%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL441-2 : 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 : n002.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 2.24s 1.43s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 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; 4 con; 0-3 aty)
% Number of variables : 12 ( 12 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_insert > c_PropLog_Opl_Oop_A_N_62 > c_PropLog_Othms > c_PropLog_Opl_Ovar > #nlpp > tc_PropLog_Opl > v_a > 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(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_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(v_a,type,
v_a: $i ).
tff(tc_PropLog_Opl,type,
tc_PropLog_Opl: $i > $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(f_37,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_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_30,axiom,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
file(unknown,unknown) ).
tff(c_6,plain,
! [V_x_4,V_B_5,T_a_6] : c_in(V_x_4,c_insert(V_x_4,V_B_5,T_a_6),T_a_6),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_4,plain,
! [V_p_1,V_H_2,T_a_3] :
( c_in(V_p_1,c_PropLog_Othms(V_H_2,T_a_3),tc_PropLog_Opl(T_a_3))
| ~ c_in(V_p_1,V_H_2,tc_PropLog_Opl(T_a_3)) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_2,plain,
( ~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_9,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(splitLeft,[status(thm)],[c_2]) ).
tff(c_12,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[c_4,c_9]) ).
tff(c_16,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_12]) ).
tff(c_17,plain,
~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(splitRight,[status(thm)],[c_2]) ).
tff(c_21,plain,
~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[c_4,c_17]) ).
tff(c_25,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL441-2 : 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
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sat Sep 5 08:08:05 UTC 2026
% 0.12/0.36 % CPUTime :
% 2.24/1.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.24/1.43
% 2.24/1.43 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------