%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL430-2 : TPTP v9.3.1. 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:11:55 AM UTC 2026
% Result : Unsatisfiable 3.79s 2.33s
% Output : CNFRefutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 26 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 92 ( 92 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_in > c_minus > c_insert > c_PropLog_Opl_Oop_A_N_62 > c_PropLog_Ohyps > c_PropLog_Othms > c_PropLog_Opl_Ovar > #nlpp > tc_set > tc_PropLog_Opl > v_v > v_t > v_p > v_F > t_a > c_emptyset > c_PropLog_Opl_Ofalse
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_PropLog_Opl_Oop_A_N_62,type,
c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i ).
tff(c_PropLog_Opl_Ofalse,type,
c_PropLog_Opl_Ofalse: $i ).
tff(tc_set,type,
tc_set: $i > $i ).
tff(c_minus,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(c_emptyset,type,
c_emptyset: $i ).
tff(t_a,type,
t_a: $i ).
tff(c_PropLog_Othms,type,
c_PropLog_Othms: ( $i * $i ) > $i ).
tff(c_PropLog_Ohyps,type,
c_PropLog_Ohyps: ( $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(tc_PropLog_Opl,type,
tc_PropLog_Opl: $i > $i ).
tff(v_v,type,
v_v: $i ).
tff(v_F,type,
v_F: $i ).
tff(v_p,type,
v_p: $i ).
tff(c_insert,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(c_PropLog_Opl_Ovar,type,
c_PropLog_Opl_Ovar: ( $i * $i ) > $i ).
tff(v_t,type,
v_t: $i ).
tff(f_57,axiom,
! [V_U] : c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,V_U,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
file(unknown,unknown) ).
tff(f_35,axiom,
! [V_p,V_v,V_t,T_a] : c_lessequals(c_PropLog_Ohyps(V_p,c_insert(V_v,V_t,T_a),T_a),c_insert(c_PropLog_Opl_Ovar(V_v,T_a),c_minus(c_PropLog_Ohyps(V_p,V_t,T_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(V_v,T_a),c_PropLog_Opl_Ofalse,T_a),c_emptyset,tc_PropLog_Opl(T_a)),tc_set(tc_PropLog_Opl(T_a))),tc_PropLog_Opl(T_a)),tc_set(tc_PropLog_Opl(T_a))),
file(unknown,unknown) ).
tff(f_33,axiom,
! [V_B,T_a,V_A,V_C,V_p] :
( ~ c_in(V_p,c_PropLog_Othms(c_minus(V_A,V_B,tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(tc_PropLog_Opl(T_a)))
| c_in(V_p,c_PropLog_Othms(c_minus(V_C,V_B,tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) ),
file(unknown,unknown) ).
tff(f_39,axiom,
! [V_B,V_a,T_a,V_c,V_D] : c_lessequals(c_minus(c_insert(V_a,c_minus(V_B,c_insert(V_c,c_emptyset,T_a),tc_set(T_a)),T_a),V_D,tc_set(T_a)),c_insert(V_a,c_minus(V_B,c_insert(V_c,V_D,T_a),tc_set(T_a)),T_a),tc_set(T_a)),
file(unknown,unknown) ).
tff(f_55,axiom,
! [V_p,V_G,T_a,V_H] :
( ~ c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a))
| ~ c_lessequals(V_G,V_H,tc_set(tc_PropLog_Opl(T_a)))
| c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
file(unknown,unknown) ).
tff(f_37,axiom,
! [V_B,V_C,T_a,V_a] : c_lessequals(c_minus(V_B,V_C,tc_set(T_a)),c_insert(V_a,c_minus(V_B,c_insert(V_a,V_C,T_a),tc_set(T_a)),T_a),tc_set(T_a)),
file(unknown,unknown) ).
tff(f_47,axiom,
! [V_q,V_p,V_H,T_a] :
( ~ c_in(V_q,c_PropLog_Othms(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a))
| c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
file(unknown,unknown) ).
tff(f_59,axiom,
~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
file(unknown,unknown) ).
tff(c_14,plain,
! [V_U_27] : c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,V_U_27,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_45,plain,
! [V_p_56,V_v_57,V_t_58,T_a_59] : c_lessequals(c_PropLog_Ohyps(V_p_56,c_insert(V_v_57,V_t_58,T_a_59),T_a_59),c_insert(c_PropLog_Opl_Ovar(V_v_57,T_a_59),c_minus(c_PropLog_Ohyps(V_p_56,V_t_58,T_a_59),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(V_v_57,T_a_59),c_PropLog_Opl_Ofalse,T_a_59),c_emptyset,tc_PropLog_Opl(T_a_59)),tc_set(tc_PropLog_Opl(T_a_59))),tc_PropLog_Opl(T_a_59)),tc_set(tc_PropLog_Opl(T_a_59))),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_2,plain,
! [V_A_3,V_p_5,T_a_2,V_C_4,V_B_1] :
( c_in(V_p_5,c_PropLog_Othms(c_minus(V_C_4,V_B_1,tc_set(tc_PropLog_Opl(T_a_2))),T_a_2),tc_PropLog_Opl(T_a_2))
| ~ c_lessequals(V_A_3,V_C_4,tc_set(tc_PropLog_Opl(T_a_2)))
| ~ c_in(V_p_5,c_PropLog_Othms(c_minus(V_A_3,V_B_1,tc_set(tc_PropLog_Opl(T_a_2))),T_a_2),tc_PropLog_Opl(T_a_2)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_66,plain,
! [V_p_83,V_B_84,V_t_82,V_v_87,V_p_85,T_a_86] :
( c_in(V_p_83,c_PropLog_Othms(c_minus(c_insert(c_PropLog_Opl_Ovar(V_v_87,T_a_86),c_minus(c_PropLog_Ohyps(V_p_85,V_t_82,T_a_86),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(V_v_87,T_a_86),c_PropLog_Opl_Ofalse,T_a_86),c_emptyset,tc_PropLog_Opl(T_a_86)),tc_set(tc_PropLog_Opl(T_a_86))),tc_PropLog_Opl(T_a_86)),V_B_84,tc_set(tc_PropLog_Opl(T_a_86))),T_a_86),tc_PropLog_Opl(T_a_86))
| ~ c_in(V_p_83,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p_85,c_insert(V_v_87,V_t_82,T_a_86),T_a_86),V_B_84,tc_set(tc_PropLog_Opl(T_a_86))),T_a_86),tc_PropLog_Opl(T_a_86)) ),
inference(resolution,[status(thm)],[c_45,c_2]) ).
tff(c_24,plain,
! [V_B_38,T_a_40,V_c_39,V_a_37,V_D_41] : c_lessequals(c_minus(c_insert(V_a_37,c_minus(V_B_38,c_insert(V_c_39,c_emptyset,T_a_40),tc_set(T_a_40)),T_a_40),V_D_41,tc_set(T_a_40)),c_insert(V_a_37,c_minus(V_B_38,c_insert(V_c_39,V_D_41,T_a_40),tc_set(T_a_40)),T_a_40),tc_set(T_a_40)),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_12,plain,
! [V_p_23,V_H_26,T_a_25,V_G_24] :
( c_in(V_p_23,c_PropLog_Othms(V_H_26,T_a_25),tc_PropLog_Opl(T_a_25))
| ~ c_lessequals(V_G_24,V_H_26,tc_set(tc_PropLog_Opl(T_a_25)))
| ~ c_in(V_p_23,c_PropLog_Othms(V_G_24,T_a_25),tc_PropLog_Opl(T_a_25)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_28,plain,
! [V_B_38,V_p_23,V_c_39,V_a_37,V_D_41,T_a_25] :
( c_in(V_p_23,c_PropLog_Othms(c_insert(V_a_37,c_minus(V_B_38,c_insert(V_c_39,V_D_41,tc_PropLog_Opl(T_a_25)),tc_set(tc_PropLog_Opl(T_a_25))),tc_PropLog_Opl(T_a_25)),T_a_25),tc_PropLog_Opl(T_a_25))
| ~ c_in(V_p_23,c_PropLog_Othms(c_minus(c_insert(V_a_37,c_minus(V_B_38,c_insert(V_c_39,c_emptyset,tc_PropLog_Opl(T_a_25)),tc_set(tc_PropLog_Opl(T_a_25))),tc_PropLog_Opl(T_a_25)),V_D_41,tc_set(tc_PropLog_Opl(T_a_25))),T_a_25),tc_PropLog_Opl(T_a_25)) ),
inference(resolution,[status(thm)],[c_24,c_12]) ).
tff(c_70,plain,
! [V_p_83,V_B_84,V_t_82,V_v_87,V_p_85,T_a_86] :
( c_in(V_p_83,c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(V_v_87,T_a_86),c_minus(c_PropLog_Ohyps(V_p_85,V_t_82,T_a_86),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(V_v_87,T_a_86),c_PropLog_Opl_Ofalse,T_a_86),V_B_84,tc_PropLog_Opl(T_a_86)),tc_set(tc_PropLog_Opl(T_a_86))),tc_PropLog_Opl(T_a_86)),T_a_86),tc_PropLog_Opl(T_a_86))
| ~ c_in(V_p_83,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p_85,c_insert(V_v_87,V_t_82,T_a_86),T_a_86),V_B_84,tc_set(tc_PropLog_Opl(T_a_86))),T_a_86),tc_PropLog_Opl(T_a_86)) ),
inference(resolution,[status(thm)],[c_66,c_28]) ).
tff(c_6,plain,
! [V_B_10,V_C_11,T_a_12,V_a_13] : c_lessequals(c_minus(V_B_10,V_C_11,tc_set(T_a_12)),c_insert(V_a_13,c_minus(V_B_10,c_insert(V_a_13,V_C_11,T_a_12),tc_set(T_a_12)),T_a_12),tc_set(T_a_12)),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_19,plain,
! [V_p_33,V_H_34,T_a_35,V_G_36] :
( c_in(V_p_33,c_PropLog_Othms(V_H_34,T_a_35),tc_PropLog_Opl(T_a_35))
| ~ c_lessequals(V_G_36,V_H_34,tc_set(tc_PropLog_Opl(T_a_35)))
| ~ c_in(V_p_33,c_PropLog_Othms(V_G_36,T_a_35),tc_PropLog_Opl(T_a_35)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_39,plain,
! [T_a_53,V_a_52,V_B_55,V_C_51,V_p_54] :
( c_in(V_p_54,c_PropLog_Othms(c_insert(V_a_52,c_minus(V_B_55,c_insert(V_a_52,V_C_51,tc_PropLog_Opl(T_a_53)),tc_set(tc_PropLog_Opl(T_a_53))),tc_PropLog_Opl(T_a_53)),T_a_53),tc_PropLog_Opl(T_a_53))
| ~ c_in(V_p_54,c_PropLog_Othms(c_minus(V_B_55,V_C_51,tc_set(tc_PropLog_Opl(T_a_53))),T_a_53),tc_PropLog_Opl(T_a_53)) ),
inference(resolution,[status(thm)],[c_6,c_19]) ).
tff(c_10,plain,
! [V_q_19,V_H_21,T_a_22,V_p_20] :
( c_in(V_q_19,c_PropLog_Othms(V_H_21,T_a_22),tc_PropLog_Opl(T_a_22))
| ~ c_in(V_q_19,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V_p_20,c_PropLog_Opl_Ofalse,T_a_22),V_H_21,tc_PropLog_Opl(T_a_22)),T_a_22),tc_PropLog_Opl(T_a_22))
| ~ c_in(V_q_19,c_PropLog_Othms(c_insert(V_p_20,V_H_21,tc_PropLog_Opl(T_a_22)),T_a_22),tc_PropLog_Opl(T_a_22)) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_73,plain,
! [V_B_103,V_p_104,V_C_102,V_p_105,T_a_101] :
( c_in(V_p_104,c_PropLog_Othms(c_minus(V_B_103,c_insert(c_PropLog_Opl_Oop_A_N_62(V_p_105,c_PropLog_Opl_Ofalse,T_a_101),V_C_102,tc_PropLog_Opl(T_a_101)),tc_set(tc_PropLog_Opl(T_a_101))),T_a_101),tc_PropLog_Opl(T_a_101))
| ~ c_in(V_p_104,c_PropLog_Othms(c_insert(V_p_105,c_minus(V_B_103,c_insert(c_PropLog_Opl_Oop_A_N_62(V_p_105,c_PropLog_Opl_Ofalse,T_a_101),V_C_102,tc_PropLog_Opl(T_a_101)),tc_set(tc_PropLog_Opl(T_a_101))),tc_PropLog_Opl(T_a_101)),T_a_101),tc_PropLog_Opl(T_a_101))
| ~ c_in(V_p_104,c_PropLog_Othms(c_minus(V_B_103,V_C_102,tc_set(tc_PropLog_Opl(T_a_101))),T_a_101),tc_PropLog_Opl(T_a_101)) ),
inference(resolution,[status(thm)],[c_39,c_10]) ).
tff(c_83,plain,
! [V_v_111,V_p_114,V_t_115,T_a_113,V_p_112,V_B_116] :
( c_in(V_p_114,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p_112,V_t_115,T_a_113),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(V_v_111,T_a_113),c_PropLog_Opl_Ofalse,T_a_113),V_B_116,tc_PropLog_Opl(T_a_113)),tc_set(tc_PropLog_Opl(T_a_113))),T_a_113),tc_PropLog_Opl(T_a_113))
| ~ c_in(V_p_114,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p_112,V_t_115,T_a_113),V_B_116,tc_set(tc_PropLog_Opl(T_a_113))),T_a_113),tc_PropLog_Opl(T_a_113))
| ~ c_in(V_p_114,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p_112,c_insert(V_v_111,V_t_115,T_a_113),T_a_113),V_B_116,tc_set(tc_PropLog_Opl(T_a_113))),T_a_113),tc_PropLog_Opl(T_a_113)) ),
inference(resolution,[status(thm)],[c_70,c_73]) ).
tff(c_16,plain,
~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_86,plain,
( ~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,c_insert(v_v,v_t,t_a),t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolution,[status(thm)],[c_83,c_16]) ).
tff(c_90,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_14,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL430-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % 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
% 0.12/0.37 % Computer : n016.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 4 19:45:43 UTC 2026
% 0.12/0.37 % CPUTime :
% 3.79/2.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.79/2.34
% 3.79/2.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------