%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL431-2 : 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 : n028.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 2.75s 2.03s
% Output : CNFRefutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 14 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 14 ( 14 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_PropLog_Osat > c_minus > c_PropLog_Ohyps > c_PropLog_Othms > #nlpp > tc_set > tc_PropLog_Opl > v_p > t_a > c_emptyset
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(tc_set,type,
tc_set: $i > $i ).
tff(c_minus,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(c_emptyset,type,
c_emptyset: $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_PropLog_Ohyps,type,
c_PropLog_Ohyps: ( $i * $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_p,type,
v_p: $i ).
tff(f_26,axiom,
c_PropLog_Osat(c_emptyset,v_p,t_a),
file(unknown,unknown) ).
tff(f_35,axiom,
! [V_A,T_a] : ( c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset ),
file(unknown,unknown) ).
tff(f_33,axiom,
! [V_p,T_a,V_U,V_t0] :
( ~ c_PropLog_Osat(c_emptyset,V_p,T_a)
| c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) ),
file(unknown,unknown) ).
tff(f_28,axiom,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
file(unknown,unknown) ).
tff(c_2,plain,
c_PropLog_Osat(c_emptyset,v_p,t_a),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_8,plain,
! [V_A_5,T_a_6] : ( c_minus(V_A_5,V_A_5,tc_set(T_a_6)) = c_emptyset ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_16,plain,
! [V_p_9,V_U_10,T_a_11,V_t0_12] :
( c_in(V_p_9,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p_9,V_U_10,T_a_11),c_PropLog_Ohyps(V_p_9,V_t0_12,T_a_11),tc_set(tc_PropLog_Opl(T_a_11))),T_a_11),tc_PropLog_Opl(T_a_11))
| ~ c_PropLog_Osat(c_emptyset,V_p_9,T_a_11) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_20,plain,
! [V_p_13,T_a_14] :
( c_in(V_p_13,c_PropLog_Othms(c_emptyset,T_a_14),tc_PropLog_Opl(T_a_14))
| ~ c_PropLog_Osat(c_emptyset,V_p_13,T_a_14) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_16]) ).
tff(c_4,plain,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_23,plain,
~ c_PropLog_Osat(c_emptyset,v_p,t_a),
inference(resolution,[status(thm)],[c_20,c_4]) ).
tff(c_27,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL431-2 : 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
% 0.09/0.36 % Computer : n028.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 : Fri Sep 4 17:25:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 2.75/2.03 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.75/2.04
% 2.75/2.04 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------