%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL446-2 : 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 : n027.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 11:11:58 AM UTC 2026
% Result : Unsatisfiable 2.86s 2.13s
% Output : CNFRefutation 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 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 : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 43 ( 43 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_PropLog_Opl_Oop_A_N_62 > c_PropLog_Othms > #nlpp > tc_PropLog_Opl > v_p > v_H > t_a
%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(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(f_29,axiom,
! [V_p,V_q,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_p,T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
file(unknown,unknown) ).
tff(f_39,axiom,
! [V_r,T_a,V_H,V_p,V_q] : c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Oop_A_N_62(V_q,V_r,T_a),T_a),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Opl_Oop_A_N_62(V_p,V_r,T_a),T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
file(unknown,unknown) ).
tff(f_37,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_27,axiom,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_p,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file(unknown,unknown) ).
tff(c_4,plain,
! [V_p_1,V_q_2,T_a_3,V_H_4] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p_1,c_PropLog_Opl_Oop_A_N_62(V_q_2,V_p_1,T_a_3),T_a_3),c_PropLog_Othms(V_H_4,T_a_3),tc_PropLog_Opl(T_a_3)),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_24,plain,
! [V_r_26,V_H_30,V_p_29,T_a_28,V_q_27] : c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p_29,c_PropLog_Opl_Oop_A_N_62(V_q_27,V_r_26,T_a_28),T_a_28),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p_29,V_q_27,T_a_28),c_PropLog_Opl_Oop_A_N_62(V_p_29,V_r_26,T_a_28),T_a_28),T_a_28),c_PropLog_Othms(V_H_30,T_a_28),tc_PropLog_Opl(T_a_28)),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_6,plain,
! [V_q_8,V_H_6,T_a_7,V_p_5] :
( c_in(V_q_8,c_PropLog_Othms(V_H_6,T_a_7),tc_PropLog_Opl(T_a_7))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_5,V_q_8,T_a_7),c_PropLog_Othms(V_H_6,T_a_7),tc_PropLog_Opl(T_a_7))
| ~ c_in(V_p_5,c_PropLog_Othms(V_H_6,T_a_7),tc_PropLog_Opl(T_a_7)) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_29,plain,
! [V_r_34,V_q_32,V_H_33,V_p_35,T_a_31] :
( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p_35,V_q_32,T_a_31),c_PropLog_Opl_Oop_A_N_62(V_p_35,V_r_34,T_a_31),T_a_31),c_PropLog_Othms(V_H_33,T_a_31),tc_PropLog_Opl(T_a_31))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_35,c_PropLog_Opl_Oop_A_N_62(V_q_32,V_r_34,T_a_31),T_a_31),c_PropLog_Othms(V_H_33,T_a_31),tc_PropLog_Opl(T_a_31)) ),
inference(resolution,[status(thm)],[c_24,c_6]) ).
tff(c_34,plain,
! [V_p_37,V_H_36,T_a_40,V_r_39,V_q_38] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p_37,V_r_39,T_a_40),c_PropLog_Othms(V_H_36,T_a_40),tc_PropLog_Opl(T_a_40))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_37,V_q_38,T_a_40),c_PropLog_Othms(V_H_36,T_a_40),tc_PropLog_Opl(T_a_40))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_37,c_PropLog_Opl_Oop_A_N_62(V_q_38,V_r_39,T_a_40),T_a_40),c_PropLog_Othms(V_H_36,T_a_40),tc_PropLog_Opl(T_a_40)) ),
inference(resolution,[status(thm)],[c_29,c_6]) ).
tff(c_52,plain,
! [V_p_41,T_a_42,V_H_43,V_q_44] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p_41,V_p_41,T_a_42),c_PropLog_Othms(V_H_43,T_a_42),tc_PropLog_Opl(T_a_42))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_41,V_q_44,T_a_42),c_PropLog_Othms(V_H_43,T_a_42),tc_PropLog_Opl(T_a_42)) ),
inference(resolution,[status(thm)],[c_4,c_34]) ).
tff(c_64,plain,
! [V_p_1,T_a_3,V_H_4] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p_1,V_p_1,T_a_3),c_PropLog_Othms(V_H_4,T_a_3),tc_PropLog_Opl(T_a_3)),
inference(resolution,[status(thm)],[c_4,c_52]) ).
tff(c_2,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_p,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_68,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_64,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL446-2 : 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
% 0.10/0.37 % Computer : n027.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 5 14:14:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 2.86/2.13 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.08/2.14
% 3.08/2.14 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------