%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL439-2 : 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/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 : n020.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 11:11:57 AM UTC 2026
% Result : Unsatisfiable 7.45s 2.61s
% Output : CNFRefutation 7.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 50 ( 50 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_insert > c_PropLog_Opl_Oop_A_N_62 > c_PropLog_Othms > #nlpp > tc_PropLog_Opl > v_q > v_p > v_H > t_a > 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(v_q,type,
v_q: $i ).
tff(t_a,type,
t_a: $i ).
tff(c_PropLog_Othms,type,
c_PropLog_Othms: ( $i * $i ) > $i ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(v_H,type,
v_H: $i ).
tff(tc_PropLog_Opl,type,
tc_PropLog_Opl: $i > $i ).
tff(v_p,type,
v_p: $i ).
tff(c_insert,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(f_50,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_51,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file(unknown,unknown) ).
tff(f_35,axiom,
! [V_p,V_H,T_a] :
( ~ c_in(V_p,V_H,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_48,axiom,
! [V_p,V_G,T_a,V_a] :
( ~ c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(c_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ),
file(unknown,unknown) ).
tff(f_43,axiom,
! [V_p,V_H,T_a,V_q] :
( ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),c_PropLog_Othms(V_H,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_30,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(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
file(unknown,unknown) ).
tff(f_53,axiom,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file(unknown,unknown) ).
tff(c_10,plain,
! [V_x_16,V_B_17,T_a_18] : c_in(V_x_16,c_insert(V_x_16,V_B_17,T_a_18),T_a_18),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_12,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_4,plain,
! [V_p_5,V_H_6,T_a_7] :
( c_in(V_p_5,c_PropLog_Othms(V_H_6,T_a_7),tc_PropLog_Opl(T_a_7))
| ~ c_in(V_p_5,V_H_6,tc_PropLog_Opl(T_a_7)) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_8,plain,
! [V_p_12,V_a_15,V_G_13,T_a_14] :
( c_in(V_p_12,c_PropLog_Othms(c_insert(V_a_15,V_G_13,tc_PropLog_Opl(T_a_14)),T_a_14),tc_PropLog_Opl(T_a_14))
| ~ c_in(V_p_12,c_PropLog_Othms(V_G_13,T_a_14),tc_PropLog_Opl(T_a_14)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_46,plain,
! [V_q_37,V_H_38,T_a_39,V_p_40] :
( c_in(V_q_37,c_PropLog_Othms(V_H_38,T_a_39),tc_PropLog_Opl(T_a_39))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_40,c_PropLog_Opl_Ofalse,T_a_39),c_PropLog_Othms(V_H_38,T_a_39),tc_PropLog_Opl(T_a_39))
| ~ c_in(V_p_40,c_PropLog_Othms(V_H_38,T_a_39),tc_PropLog_Opl(T_a_39)) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_160,plain,
! [V_q_64,V_p_62,V_a_61,T_a_65,V_G_63] :
( c_in(V_q_64,c_PropLog_Othms(c_insert(V_a_61,V_G_63,tc_PropLog_Opl(T_a_65)),T_a_65),tc_PropLog_Opl(T_a_65))
| ~ c_in(V_p_62,c_PropLog_Othms(c_insert(V_a_61,V_G_63,tc_PropLog_Opl(T_a_65)),T_a_65),tc_PropLog_Opl(T_a_65))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_62,c_PropLog_Opl_Ofalse,T_a_65),c_PropLog_Othms(V_G_63,T_a_65),tc_PropLog_Opl(T_a_65)) ),
inference(resolution,[status(thm)],[c_8,c_46]) ).
tff(c_1873,plain,
! [T_a_303,V_a_306,V_q_304,V_p_305,V_G_307] :
( c_in(V_q_304,c_PropLog_Othms(c_insert(V_a_306,V_G_307,tc_PropLog_Opl(T_a_303)),T_a_303),tc_PropLog_Opl(T_a_303))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_305,c_PropLog_Opl_Ofalse,T_a_303),c_PropLog_Othms(V_G_307,T_a_303),tc_PropLog_Opl(T_a_303))
| ~ c_in(V_p_305,c_insert(V_a_306,V_G_307,tc_PropLog_Opl(T_a_303)),tc_PropLog_Opl(T_a_303)) ),
inference(resolution,[status(thm)],[c_4,c_160]) ).
tff(c_1977,plain,
! [V_q_308,V_a_309] :
( c_in(V_q_308,c_PropLog_Othms(c_insert(V_a_309,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(v_p,c_insert(V_a_309,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)) ),
inference(resolution,[status(thm)],[c_12,c_1873]) ).
tff(c_2,plain,
! [V_p_2,V_q_1,T_a_4,V_H_3] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p_2,V_q_1,T_a_4),c_PropLog_Othms(V_H_3,T_a_4),tc_PropLog_Opl(T_a_4))
| ~ c_in(V_q_1,c_PropLog_Othms(c_insert(V_p_2,V_H_3,tc_PropLog_Opl(T_a_4)),T_a_4),tc_PropLog_Opl(T_a_4)) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_2076,plain,
! [V_a_314,V_q_315] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_a_314,V_q_315,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| ~ c_in(v_p,c_insert(V_a_314,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)) ),
inference(resolution,[status(thm)],[c_1977,c_2]) ).
tff(c_14,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_2106,plain,
~ c_in(v_p,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[c_2076,c_14]) ).
tff(c_2119,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_2106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL439-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % 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
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun Sep 6 01:32:42 UTC 2026
% 0.13/0.36 % CPUTime :
% 7.45/2.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.45/2.63
% 7.45/2.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------