals(V_A_4,V_C_2,tc_set(T_a_3))
| ~ c_lessequals(V_A_4,V_B_1,tc_set(T_a_3))
| ~ c_lessequals(V_B_1,V_C_2,tc_set(T_a_3)) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_1435,plain,
! [V_C_235,T_a_238,V_m_234,V_n_237,V_S_236] :
( c_lessequals(c_Zorn_Osucc(V_S_236,V_m_234,T_a_238),V_C_235,tc_set(tc_set(T_a_238)))
| ~ c_lessequals(V_n_237,V_C_235,tc_set(tc_set(T_a_238)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S_236,V_m_234,T_a_238),V_m_234,tc_set(tc_set(T_a_238)))
| c_lessequals(V_n_237,V_m_234,tc_set(tc_set(T_a_238)))
| ~ c_in(V_n_237,c_Zorn_OTFin(V_S_236,T_a_238),tc_set(tc_set(T_a_238)))
| ~ c_in(V_m_234,c_Zorn_OTFin(V_S_236,T_a_238),tc_set(tc_set(T_a_238))) ),
inference(resolution,[status(thm)],[c_184,c_10]) ).
tff(c_4340,plain,
! [T_a_412,V_S_415,V_m_413,V_S_411,V_x_414] :
( c_lessequals(c_Zorn_Osucc(V_S_415,V_m_413,T_a_412),c_Zorn_Osucc(V_S_411,V_x_414,T_a_412),tc_set(tc_set(T_a_412)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S_415,V_m_413,T_a_412),V_m_413,tc_set(tc_set(T_a_412)))
| c_lessequals(V_x_414,V_m_413,tc_set(tc_set(T_a_412)))
| ~ c_in(V_x_414,c_Zorn_OTFin(V_S_415,T_a_412),tc_set(tc_set(T_a_412)))
| ~ c_in(V_m_413,c_Zorn_OTFin(V_S_415,T_a_412),tc_set(tc_set(T_a_412))) ),
inference(resolution,[status(thm)],[c_12,c_1435]) ).
tff(c_52,plain,
! [V_m_48,V_U_49,V_S_50,T_a_51] :
( ( V_m_48 = V_U_49 )
| c_lessequals(c_Zorn_Osucc(V_S_50,V_U_49,T_a_51),V_m_48,tc_set(tc_set(T_a_51)))
| ~ c_lessequals(V_U_49,V_m_48,tc_set(tc_set(T_a_51)))
| ~ c_in(V_m_48,c_Zorn_OTFin(V_S_50,T_a_51),tc_set(tc_set(T_a_51)))
| ~ c_in(V_U_49,c_Zorn_OTFin(V_S_50,T_a_51),tc_set(tc_set(T_a_51))) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_472,plain,
! [T_a_143,V_U_144,V_C_145,V_S_146,V_m_147] :
( c_lessequals(c_Zorn_Osucc(V_S_146,V_U_144,T_a_143),V_C_145,tc_set(tc_set(T_a_143)))
| ~ c_lessequals(V_m_147,V_C_145,tc_set(tc_set(T_a_143)))
| ( V_m_147 = V_U_144 )
| ~ c_lessequals(V_U_144,V_m_147,tc_set(tc_set(T_a_143)))
| ~ c_in(V_m_147,c_Zorn_OTFin(V_S_146,T_a_143),tc_set(tc_set(T_a_143)))
| ~ c_in(V_U_144,c_Zorn_OTFin(V_S_146,T_a_143),tc_set(tc_set(T_a_143))) ),
inference(resolution,[status(thm)],[c_52,c_10]) ).
tff(c_706,plain,
! [V_S_183,V_S_180,V_U_182,T_a_181,V_x_184] :
( c_lessequals(c_Zorn_Osucc(V_S_183,V_U_182,T_a_181),c_Zorn_Osucc(V_S_180,V_x_184,T_a_181),tc_set(tc_set(T_a_181)))
| ( V_x_184 = V_U_182 )
| ~ c_lessequals(V_U_182,V_x_184,tc_set(tc_set(T_a_181)))
| ~ c_in(V_x_184,c_Zorn_OTFin(V_S_183,T_a_181),tc_set(tc_set(T_a_181)))
| ~ c_in(V_U_182,c_Zorn_OTFin(V_S_183,T_a_181),tc_set(tc_set(T_a_181))) ),
inference(resolution,[status(thm)],[c_12,c_472]) ).
tff(c_754,plain,
! [V_U_185,T_a_188,V_S_187,V_x_189,V_S_186] :
( c_lessequals(V_U_185,c_Zorn_Osucc(V_S_186,V_x_189,T_a_188),tc_set(tc_set(T_a_188)))
| ( V_x_189 = V_U_185 )
| ~ c_lessequals(V_U_185,V_x_189,tc_set(tc_set(T_a_188)))
| ~ c_in(V_x_189,c_Zorn_OTFin(V_S_187,T_a_188),tc_set(tc_set(T_a_188)))
| ~ c_in(V_U_185,c_Zorn_OTFin(V_S_187,T_a_188),tc_set(tc_set(T_a_188))) ),
inference(resolution,[status(thm)],[c_706,c_27]) ).
tff(c_764,plain,
! [V_U_190,V_S_191] :
( c_lessequals(V_U_190,c_Zorn_Osucc(V_S_191,v_n,t_a),tc_set(tc_set(t_a)))
| ( v_n = V_U_190 )
| ~ c_lessequals(V_U_190,v_n,tc_set(tc_set(t_a)))
| ~ c_in(V_U_190,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_4,c_754]) ).
tff(c_812,plain,
! [V_U_190,V_C_2,V_S_191] :
( c_lessequals(V_U_190,V_C_2,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(V_S_191,v_n,t_a),V_C_2,tc_set(tc_set(t_a)))
| ( v_n = V_U_190 )
| ~ c_lessequals(V_U_190,v_n,tc_set(tc_set(t_a)))
| ~ c_in(V_U_190,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_764,c_10]) ).
tff(c_230070,plain,
! [V_U_3815,V_S_3816,V_x_3817,V_S_3818] :
( c_lessequals(V_U_3815,c_Zorn_Osucc(V_S_3816,V_x_3817,t_a),tc_set(tc_set(t_a)))
| ( v_n = V_U_3815 )
| ~ c_lessequals(V_U_3815,v_n,tc_set(tc_set(t_a)))
| ~ c_in(V_U_3815,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S_3818,v_n,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(V_x_3817,v_n,tc_set(tc_set(t_a)))
| ~ c_in(V_x_3817,c_Zorn_OTFin(V_S_3818,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(V_S_3818,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_4340,c_812]) ).
tff(c_230172,plain,
! [V_U_3815,V_S_3816] :
( c_lessequals(V_U_3815,c_Zorn_Osucc(V_S_3816,v_m,t_a),tc_set(tc_set(t_a)))
| ( v_n = V_U_3815 )
| ~ c_lessequals(V_U_3815,v_n,tc_set(tc_set(t_a)))
| ~ c_in(V_U_3815,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_2,c_230070]) ).
tff(c_230262,plain,
! [V_U_3815,V_S_3816] :
( c_lessequals(V_U_3815,c_Zorn_Osucc(V_S_3816,v_m,t_a),tc_set(tc_set(t_a)))
| ( v_n = V_U_3815 )
| ~ c_lessequals(V_U_3815,v_n,tc_set(tc_set(t_a)))
| ~ c_in(V_U_3815,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_230172]) ).
tff(c_230263,plain,
! [V_U_3815,V_S_3816] :
( c_lessequals(V_U_3815,c_Zorn_Osucc(V_S_3816,v_m,t_a),tc_set(tc_set(t_a)))
| ( v_n = V_U_3815 )
| ~ c_lessequals(V_U_3815,v_n,tc_set(tc_set(t_a)))
| ~ c_in(V_U_3815,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(negUnitSimplification,[status(thm)],[c_8,c_230262]) ).
tff(c_230264,plain,
c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a))),
inference(splitLeft,[status(thm)],[c_230263]) ).
tff(c_22,plain,
! [V_m_27,V_U_24,V_S_25,T_a_26] :
( ( V_m_27 = V_U_24 )
| c_lessequals(c_Zorn_Osucc(V_S_25,V_U_24,T_a_26),V_m_27,tc_set(tc_set(T_a_26)))
| ~ c_lessequals(V_U_24,V_m_27,tc_set(tc_set(T_a_26)))
| ~ c_in(V_m_27,c_Zorn_OTFin(V_S_25,T_a_26),tc_set(tc_set(T_a_26)))
| ~ c_in(V_U_24,c_Zorn_OTFin(V_S_25,T_a_26),tc_set(tc_set(T_a_26))) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_391,plain,
! [V_S_130,V_m_131,T_a_132,V_n_133] :
( c_lessequals(c_Zorn_Osucc(V_S_130,V_m_131,T_a_132),V_n_133,tc_set(tc_set(T_a_132)))
| c_lessequals(V_n_133,V_m_131,tc_set(tc_set(T_a_132)))
| ~ c_lessequals(c_Zorn_Osucc(V_S_130,c_Zorn_OTFin__linear__lemma1__1(V_S_130,V_m_131,T_a_132),T_a_132),V_m_131,tc_set(tc_set(T_a_132)))
| ~ c_in(V_n_133,c_Zorn_OTFin(V_S_130,T_a_132),tc_set(tc_set(T_a_132)))
| ~ c_in(V_m_131,c_Zorn_OTFin(V_S_130,T_a_132),tc_set(tc_set(T_a_132))) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_404,plain,
! [V_S_25,V_m_27,T_a_26,V_n_133] :
( c_lessequals(c_Zorn_Osucc(V_S_25,V_m_27,T_a_26),V_n_133,tc_set(tc_set(T_a_26)))
| c_lessequals(V_n_133,V_m_27,tc_set(tc_set(T_a_26)))
| ~ c_in(V_n_133,c_Zorn_OTFin(V_S_25,T_a_26),tc_set(tc_set(T_a_26)))
| ( c_Zorn_OTFin__linear__lemma1__1(V_S_25,V_m_27,T_a_26) = V_m_27 )
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S_25,V_m_27,T_a_26),V_m_27,tc_set(tc_set(T_a_26)))
| ~ c_in(V_m_27,c_Zorn_OTFin(V_S_25,T_a_26),tc_set(tc_set(T_a_26)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(V_S_25,V_m_27,T_a_26),c_Zorn_OTFin(V_S_25,T_a_26),tc_set(tc_set(T_a_26))) ),
inference(resolution,[status(thm)],[c_22,c_391]) ).
tff(c_230318,plain,
! [V_n_133] :
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),V_n_133,tc_set(tc_set(t_a)))
| c_lessequals(V_n_133,v_n,tc_set(tc_set(t_a)))
| ~ c_in(V_n_133,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) = v_n )
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_230264,c_404]) ).
tff(c_230384,plain,
! [V_n_133] :
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),V_n_133,tc_set(tc_set(t_a)))
| c_lessequals(V_n_133,v_n,tc_set(tc_set(t_a)))
| ~ c_in(V_n_133,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) = v_n )
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_230318]) ).
tff(c_230385,plain,
! [V_n_133] :
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),V_n_133,tc_set(tc_set(t_a)))
| c_lessequals(V_n_133,v_n,tc_set(tc_set(t_a)))
| ~ c_in(V_n_133,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(negUnitSimplification,[status(thm)],[c_538,c_230384]) ).
tff(c_241591,plain,
~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(splitLeft,[status(thm)],[c_230385]) ).
tff(c_241609,plain,
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_4070,c_241591]) ).
tff(c_241628,plain,
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_241609]) ).
tff(c_241630,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_6,c_241628]) ).
tff(c_242022,plain,
! [V_n_3887] :
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),V_n_3887,tc_set(tc_set(t_a)))
| c_lessequals(V_n_3887,v_n,tc_set(tc_set(t_a)))
| ~ c_in(V_n_3887,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(splitRight,[status(thm)],[c_230385]) ).
tff(c_243555,plain,
! [V_n_3894] :
( c_lessequals(v_n,V_n_3894,tc_set(tc_set(t_a)))
| c_lessequals(V_n_3894,v_n,tc_set(tc_set(t_a)))
| ~ c_in(V_n_3894,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_242022,c_27]) ).
tff(c_243682,plain,
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_2,c_243555]) ).
tff(c_243720,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_6,c_243682]) ).
tff(c_243722,plain,
~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a))),
inference(splitRight,[status(thm)],[c_230263]) ).
tff(c_243832,plain,
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_1946,c_243722]) ).
tff(c_243909,plain,
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_243832]) ).
tff(c_243911,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_6,c_243909]) ).
tff(c_243913,plain,
c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) = v_n,
inference(splitRight,[status(thm)],[c_534]) ).
tff(c_243928,plain,
! [V_m_3895] :
( c_lessequals(V_m_3895,v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,V_m_3895,tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(v_S,V_m_3895,t_a) != V_m_3895 )
| ~ c_in(V_m_3895,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_2,c_512]) ).
tff(c_243935,plain,
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) != v_n ) ),
inference(resolution,[status(thm)],[c_4,c_243928]) ).
tff(c_243942,plain,
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
inference(demodulation,[status(thm),theory(equality)],[c_243913,c_243935]) ).
tff(c_243944,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_6,c_243942]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET858-2 : 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
% 0.15/0.36 % Computer : n007.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 16:37:23 EDT 2023
% 0.15/0.36 % CPUTime :
% 272.97/167.69 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 273.07/167.71
% 273.07/167.71 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 273.07/167.74
% 273.07/167.74 Inference rules
% 273.07/167.74 ----------------------
% 273.07/167.74 #Ref : 0
% 273.07/167.74 #Sup : 62246
% 273.07/167.74 #Fact : 46
% 273.07/167.74 #Define : 0
% 273.07/167.74 #Split : 7
% 273.07/167.74 #Chain : 0
% 273.07/167.74 #Close : 0
% 273.07/167.74
% 273.07/167.74 Ordering : KBO
% 273.07/167.74
% 273.07/167.74 Simplification rules
% 273.07/167.74 ----------------------
% 273.07/167.74 #Subsume : 7295
% 273.07/167.74 #Demod : 6915
% 273.07/167.74 #Tautology : 1385
% 273.07/167.74 #SimpNegUnit : 69
% 273.07/167.74 #BackRed : 0
% 273.07/167.74
% 273.07/167.74 #Partial instantiations: 0
% 273.07/167.74 #Strategies tried : 1
% 273.07/167.74
% 273.07/167.74 Timing (in seconds)
% 273.07/167.74 ----------------------
% 273.07/167.75 Preprocessing : 0.47
% 273.07/167.75 Parsing : 0.27
% 273.07/167.75 CNF conversion : 0.02
% 273.07/167.75 Main loop : 166.18
% 273.07/167.75 Inferencing : 7.92
% 273.07/167.75 Reduction : 17.47
% 273.07/167.75 Demodulation : 13.43
% 273.07/167.75 BG Simplification : 1.34
% 273.07/167.75 Subsumption : 134.39
% 273.07/167.75 Abstraction : 2.22
% 273.07/167.75 MUC search : 0.00
% 273.07/167.75 Cooper : 0.00
% 273.07/167.75 Total : 166.72
% 273.07/167.75 Index Insertion : 0.00
% 273.07/167.75 Index Deletion : 0.00
% 273.07/167.75 Index Matching : 0.00
% 273.07/167.75 BG Taut test : 0.00
%------------------------------------------------------------------------------