%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL442-2 : 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 : n016.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 4.08s 2.54s
% Output : CNFRefutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 81 ( 46 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 60 ( 60 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_PropLog_Oeval > c_union > c_PropLog_Opl_Oop_A_N_62 > c_PropLog_Ohyps > c_PropLog_Othms > #nlpp > tc_PropLog_Opl > v_tt > v_pl2 > v_pl1 > t_a > c_PropLog_Opl_Ofalse
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_tt,type,
v_tt: $i ).
tff(c_PropLog_Opl_Oop_A_N_62,type,
c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i ).
tff(c_PropLog_Opl_Ofalse,type,
c_PropLog_Opl_Ofalse: $i ).
tff(v_pl2,type,
v_pl2: $i ).
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(c_union,type,
c_union: ( $i * $i * $i ) > $i ).
tff(tc_PropLog_Opl,type,
tc_PropLog_Opl: $i > $i ).
tff(v_pl1,type,
v_pl1: $i ).
tff(c_PropLog_Oeval,type,
c_PropLog_Oeval: ( $i * $i * $i ) > $o ).
tff(f_36,axiom,
( c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| ~ c_PropLog_Oeval(v_tt,v_pl2,t_a) ),
file(unknown,unknown) ).
tff(f_39,axiom,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_PropLog_Oeval(v_tt,v_pl2,t_a) ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [V_p,T_a,V_H,V_q] :
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,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_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
file(unknown,unknown) ).
tff(f_78,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_union(V_A,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ),
file(unknown,unknown) ).
tff(f_29,axiom,
( c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| ~ c_PropLog_Oeval(v_tt,v_pl1,t_a) ),
file(unknown,unknown) ).
tff(f_32,axiom,
( c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a))
| c_PropLog_Oeval(v_tt,v_pl1,t_a) ),
file(unknown,unknown) ).
tff(f_73,axiom,
! [V_p,V_G,T_a,V_B] :
( ~ c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a))
| c_in(V_p,c_PropLog_Othms(c_union(V_G,V_B,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ),
file(unknown,unknown) ).
tff(f_43,axiom,
( c_PropLog_Oeval(v_tt,v_pl1,t_a)
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
file(unknown,unknown) ).
tff(f_68,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_q,c_PropLog_Opl_Ofalse,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Opl_Ofalse,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
file(unknown,unknown) ).
tff(f_55,axiom,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_PropLog_Oeval(v_tt,v_pl2,t_a)
| ~ c_PropLog_Oeval(v_tt,v_pl1,t_a) ),
file(unknown,unknown) ).
tff(f_83,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_48,axiom,
( ~ c_PropLog_Oeval(v_tt,v_pl2,t_a)
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
file(unknown,unknown) ).
tff(c_6,plain,
( ~ c_PropLog_Oeval(v_tt,v_pl2,t_a)
| c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_25,plain,
~ c_PropLog_Oeval(v_tt,v_pl2,t_a),
inference(splitLeft,[status(thm)],[c_6]) ).
tff(c_8,plain,
( c_PropLog_Oeval(v_tt,v_pl2,t_a)
| c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_93,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(negUnitSimplification,[status(thm)],[c_25,c_8]) ).
tff(c_96,plain,
! [V_p_55,V_q_56,T_a_57,V_H_58] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p_55,V_q_56,T_a_57),c_PropLog_Othms(V_H_58,T_a_57),tc_PropLog_Opl(T_a_57))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_55,c_PropLog_Opl_Ofalse,T_a_57),c_PropLog_Othms(V_H_58,T_a_57),tc_PropLog_Opl(T_a_57)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_110,plain,
! [V_q_56] : c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,V_q_56,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[c_93,c_96]) ).
tff(c_22,plain,
! [V_p_13,V_A_16,V_G_14,T_a_15] :
( c_in(V_p_13,c_PropLog_Othms(c_union(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_78]) ).
tff(c_109,plain,
! [T_a_15,V_G_14,V_p_55,V_A_16,V_q_56] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p_55,V_q_56,T_a_15),c_PropLog_Othms(c_union(V_A_16,V_G_14,tc_PropLog_Opl(T_a_15)),T_a_15),tc_PropLog_Opl(T_a_15))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_55,c_PropLog_Opl_Ofalse,T_a_15),c_PropLog_Othms(V_G_14,T_a_15),tc_PropLog_Opl(T_a_15)) ),
inference(resolution,[status(thm)],[c_22,c_96]) ).
tff(c_2,plain,
( ~ c_PropLog_Oeval(v_tt,v_pl1,t_a)
| c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_26,plain,
~ c_PropLog_Oeval(v_tt,v_pl1,t_a),
inference(splitLeft,[status(thm)],[c_2]) ).
tff(c_4,plain,
( c_PropLog_Oeval(v_tt,v_pl1,t_a)
| c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_28,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(negUnitSimplification,[status(thm)],[c_26,c_4]) ).
tff(c_32,plain,
! [V_p_33,V_q_34,T_a_35,V_H_36] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p_33,V_q_34,T_a_35),c_PropLog_Othms(V_H_36,T_a_35),tc_PropLog_Opl(T_a_35))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_33,c_PropLog_Opl_Ofalse,T_a_35),c_PropLog_Othms(V_H_36,T_a_35),tc_PropLog_Opl(T_a_35)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_49,plain,
! [V_q_34] : c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,V_q_34,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[c_28,c_32]) ).
tff(c_20,plain,
! [V_p_9,V_G_10,V_B_12,T_a_11] :
( c_in(V_p_9,c_PropLog_Othms(c_union(V_G_10,V_B_12,tc_PropLog_Opl(T_a_11)),T_a_11),tc_PropLog_Opl(T_a_11))
| ~ c_in(V_p_9,c_PropLog_Othms(V_G_10,T_a_11),tc_PropLog_Opl(T_a_11)) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_10,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| c_PropLog_Oeval(v_tt,v_pl1,t_a) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_70,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(negUnitSimplification,[status(thm)],[c_26,c_10]) ).
tff(c_79,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[c_20,c_70]) ).
tff(c_88,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_49,c_79]) ).
tff(c_89,plain,
c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(splitRight,[status(thm)],[c_2]) ).
tff(c_135,plain,
! [V_p_74,V_q_75,T_a_76,V_H_77] :
( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p_74,V_q_75,T_a_76),c_PropLog_Opl_Ofalse,T_a_76),c_PropLog_Othms(V_H_77,T_a_76),tc_PropLog_Opl(T_a_76))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_q_75,c_PropLog_Opl_Ofalse,T_a_76),c_PropLog_Othms(V_H_77,T_a_76),tc_PropLog_Opl(T_a_76))
| ~ c_in(V_p_74,c_PropLog_Othms(V_H_77,T_a_76),tc_PropLog_Opl(T_a_76)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_16,plain,
! [V_p_1,V_q_4,T_a_2,V_H_3] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p_1,V_q_4,T_a_2),c_PropLog_Othms(V_H_3,T_a_2),tc_PropLog_Opl(T_a_2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p_1,c_PropLog_Opl_Ofalse,T_a_2),c_PropLog_Othms(V_H_3,T_a_2),tc_PropLog_Opl(T_a_2)) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_138,plain,
! [V_q_75,V_H_77,V_p_74,T_a_76,V_q_4] :
( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p_74,V_q_75,T_a_76),V_q_4,T_a_76),c_PropLog_Othms(V_H_77,T_a_76),tc_PropLog_Opl(T_a_76))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_q_75,c_PropLog_Opl_Ofalse,T_a_76),c_PropLog_Othms(V_H_77,T_a_76),tc_PropLog_Opl(T_a_76))
| ~ c_in(V_p_74,c_PropLog_Othms(V_H_77,T_a_76),tc_PropLog_Opl(T_a_76)) ),
inference(resolution,[status(thm)],[c_135,c_16]) ).
tff(c_90,plain,
c_PropLog_Oeval(v_tt,v_pl1,t_a),
inference(splitRight,[status(thm)],[c_2]) ).
tff(c_14,plain,
( ~ c_PropLog_Oeval(v_tt,v_pl1,t_a)
| c_PropLog_Oeval(v_tt,v_pl2,t_a)
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_145,plain,
( c_PropLog_Oeval(v_tt,v_pl2,t_a)
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(demodulation,[status(thm),theory(equality)],[c_90,c_14]) ).
tff(c_146,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(negUnitSimplification,[status(thm)],[c_25,c_145]) ).
tff(c_168,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(v_pl1,c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolution,[status(thm)],[c_138,c_146]) ).
tff(c_219,plain,
~ c_in(v_pl1,c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(splitLeft,[status(thm)],[c_168]) ).
tff(c_222,plain,
~ c_in(v_pl1,c_PropLog_Othms(c_PropLog_Ohyps(v_pl1,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[c_20,c_219]) ).
tff(c_229,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_89,c_222]) ).
tff(c_230,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(splitRight,[status(thm)],[c_168]) ).
tff(c_234,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl2,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[c_109,c_230]) ).
tff(c_253,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_110,c_234]) ).
tff(c_254,plain,
c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(splitRight,[status(thm)],[c_6]) ).
tff(c_24,plain,
! [V_p_20,V_q_17,T_a_19,V_H_18] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p_20,V_q_17,T_a_19),c_PropLog_Othms(V_H_18,T_a_19),tc_PropLog_Opl(T_a_19))
| ~ c_in(V_q_17,c_PropLog_Othms(V_H_18,T_a_19),tc_PropLog_Opl(T_a_19)) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_255,plain,
c_PropLog_Oeval(v_tt,v_pl2,t_a),
inference(splitRight,[status(thm)],[c_6]) ).
tff(c_12,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_PropLog_Oeval(v_tt,v_pl2,t_a) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_322,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_union(c_PropLog_Ohyps(v_pl1,v_tt,t_a),c_PropLog_Ohyps(v_pl2,v_tt,t_a),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(demodulation,[status(thm),theory(equality)],[c_255,c_12]) ).
tff(c_333,plain,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_pl1,v_pl2,t_a),c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[c_22,c_322]) ).
tff(c_341,plain,
~ c_in(v_pl2,c_PropLog_Othms(c_PropLog_Ohyps(v_pl2,v_tt,t_a),t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[c_24,c_333]) ).
tff(c_345,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_254,c_341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL442-2 : 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 : n016.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 20:38:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 4.08/2.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.08/2.55
% 4.08/2.55 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------