%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV282-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 02:47:09 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 13
% Syntax : Number of formulae : 106 ( 32 unt; 0 def)
% Number of atoms : 257 ( 161 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 196 ( 45 ~; 151 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 141 ( 141 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [V_U,V_W,V_V] :
( c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_V),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_W),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| V_U = V_V
| V_V = V_W
| V_U = V_W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_y] : c_Binomial_Obinomial(V_y,c_Suc(c_0)) = V_y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_n,V_k] : c_Binomial_Obinomial(c_Suc(V_n),c_Suc(V_k)) = c_plus(c_Binomial_Obinomial(V_n,V_k),c_Binomial_Obinomial(V_n,c_Suc(V_k)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_n] : c_Binomial_Obinomial(V_n,c_0) = c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
c_1 = c_Suc(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_m,V_n] :
( c_lessequals(V_m,V_n,tc_nat)
| c_minus(V_m,V_n,tc_nat) != c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_m] : c_minus(V_m,V_m,tc_nat) = c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [V_n,V_m] : c_lessequals(V_n,c_plus(V_n,V_m,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [V_n] : c_less(V_n,c_Suc(V_n),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [V_m,V_n] :
( c_less(V_m,c_Suc(V_n),tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [V_k,V_m,V_n] :
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_plus(V_k,V_m,tc_nat),c_plus(V_k,V_n,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [V_j,V_i] : ~ c_less(c_plus(V_j,V_i,tc_nat),V_i,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [V_U,V_evs] :
( ~ c_lessequals(v_sko__urX(V_evs),V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(V_evs),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [V_U] :
( c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_evs),tc_Message_Omsg)
| ! [V_V] :
( c_in(c_Message_Omsg_ONonce(V_V),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| ! [V_W] :
( c_in(c_Message_Omsg_ONonce(V_W),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| V_U = V_V
| V_V = V_W
| V_U = V_W ) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0,X1,X2] :
( c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| X0 = X2
| X2 = X1
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0] : c_Binomial_Obinomial(X0,c_Suc(c_0)) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0,X1] : c_Binomial_Obinomial(c_Suc(X0),c_Suc(X1)) = c_plus(c_Binomial_Obinomial(X0,X1),c_Binomial_Obinomial(X0,c_Suc(X1)),tc_nat),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0] : c_Binomial_Obinomial(X0,c_0) = c_1,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
c_1 = c_Suc(c_0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_minus(X0,X1,tc_nat) != c_0 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0] : c_minus(X0,X0,tc_nat) = c_0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0,X1] : c_lessequals(X0,c_plus(X0,X1,tc_nat),tc_nat),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
! [X0] : c_less(X0,c_Suc(X0),tc_nat),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1] :
( c_less(X0,c_Suc(X1),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [V_m,V_n] :
( c_lessequals(V_m,V_n,tc_nat)
| ! [V_k] : ~ c_lessequals(c_plus(V_k,V_m,tc_nat),c_plus(V_k,V_n,tc_nat),tc_nat) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f27,plain,
! [X0,X1,X2] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_plus(X0,X1,tc_nat),c_plus(X0,X2,tc_nat),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] : ~ c_less(c_plus(X0,X1,tc_nat),X1,tc_nat),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
! [X0,X1] :
( ~ c_lessequals(v_sko__urX(X1),X0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(X1),tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f31,plain,
! [X0] : c_Binomial_Obinomial(X0,c_1) = X0,
inference(forward_demodulation,[status(thm)],[f20,f17]) ).
fof(f33,plain,
! [X0] : c_Binomial_Obinomial(c_Suc(X0),c_Suc(c_0)) = c_plus(c_1,c_Binomial_Obinomial(X0,c_Suc(c_0)),tc_nat),
inference(paramodulation,[status(thm)],[f19,f18]) ).
fof(f34,plain,
! [X0] : c_Binomial_Obinomial(c_Suc(X0),c_Suc(c_1)) = c_plus(X0,c_Binomial_Obinomial(X0,c_Suc(c_1)),tc_nat),
inference(paramodulation,[status(thm)],[f31,f18]) ).
fof(f36,plain,
! [X0] : c_Binomial_Obinomial(c_Suc(X0),c_1) = c_plus(c_1,c_Binomial_Obinomial(X0,c_Suc(c_0)),tc_nat),
inference(forward_demodulation,[status(thm)],[f20,f33]) ).
fof(f37,plain,
! [X0] : c_Suc(X0) = c_plus(c_1,c_Binomial_Obinomial(X0,c_Suc(c_0)),tc_nat),
inference(forward_demodulation,[status(thm)],[f31,f36]) ).
fof(f38,plain,
! [X0] : c_Suc(X0) = c_plus(c_1,c_Binomial_Obinomial(X0,c_1),tc_nat),
inference(forward_demodulation,[status(thm)],[f20,f37]) ).
fof(f39,plain,
! [X0] : c_Suc(X0) = c_plus(c_1,X0,tc_nat),
inference(forward_demodulation,[status(thm)],[f31,f38]) ).
fof(f44,plain,
! [X0] : c_lessequals(X0,X0,tc_nat),
inference(resolution,[status(thm)],[f21,f22]) ).
fof(f51,plain,
! [X0,X1] : c_less(X0,c_Suc(c_plus(X0,X1,tc_nat)),tc_nat),
inference(resolution,[status(thm)],[f25,f23]) ).
fof(f54,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_Suc(X0),c_plus(c_1,X1,tc_nat),tc_nat) ),
inference(paramodulation,[status(thm)],[f39,f27]) ).
fof(f58,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) ),
inference(forward_demodulation,[status(thm)],[f39,f54]) ).
fof(f60,plain,
! [X0] : ~ c_less(c_Suc(X0),X0,tc_nat),
inference(paramodulation,[status(thm)],[f39,f28]) ).
fof(f63,plain,
! [X0,X1,X2] :
( c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| X0 = X2
| X2 = X1
| X0 = X1
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat) ),
inference(resolution,[status(thm)],[f29,f16]) ).
fof(f64,plain,
! [X0,X1,X2] :
( c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| X1 = X0
| X0 = X2
| X1 = X2
| ~ c_lessequals(v_sko__urX(v_evs_H),X0,tc_nat) ),
inference(resolution,[status(thm)],[f29,f16]) ).
fof(f67,plain,
! [X0,X1] :
( c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| v_sko__urX(v_evs) = X1
| X1 = X0
| v_sko__urX(v_evs) = X0 ),
inference(resolution,[status(thm)],[f63,f44]) ).
fof(f68,plain,
! [X0,X1] :
( ~ c_lessequals(v_sko__urX(v_evs_H_H),X0,tc_nat)
| c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| v_sko__urX(v_evs) = X1
| X1 = X0
| v_sko__urX(v_evs) = X0 ),
inference(resolution,[status(thm)],[f67,f29]) ).
fof(f69,plain,
! [X0,X1] :
( ~ c_lessequals(v_sko__urX(v_evs_H),X1,tc_nat)
| c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| v_sko__urX(v_evs) = X1
| X1 = X0
| v_sko__urX(v_evs) = X0 ),
inference(resolution,[status(thm)],[f67,f29]) ).
fof(f70,plain,
! [X0,X1] :
( c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| v_sko__urX(v_evs) = X1
| X1 = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(resolution,[status(thm)],[f68,f23]) ).
fof(f71,plain,
! [X0] :
( c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| v_sko__urX(v_evs) = X0
| X0 = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f68,f44]) ).
fof(f72,plain,
! [X0] :
( ~ c_lessequals(v_sko__urX(v_evs_H),X0,tc_nat)
| v_sko__urX(v_evs) = X0
| X0 = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f71,f29]) ).
fof(f74,plain,
! [X0,X1] :
( c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| X0 = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = X1
| X0 = X1 ),
inference(resolution,[status(thm)],[f64,f44]) ).
fof(f136,plain,
! [X0] :
( v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H),X0,tc_nat)
| c_plus(v_sko__urX(v_evs_H),X0,tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f72,f23]) ).
fof(f144,plain,
! [X0] :
( c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = X0
| v_sko__urX(v_evs) = X0 ),
inference(resolution,[status(thm)],[f69,f44]) ).
fof(f145,plain,
! [X0] :
( ~ c_lessequals(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = X0
| v_sko__urX(v_evs) = X0 ),
inference(resolution,[status(thm)],[f144,f29]) ).
fof(f147,plain,
! [X0] :
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(resolution,[status(thm)],[f145,f23]) ).
fof(f149,plain,
! [X0,X1] :
( ~ c_lessequals(v_sko__urX(v_evs_H_H),X1,tc_nat)
| c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg)
| X0 = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = X1
| X0 = X1 ),
inference(resolution,[status(thm)],[f74,f29]) ).
fof(f191,plain,
! [X0] :
( c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg)
| X0 = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f149,f44]) ).
fof(f192,plain,
! [X0] :
( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f191,f29]) ).
fof(f196,plain,
! [X0] :
( c_plus(v_sko__urX(v_evs),X0,tc_nat) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| c_plus(v_sko__urX(v_evs),X0,tc_nat) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f192,f23]) ).
fof(f245,plain,
! [X0] :
( c_plus(v_sko__urX(v_evs_H),X0,tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| ~ c_less(v_sko__urX(v_evs),X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f136,f28]) ).
fof(f253,plain,
! [X0] :
( c_plus(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X0,tc_nat)),tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f245,f51]) ).
fof(f358,plain,
! [X0] :
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| ~ c_less(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs),X0,tc_nat)),tc_nat) ),
inference(paramodulation,[status(thm)],[f253,f28]) ).
fof(f365,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| ~ c_less(v_sko__urX(v_evs_H_H),c_Suc(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs)),c_Suc(c_1))),tc_nat) ),
inference(paramodulation,[status(thm)],[f34,f358]) ).
fof(f432,plain,
! [X0,X1] :
( ~ c_lessequals(v_sko__urX(v_evs_H),X1,tc_nat)
| v_sko__urX(v_evs) = X1
| X1 = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(resolution,[status(thm)],[f70,f29]) ).
fof(f438,plain,
! [X0] :
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| ~ c_less(v_sko__urX(v_evs),X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f147,f28]) ).
fof(f446,plain,
! [X0] :
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs),X0,tc_nat)),tc_nat) ),
inference(resolution,[status(thm)],[f438,f51]) ).
fof(f447,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat) ),
inference(resolution,[status(thm)],[f438,f24]) ).
fof(f454,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat) ),
inference(paramodulation,[status(thm)],[f447,f51]) ).
fof(f512,plain,
! [X0] :
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| ~ c_less(v_sko__urX(v_evs_H),c_Suc(c_plus(v_sko__urX(v_evs),X0,tc_nat)),tc_nat) ),
inference(paramodulation,[status(thm)],[f446,f28]) ).
fof(f534,plain,
! [X0] :
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| c_plus(v_sko__urX(v_evs),X0,tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| ~ c_less(v_sko__urX(v_evs_H),c_Suc(v_sko__urX(v_evs_H)),tc_nat) ),
inference(paramodulation,[status(thm)],[f196,f512]) ).
fof(f542,plain,
! [X0] :
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| c_plus(v_sko__urX(v_evs),X0,tc_nat) = v_sko__urX(v_evs_H_H)
| ~ c_less(v_sko__urX(v_evs_H),X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f196,f28]) ).
fof(f549,plain,
! [X0] :
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| c_plus(v_sko__urX(v_evs),X0,tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H) ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f24]) ).
fof(f563,plain,
! [X0] :
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| ~ c_less(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f549,f28]) ).
fof(f574,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H) ),
inference(resolution,[status(thm)],[f563,f454]) ).
fof(f578,plain,
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H) ),
inference(duplicate_literals_removal,[status(thm)],[f574]) ).
fof(f621,plain,
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| c_plus(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H)),tc_nat) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f542,f24]) ).
fof(f632,plain,
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| ~ c_less(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) ),
inference(paramodulation,[status(thm)],[f621,f358]) ).
fof(f644,plain,
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(forward_subsumption_resolution,[status(thm)],[f632,f24]) ).
fof(f645,plain,
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H) ),
inference(paramodulation,[status(thm)],[f578,f644]) ).
fof(f669,plain,
v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H),
inference(duplicate_literals_removal,[status(thm)],[f645]) ).
fof(f694,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat) ),
inference(backward_demodulation,[status(thm)],[f669,f447]) ).
fof(f695,plain,
! [X0] :
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| ~ c_less(v_sko__urX(v_evs),X0,tc_nat) ),
inference(backward_demodulation,[status(thm)],[f669,f438]) ).
fof(f736,plain,
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(v_sko__urX(v_evs)),tc_nat) ),
inference(forward_demodulation,[status(thm)],[f669,f694]) ).
fof(f737,plain,
! [X0] :
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| ~ c_less(v_sko__urX(v_evs),X0,tc_nat) ),
inference(forward_demodulation,[status(thm)],[f669,f695]) ).
fof(f764,plain,
! [X0] :
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| c_lessequals(c_Suc(v_sko__urX(v_evs)),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H_H),c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat),tc_nat) ),
inference(paramodulation,[status(thm)],[f736,f27]) ).
fof(f767,plain,
! [X0] :
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| c_lessequals(c_Suc(v_sko__urX(v_evs)),X0,tc_nat) ),
inference(forward_subsumption_resolution,[status(thm)],[f764,f23]) ).
fof(f772,plain,
! [X0] :
( c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f767,f58]) ).
fof(f777,plain,
! [X0] :
( c_less(v_sko__urX(v_evs),c_Suc(X0),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f772,f25]) ).
fof(f833,plain,
! [X0] :
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(X0),tc_nat) ),
inference(resolution,[status(thm)],[f737,f777]) ).
fof(f839,plain,
! [X0] :
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(X0),tc_nat) ),
inference(duplicate_literals_removal,[status(thm)],[f833]) ).
fof(f866,plain,
! [X0,X1] :
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| c_lessequals(c_Suc(X1),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H_H),c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat),tc_nat) ),
inference(paramodulation,[status(thm)],[f839,f27]) ).
fof(f869,plain,
! [X0,X1] :
( v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H)
| c_lessequals(c_Suc(X0),X1,tc_nat) ),
inference(forward_subsumption_resolution,[status(thm)],[f866,f23]) ).
fof(f872,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f869,f58]) ).
fof(f904,plain,
! [X0,X1] :
( c_less(X0,c_Suc(X1),tc_nat)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f872,f25]) ).
fof(f940,plain,
v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H),
inference(backward_subsumption_resolution,[status(thm)],[f365,f904]) ).
fof(f1218,plain,
! [X0,X1] :
( ~ c_lessequals(v_sko__urX(v_evs_H),X1,tc_nat)
| v_sko__urX(v_evs) = X1
| X1 = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(forward_demodulation,[status(thm)],[f940,f432]) ).
fof(f1219,plain,
! [X0,X1] :
( ~ c_lessequals(v_sko__urX(v_evs_H),X1,tc_nat)
| v_sko__urX(v_evs_H_H) = X1
| X1 = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(forward_demodulation,[status(thm)],[f940,f1218]) ).
fof(f1220,plain,
! [X0,X1] :
( ~ c_lessequals(v_sko__urX(v_evs_H_H),X1,tc_nat)
| v_sko__urX(v_evs_H_H) = X1
| X1 = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(forward_demodulation,[status(thm)],[f669,f1219]) ).
fof(f1222,plain,
! [X0,X1] :
( v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),X1,tc_nat)
| c_plus(v_sko__urX(v_evs_H_H),X1,tc_nat) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(resolution,[status(thm)],[f1220,f23]) ).
fof(f1424,plain,
! [X0,X1] :
( v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),X1,tc_nat)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| ~ c_less(c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat),X1,tc_nat) ),
inference(paramodulation,[status(thm)],[f1222,f28]) ).
fof(f1448,plain,
! [X0] :
( v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)),tc_nat)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(resolution,[status(thm)],[f1424,f24]) ).
fof(f1469,plain,
! [X0] :
( v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)
| ~ c_less(v_sko__urX(v_evs_H_H),c_Suc(c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat)),tc_nat) ),
inference(paramodulation,[status(thm)],[f1448,f28]) ).
fof(f1481,plain,
! [X0] : v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat),
inference(forward_subsumption_resolution,[status(thm)],[f1469,f51]) ).
fof(f1508,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_plus(v_sko__urX(v_evs_H_H),X0,tc_nat),v_sko__urX(v_evs_H_H),tc_nat) ),
inference(paramodulation,[status(thm)],[f1481,f27]) ).
fof(f1526,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H_H),tc_nat) ),
inference(forward_demodulation,[status(thm)],[f1481,f1508]) ).
fof(f1527,plain,
! [X0,X1] : c_lessequals(X0,X1,tc_nat),
inference(forward_subsumption_resolution,[status(thm)],[f1526,f44]) ).
fof(f1541,plain,
! [X0,X1] : c_less(X0,c_Suc(X1),tc_nat),
inference(backward_subsumption_resolution,[status(thm)],[f25,f1527]) ).
fof(f1559,plain,
$false,
inference(resolution,[status(thm)],[f1541,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV282-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 08:37:51 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.12/0.43 % Refutation found
% 0.12/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.140595 seconds
% 0.12/0.44 % CPU time: 0.907430 seconds
% 0.12/0.44 % Total memory used: 129.693 MB
% 0.12/0.44 % Net memory used: 128.022 MB
%------------------------------------------------------------------------------