%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 01:07:44 PM UTC 2026
% Result : Unsatisfiable 0.89s 0.55s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 64 ( 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_p,V_q,T_a,V_H] : ifeq(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)),true,ifeq(c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),true,c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_q,V_p,V_H,T_a] : ifeq(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)),true,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)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_p,V_H,T_a] : ifeq(c_in(V_p,V_H,tc_PropLog_Opl(T_a)),true,c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_p,V_G,T_a,V_a] : ifeq(c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a)),true,c_in(V_p,c_PropLog_Othms(c_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
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)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
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)) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1,X2,X3] : ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true,ifeq(c_in(X0,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true,c_in(X1,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),true),true) = true,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1,X2,X3] : ifeq(c_in(X0,c_PropLog_Othms(c_insert(X1,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),true,c_in(c_PropLog_Opl_Oop_A_N_62(X1,X0,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true) = true,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1,X2] : ifeq(c_in(X0,X1,tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true) = true,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : ifeq(c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true) = true,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1,X2] : c_in(X0,c_insert(X0,X1,X2),X2) = true,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
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)) = true,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f18,plain,
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)) != true,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f45,plain,
! [X0,X1,X2] : true = ifeq(true,true,c_in(X0,c_PropLog_Othms(c_insert(X0,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true),
inference(paramodulation,[status(thm)],[f15,f13]) ).
fof(f50,plain,
! [X0,X1,X2] : true = c_in(X0,c_PropLog_Othms(c_insert(X0,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),
inference(forward_demodulation,[status(thm)],[f10,f45]) ).
fof(f51,plain,
! [X0,X1,X2,X3] : true = ifeq(true,true,ifeq(c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),X3,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true,c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),X3,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true),true),
inference(paramodulation,[status(thm)],[f50,f11]) ).
fof(f56,plain,
! [X0,X1,X2,X3] : true = ifeq(c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),X3,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true,c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),X3,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true),
inference(forward_demodulation,[status(thm)],[f10,f51]) ).
fof(f98,plain,
! [X0] : true = ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(paramodulation,[status(thm)],[f17,f14]) ).
fof(f101,plain,
! [X0] : true = ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(paramodulation,[status(thm)],[f16,f14]) ).
fof(f106,plain,
! [X0] : true = c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(forward_demodulation,[status(thm)],[f10,f98]) ).
fof(f109,plain,
! [X0] : true = c_in(v_p,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(forward_demodulation,[status(thm)],[f10,f101]) ).
fof(f584,plain,
! [X0] : true = ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),
inference(paramodulation,[status(thm)],[f106,f11]) ).
fof(f594,plain,
! [X0] : true = ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X0,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(forward_demodulation,[status(thm)],[f10,f584]) ).
fof(f962,plain,
! [X0] : true = ifeq(true,true,c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X0,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(paramodulation,[status(thm)],[f109,f56]) ).
fof(f991,plain,
! [X0] : true = c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X0,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(forward_demodulation,[status(thm)],[f10,f962]) ).
fof(f1729,plain,
true = ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(paramodulation,[status(thm)],[f991,f594]) ).
fof(f1761,plain,
true = c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(forward_demodulation,[status(thm)],[f10,f1729]) ).
fof(f1946,plain,
true = ifeq(true,true,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)),true),
inference(paramodulation,[status(thm)],[f1761,f12]) ).
fof(f1953,plain,
true = 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)),
inference(forward_demodulation,[status(thm)],[f10,f1946]) ).
fof(f1954,plain,
$false,
inference(resolution,[status(thm)],[f1953,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.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 00:30:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.89/0.55 % Refutation found
% 0.89/0.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.89/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.89/0.58 % Elapsed time: 0.199399 seconds
% 0.89/0.58 % CPU time: 1.404210 seconds
% 0.89/0.58 % Total memory used: 73.171 MB
% 0.89/0.58 % Net memory used: 72.584 MB
%------------------------------------------------------------------------------