%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL430-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 : Thu Sep 24 01:07:41 PM UTC 2026
% Result : Unsatisfiable 0.28s 0.59s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 14 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 86 ( 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1368,axiom,
! [V_p,V_A,V_B,T_a,V_C] :
( c_in(V_p,c_PropLog_Othms(c_minus(V_C,V_B,tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(tc_PropLog_Opl(T_a)))
| ~ c_in(V_p,c_PropLog_Othms(c_minus(V_A,V_B,tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1371,axiom,
! [V_p,V_v,V_t,T_a] : c_lessequals(c_PropLog_Ohyps(V_p,c_insert(V_v,V_t,T_a),T_a),c_insert(c_PropLog_Opl_Ovar(V_v,T_a),c_minus(c_PropLog_Ohyps(V_p,V_t,T_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(V_v,T_a),c_PropLog_Opl_Ofalse,T_a),c_emptyset,tc_PropLog_Opl(T_a)),tc_set(tc_PropLog_Opl(T_a))),tc_PropLog_Opl(T_a)),tc_set(tc_PropLog_Opl(T_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1372,axiom,
! [V_B,V_C,T_a,V_a] : c_lessequals(c_minus(V_B,V_C,tc_set(T_a)),c_insert(V_a,c_minus(V_B,c_insert(V_a,V_C,T_a),tc_set(T_a)),T_a),tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1373,axiom,
! [V_a,V_B,V_c,T_a,V_D] : c_lessequals(c_minus(c_insert(V_a,c_minus(V_B,c_insert(V_c,c_emptyset,T_a),tc_set(T_a)),T_a),V_D,tc_set(T_a)),c_insert(V_a,c_minus(V_B,c_insert(V_c,V_D,T_a),tc_set(T_a)),T_a),tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1375,axiom,
! [V_q,V_p,V_H,T_a] :
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_q,c_PropLog_Othms(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1376,axiom,
! [V_p,V_G,T_a,V_H] :
( c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_lessequals(V_G,V_H,tc_set(tc_PropLog_Opl(T_a)))
| ~ c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1380,negated_conjecture,
! [V_U] : c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,V_U,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1382,negated_conjecture,
~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2871,plain,
! [V_p,V_B,T_a,V_C] :
( c_in(V_p,c_PropLog_Othms(c_minus(V_C,V_B,tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a))
| ! [V_A] :
( ~ c_lessequals(V_A,V_C,tc_set(tc_PropLog_Opl(T_a)))
| ~ c_in(V_p,c_PropLog_Othms(c_minus(V_A,V_B,tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a)) ) ),
inference(miniscoping,[status(thm)],[f1368]) ).
fof(f2872,plain,
! [X0,X1,X2,X3,X4] :
( c_in(X0,c_PropLog_Othms(c_minus(X4,X2,tc_set(tc_PropLog_Opl(X3))),X3),tc_PropLog_Opl(X3))
| ~ c_lessequals(X1,X4,tc_set(tc_PropLog_Opl(X3)))
| ~ c_in(X0,c_PropLog_Othms(c_minus(X1,X2,tc_set(tc_PropLog_Opl(X3))),X3),tc_PropLog_Opl(X3)) ),
inference(cnf_transformation,[status(thm)],[f2871]) ).
fof(f2875,plain,
! [X0,X1,X2,X3] : c_lessequals(c_PropLog_Ohyps(X0,c_insert(X1,X2,X3),X3),c_insert(c_PropLog_Opl_Ovar(X1,X3),c_minus(c_PropLog_Ohyps(X0,X2,X3),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X1,X3),c_PropLog_Opl_Ofalse,X3),c_emptyset,tc_PropLog_Opl(X3)),tc_set(tc_PropLog_Opl(X3))),tc_PropLog_Opl(X3)),tc_set(tc_PropLog_Opl(X3))),
inference(cnf_transformation,[status(thm)],[f1371]) ).
fof(f2876,plain,
! [X0,X1,X2,X3] : c_lessequals(c_minus(X0,X1,tc_set(X2)),c_insert(X3,c_minus(X0,c_insert(X3,X1,X2),tc_set(X2)),X2),tc_set(X2)),
inference(cnf_transformation,[status(thm)],[f1372]) ).
fof(f2877,plain,
! [X0,X1,X2,X3,X4] : c_lessequals(c_minus(c_insert(X0,c_minus(X1,c_insert(X2,c_emptyset,X3),tc_set(X3)),X3),X4,tc_set(X3)),c_insert(X0,c_minus(X1,c_insert(X2,X4,X3),tc_set(X3)),X3),tc_set(X3)),
inference(cnf_transformation,[status(thm)],[f1373]) ).
fof(f2880,plain,
! [V_q,V_H,T_a] :
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ! [V_p] :
( ~ c_in(V_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_q,c_PropLog_Othms(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ) ),
inference(miniscoping,[status(thm)],[f1375]) ).
fof(f2881,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Ofalse,X3),X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3))
| ~ c_in(X0,c_PropLog_Othms(c_insert(X1,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)) ),
inference(cnf_transformation,[status(thm)],[f2880]) ).
fof(f2882,plain,
! [V_p,T_a,V_H] :
( c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ! [V_G] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_PropLog_Opl(T_a)))
| ~ c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a)) ) ),
inference(miniscoping,[status(thm)],[f1376]) ).
fof(f2883,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2))
| ~ c_lessequals(X1,X3,tc_set(tc_PropLog_Opl(X2)))
| ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)) ),
inference(cnf_transformation,[status(thm)],[f2882]) ).
fof(f2887,plain,
! [X0] : c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X0,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(thm)],[f1380]) ).
fof(f2889,plain,
~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(thm)],[f1382]) ).
fof(f2908,plain,
! [X0,X1] :
( c_in(v_p,c_PropLog_Othms(X1,t_a),tc_PropLog_Opl(t_a))
| ~ c_lessequals(c_minus(c_PropLog_Ohyps(v_p,X0,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),X1,tc_set(tc_PropLog_Opl(t_a))) ),
inference(resolution,[status(thm)],[f2883,f2887]) ).
fof(f2914,plain,
! [X0,X1] :
( c_in(v_p,c_PropLog_Othms(c_minus(X1,v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))
| ~ c_lessequals(c_PropLog_Ohyps(v_p,X0,t_a),X1,tc_set(tc_PropLog_Opl(t_a))) ),
inference(resolution,[status(thm)],[f2872,f2887]) ).
fof(f2922,plain,
! [X0,X1] : c_in(v_p,c_PropLog_Othms(c_insert(X0,c_minus(c_PropLog_Ohyps(v_p,X1,t_a),c_insert(X0,v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[f2908,f2876]) ).
fof(f2924,plain,
! [X0,X1,X2] :
( c_in(v_p,c_PropLog_Othms(X2,t_a),tc_PropLog_Opl(t_a))
| ~ c_lessequals(c_minus(X1,v_F,tc_set(tc_PropLog_Opl(t_a))),X2,tc_set(tc_PropLog_Opl(t_a)))
| ~ c_lessequals(c_PropLog_Ohyps(v_p,X0,t_a),X1,tc_set(tc_PropLog_Opl(t_a))) ),
inference(resolution,[status(thm)],[f2914,f2883]) ).
fof(f2982,plain,
! [X0,X1,X2,X3] :
( c_in(v_p,c_PropLog_Othms(c_insert(X1,c_minus(X2,c_insert(X3,v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_lessequals(c_PropLog_Ohyps(v_p,X0,t_a),c_insert(X1,c_minus(X2,c_insert(X3,c_emptyset,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))) ),
inference(resolution,[status(thm)],[f2924,f2877]) ).
fof(f3000,plain,
! [X0,X1] :
( c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X1,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Ofalse,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(v_p,c_PropLog_Othms(c_insert(X0,c_minus(c_PropLog_Ohyps(v_p,X1,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Ofalse,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolution,[status(thm)],[f2881,f2922]) ).
fof(f3274,plain,
! [X0,X1] : c_in(v_p,c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(X0,t_a),c_minus(c_PropLog_Ohyps(v_p,X1,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X0,t_a),c_PropLog_Opl_Ofalse,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[f2982,f2875]) ).
fof(f3337,plain,
! [X0,X1] : c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X0,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X1,t_a),c_PropLog_Opl_Ofalse,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[f3000,f3274]) ).
fof(f3547,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f2889,f3337]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL430-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 00:34:52 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.42 % Drodi V4.1.1
% 0.28/0.59 % Refutation found
% 0.28/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.28/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.28/0.62 % Elapsed time: 0.235367 seconds
% 0.28/0.62 % CPU time: 1.329501 seconds
% 0.28/0.62 % Total memory used: 178.435 MB
% 0.28/0.62 % Net memory used: 177.301 MB
%------------------------------------------------------------------------------