%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL433-2 : 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 : n011.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 4.23s 2.59s
% Output : CNFRefutation 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 22 ~; 19 |; 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 : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 53 ( 53 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_PropLog_Osat > c_insert > c_PropLog_Opl_Oop_A_N_62 > c_PropLog_Othms > #nlpp > tc_PropLog_Opl > v_xa > v_x > v_F > t_a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(c_PropLog_Opl_Oop_A_N_62,type,
c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i ).
tff(v_xa,type,
v_xa: $i ).
tff(c_PropLog_Osat,type,
c_PropLog_Osat: ( $i * $i * $i ) > $o ).
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(tc_PropLog_Opl,type,
tc_PropLog_Opl: $i > $i ).
tff(v_F,type,
v_F: $i ).
tff(c_insert,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(f_26,axiom,
c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a),
file(unknown,unknown) ).
tff(f_38,axiom,
! [V_p,V_H,T_a,V_q] :
( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
| c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_58,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_33,axiom,
! [V_U] :
( c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a))
| ~ c_PropLog_Osat(v_F,V_U,t_a) ),
file(unknown,unknown) ).
tff(f_43,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_56,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_51,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,V_q,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_28,axiom,
~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
file(unknown,unknown) ).
tff(c_2,plain,
c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_24,plain,
! [V_H_27,V_p_28,V_q_29,T_a_30] :
( c_PropLog_Osat(V_H_27,c_PropLog_Opl_Oop_A_N_62(V_p_28,V_q_29,T_a_30),T_a_30)
| ~ c_PropLog_Osat(c_insert(V_p_28,V_H_27,tc_PropLog_Opl(T_a_30)),V_q_29,T_a_30) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_28,plain,
c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a),
inference(resolution,[status(thm)],[c_2,c_24]) ).
tff(c_16,plain,
! [V_x_17,V_B_18,T_a_19] : c_in(V_x_17,c_insert(V_x_17,V_B_18,T_a_19),T_a_19),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_6,plain,
! [V_U_1] :
( ~ c_PropLog_Osat(v_F,V_U_1,t_a)
| c_in(V_U_1,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_10,plain,
! [V_p_6,V_H_7,T_a_8] :
( c_in(V_p_6,c_PropLog_Othms(V_H_7,T_a_8),tc_PropLog_Opl(T_a_8))
| ~ c_in(V_p_6,V_H_7,tc_PropLog_Opl(T_a_8)) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_14,plain,
! [V_p_13,V_a_16,V_G_14,T_a_15] :
( c_in(V_p_13,c_PropLog_Othms(c_insert(V_a_16,V_G_14,tc_PropLog_Opl(T_a_15)),T_a_15),tc_PropLog_Opl(T_a_15))
| ~ c_in(V_p_13,c_PropLog_Othms(V_G_14,T_a_15),tc_PropLog_Opl(T_a_15)) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_34,plain,
! [V_q_35,V_H_36,T_a_37,V_p_38] :
( c_in(V_q_35,c_PropLog_Othms(V_H_36,T_a_37),tc_PropLog_Opl(T_a_37))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_38,V_q_35,T_a_37),c_PropLog_Othms(V_H_36,T_a_37),tc_PropLog_Opl(T_a_37))
| ~ c_in(V_p_38,c_PropLog_Othms(V_H_36,T_a_37),tc_PropLog_Opl(T_a_37)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_139,plain,
! [T_a_64,V_q_63,V_G_62,V_a_61,V_p_65] :
( c_in(V_q_63,c_PropLog_Othms(c_insert(V_a_61,V_G_62,tc_PropLog_Opl(T_a_64)),T_a_64),tc_PropLog_Opl(T_a_64))
| ~ c_in(V_p_65,c_PropLog_Othms(c_insert(V_a_61,V_G_62,tc_PropLog_Opl(T_a_64)),T_a_64),tc_PropLog_Opl(T_a_64))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_65,V_q_63,T_a_64),c_PropLog_Othms(V_G_62,T_a_64),tc_PropLog_Opl(T_a_64)) ),
inference(resolution,[status(thm)],[c_14,c_34]) ).
tff(c_221,plain,
! [V_p_98,V_G_96,T_a_99,V_q_100,V_a_97] :
( c_in(V_q_100,c_PropLog_Othms(c_insert(V_a_97,V_G_96,tc_PropLog_Opl(T_a_99)),T_a_99),tc_PropLog_Opl(T_a_99))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_98,V_q_100,T_a_99),c_PropLog_Othms(V_G_96,T_a_99),tc_PropLog_Opl(T_a_99))
| ~ c_in(V_p_98,c_insert(V_a_97,V_G_96,tc_PropLog_Opl(T_a_99)),tc_PropLog_Opl(T_a_99)) ),
inference(resolution,[status(thm)],[c_10,c_139]) ).
tff(c_259,plain,
! [V_q_106,V_a_107,V_p_108] :
( c_in(V_q_106,c_PropLog_Othms(c_insert(V_a_107,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(V_p_108,c_insert(V_a_107,v_F,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a))
| ~ c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(V_p_108,V_q_106,t_a),t_a) ),
inference(resolution,[status(thm)],[c_6,c_221]) ).
tff(c_264,plain,
! [V_q_109,V_x_110] :
( c_in(V_q_109,c_PropLog_Othms(c_insert(V_x_110,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(V_x_110,V_q_109,t_a),t_a) ),
inference(resolution,[status(thm)],[c_16,c_259]) ).
tff(c_4,plain,
~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_292,plain,
~ c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a),
inference(resolution,[status(thm)],[c_264,c_4]) ).
tff(c_304,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL433-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.09/0.36 % Computer : n011.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
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 09:10:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 4.23/2.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.23/2.60
% 4.23/2.60 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------