%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL434-2 : 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 : 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 11:11:56 AM UTC 2026
% Result : Unsatisfiable 3.13s 2.13s
% Output : CNFRefutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 28 ( 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_insert > c_PropLog_Opl_Oop_A_N_62 > c_PropLog_Othms > #nlpp > tc_PropLog_Opl > 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(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(c_insert,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(f_35,axiom,
! [V_p,T_a,V_H] : 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(f_26,axiom,
c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
file(unknown,unknown) ).
tff(f_47,axiom,
! [V_a,V_b,V_A,T_a] :
( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| c_in(V_a,V_A,T_a)
| ( V_a = V_b ) ),
file(unknown,unknown) ).
tff(f_33,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_40,axiom,
! [V_q,V_H,T_a,V_p] :
( ~ c_in(V_q,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)) ),
file(unknown,unknown) ).
tff(f_28,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(c_8,plain,
! [V_p_4,T_a_5,V_H_6] : c_in(c_PropLog_Opl_Oop_A_N_62(V_p_4,V_p_4,T_a_5),c_PropLog_Othms(V_H_6,T_a_5),tc_PropLog_Opl(T_a_5)),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_2,plain,
c_in(v_pa,c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a)),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_19,plain,
! [V_b_21,V_a_22,V_A_23,T_a_24] :
( ( V_b_21 = V_a_22 )
| c_in(V_a_22,V_A_23,T_a_24)
| ~ c_in(V_a_22,c_insert(V_b_21,V_A_23,T_a_24),T_a_24) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_23,plain,
( ( v_pa = v_p )
| c_in(v_pa,v_H,tc_PropLog_Opl(t_a)) ),
inference(resolution,[status(thm)],[c_2,c_19]) ).
tff(c_24,plain,
c_in(v_pa,v_H,tc_PropLog_Opl(t_a)),
inference(splitLeft,[status(thm)],[c_23]) ).
tff(c_6,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_33]) ).
tff(c_25,plain,
! [V_p_25,V_q_26,T_a_27,V_H_28] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p_25,V_q_26,T_a_27),c_PropLog_Othms(V_H_28,T_a_27),tc_PropLog_Opl(T_a_27))
| ~ c_in(V_q_26,c_PropLog_Othms(V_H_28,T_a_27),tc_PropLog_Opl(T_a_27)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
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_28]) ).
tff(c_29,plain,
~ c_in(v_pa,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[c_25,c_4]) ).
tff(c_32,plain,
~ c_in(v_pa,v_H,tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[c_6,c_29]) ).
tff(c_36,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_32]) ).
tff(c_37,plain,
v_pa = v_p,
inference(splitRight,[status(thm)],[c_23]) ).
tff(c_40,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(demodulation,[status(thm),theory(equality)],[c_37,c_4]) ).
tff(c_44,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL434-2 : 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
% 0.09/0.35 % Computer : n020.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 6 01:31:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 3.13/2.13 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.13/2.14
% 3.13/2.14 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------