%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV280-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Thu Sep 24 02:47:08 PM UTC 2026
% Result : Unsatisfiable 44.46s 6.17s
% Output : CNFRefutation 43.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 25 unt; 0 def)
% Number of atoms : 29 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1161,axiom,
! [V_y] : c_Binomial_Obinomial(V_y,c_Suc(c_0)) = V_y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1162,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/sandbox/benchmark/theBenchmark.p') ).
fof(f1164,axiom,
! [V_n] : c_Binomial_Obinomial(V_n,c_0) = c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1344,axiom,
c_IntDef_Onat(c_1) = c_Suc(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2016,axiom,
c_1 = c_Suc(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2934,axiom,
! [V_n,V_m] : c_lessequals(V_n,c_plus(V_m,V_n,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2937,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/sandbox/benchmark/theBenchmark.p') ).
fof(f2938,negated_conjecture,
! [V_U] : c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_evs),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4141,plain,
! [X0] : c_Binomial_Obinomial(X0,c_Suc(c_0)) = X0,
inference(cnf_transformation,[status(thm)],[f1161]) ).
fof(f4142,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)],[f1162]) ).
fof(f4144,plain,
! [X0] : c_Binomial_Obinomial(X0,c_0) = c_1,
inference(cnf_transformation,[status(thm)],[f1164]) ).
fof(f4379,plain,
c_IntDef_Onat(c_1) = c_Suc(c_0),
inference(cnf_transformation,[status(thm)],[f1344]) ).
fof(f5272,plain,
c_1 = c_Suc(c_0),
inference(cnf_transformation,[status(thm)],[f2016]) ).
fof(f6524,plain,
! [X0,X1] : c_lessequals(X0,c_plus(X1,X0,tc_nat),tc_nat),
inference(cnf_transformation,[status(thm)],[f2934]) ).
fof(f6527,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)],[f2937]) ).
fof(f6528,plain,
! [X0] : c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg),
inference(cnf_transformation,[status(thm)],[f2938]) ).
fof(f6546,plain,
! [X0] : c_Binomial_Obinomial(X0,c_IntDef_Onat(c_1)) = X0,
inference(backward_demodulation,[status(thm)],[f4379,f4141]) ).
fof(f6578,plain,
c_IntDef_Onat(c_1) = c_1,
inference(backward_demodulation,[status(thm)],[f5272,f4379]) ).
fof(f6698,plain,
! [X0] : c_Binomial_Obinomial(X0,c_1) = X0,
inference(backward_demodulation,[status(thm)],[f6578,f6546]) ).
fof(f8390,plain,
! [X0] : c_Binomial_Obinomial(c_Suc(X0),c_Suc(c_0)) = c_plus(c_Binomial_Obinomial(X0,c_0),c_Binomial_Obinomial(X0,c_1),tc_nat),
inference(paramodulation,[status(thm)],[f5272,f4142]) ).
fof(f8396,plain,
! [X0] : c_Binomial_Obinomial(c_Suc(X0),c_1) = c_plus(c_Binomial_Obinomial(X0,c_0),c_Binomial_Obinomial(X0,c_1),tc_nat),
inference(forward_demodulation,[status(thm)],[f5272,f8390]) ).
fof(f8397,plain,
! [X0] : c_Suc(X0) = c_plus(c_Binomial_Obinomial(X0,c_0),c_Binomial_Obinomial(X0,c_1),tc_nat),
inference(forward_demodulation,[status(thm)],[f6698,f8396]) ).
fof(f8398,plain,
! [X0] : c_Suc(X0) = c_plus(c_1,c_Binomial_Obinomial(X0,c_1),tc_nat),
inference(forward_demodulation,[status(thm)],[f4144,f8397]) ).
fof(f8400,plain,
! [X0] : c_Suc(X0) = c_plus(c_1,X0,tc_nat),
inference(forward_demodulation,[status(thm)],[f6698,f8398]) ).
fof(f13872,plain,
! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat),
inference(paramodulation,[status(thm)],[f8400,f6524]) ).
fof(f25984,plain,
! [X0] : ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat),
inference(resolution,[status(thm)],[f6527,f6528]) ).
fof(f25989,plain,
$false,
inference(resolution,[status(thm)],[f25984,f13872]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV280-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 08:42:38 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.20/0.48 % Drodi V4.1.1
% 44.46/6.17 % Refutation found
% 44.46/6.17 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 44.46/6.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 32.04/7.52 % Elapsed time: 6.946747 seconds
% 32.04/7.52 % CPU time: 44.876817 seconds
% 32.04/7.52 % Total memory used: 1.146 GB
% 32.04/7.52 % Net memory used: 1.120 GB
%------------------------------------------------------------------------------