%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL438-2 : 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 : n031.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 2.94s 2.17s
% Output : CNFRefutation 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 28 ( 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_PropLog_Opl_Oop_A_N_62 > c_PropLog_Othms > #nlpp > tc_PropLog_Opl > v_q > v_pa > 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(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_pa,type,
v_pa: $i ).
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,
~ 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_27,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file(unknown,unknown) ).
tff(f_26,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Oop_A_N_62(v_pa,v_q,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(c_6,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_29]) ).
tff(c_4,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_2,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Oop_A_N_62(v_pa,v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_21,plain,
! [V_p_14,V_H_16,T_a_18,V_r_17,V_q_15] : c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p_14,c_PropLog_Opl_Oop_A_N_62(V_q_15,V_r_17,T_a_18),T_a_18),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p_14,V_q_15,T_a_18),c_PropLog_Opl_Oop_A_N_62(V_p_14,V_r_17,T_a_18),T_a_18),T_a_18),c_PropLog_Othms(V_H_16,T_a_18),tc_PropLog_Opl(T_a_18)),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_8,plain,
! [V_q_4,V_H_2,T_a_3,V_p_1] :
( c_in(V_q_4,c_PropLog_Othms(V_H_2,T_a_3),tc_PropLog_Opl(T_a_3))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_1,V_q_4,T_a_3),c_PropLog_Othms(V_H_2,T_a_3),tc_PropLog_Opl(T_a_3))
| ~ c_in(V_p_1,c_PropLog_Othms(V_H_2,T_a_3),tc_PropLog_Opl(T_a_3)) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_26,plain,
! [V_r_23,V_q_22,T_a_21,V_p_19,V_H_20] :
( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p_19,V_q_22,T_a_21),c_PropLog_Opl_Oop_A_N_62(V_p_19,V_r_23,T_a_21),T_a_21),c_PropLog_Othms(V_H_20,T_a_21),tc_PropLog_Opl(T_a_21))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_19,c_PropLog_Opl_Oop_A_N_62(V_q_22,V_r_23,T_a_21),T_a_21),c_PropLog_Othms(V_H_20,T_a_21),tc_PropLog_Opl(T_a_21)) ),
inference(resolution,[status(thm)],[c_21,c_8]) ).
tff(c_31,plain,
! [T_a_26,V_H_28,V_p_24,V_q_27,V_r_25] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p_24,V_r_25,T_a_26),c_PropLog_Othms(V_H_28,T_a_26),tc_PropLog_Opl(T_a_26))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_24,V_q_27,T_a_26),c_PropLog_Othms(V_H_28,T_a_26),tc_PropLog_Opl(T_a_26))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_24,c_PropLog_Opl_Oop_A_N_62(V_q_27,V_r_25,T_a_26),T_a_26),c_PropLog_Othms(V_H_28,T_a_26),tc_PropLog_Opl(T_a_26)) ),
inference(resolution,[status(thm)],[c_26,c_8]) ).
tff(c_40,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))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_pa,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(resolution,[status(thm)],[c_2,c_31]) ).
tff(c_45,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(demodulation,[status(thm),theory(equality)],[c_4,c_40]) ).
tff(c_47,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL438-2 : 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
% 0.12/0.37 % Computer : n031.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 : Sat Sep 5 00:33:24 UTC 2026
% 0.12/0.37 % CPUTime :
% 2.94/2.17 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.94/2.18
% 2.94/2.18 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------