%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SCT168+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 02:07:02 PM UTC 2026
% Result : Theorem 0.15s 10.66s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-5 aty)
% Number of variables : 64 ( 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f384,axiom,
! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f525,axiom,
! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f527,axiom,
! [V_R_2,V_Q_2,V_Pa_2,T_c,T_a,T_b] : hAPP(hAPP(c_COMBB(T_b,T_a,T_c,V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f529,axiom,
! [V_R_2,V_Q_2,V_Pa_2,T_a,T_c,T_b] : hAPP(c_COMBS(T_b,T_c,T_a,V_Pa_2,V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1797,plain,
! [X0] : X0 != hAPP(c_Nat_OSuc,X0),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f2171,plain,
! [X0,X1] : hAPP(c_COMBI(X0),X1) = X1,
inference(cnf_transformation,[status(thm)],[f525]) ).
fof(f2173,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(c_COMBB(X0,X1,X2,X3),X4),X5) = hAPP(X3,hAPP(X4,X5)),
inference(cnf_transformation,[status(thm)],[f527]) ).
fof(f2175,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(c_COMBS(X0,X1,X2,X3,X4),X5) = hAPP(hAPP(X3,X5),hAPP(X4,X5)),
inference(cnf_transformation,[status(thm)],[f529]) ).
fof(f2467,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : hAPP(c_COMBS(X0,X1,X2,c_COMBB(X3,X4,X5,X6),X7),X8) = hAPP(X6,hAPP(X8,hAPP(X7,X8))),
inference(paramodulation,[status(thm)],[f2173,f2175]) ).
fof(f2468,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : hAPP(c_COMBS(X0,X1,X2,X3,X4),X5) = hAPP(c_COMBS(X6,X7,X8,X3,X4),X5),
inference(paramodulation,[status(thm)],[f2175,f2175]) ).
fof(f2948,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : hAPP(X0,hAPP(X1,X0)) != hAPP(c_COMBS(X2,X3,X4,c_COMBB(X5,X6,X7,c_Nat_OSuc),X1),X0),
inference(paramodulation,[status(thm)],[f2467,f1797]) ).
fof(f3579,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : hAPP(X0,X0) != hAPP(c_COMBS(X1,X2,X3,c_COMBB(X4,X5,X6,c_Nat_OSuc),c_COMBI(X7)),X0),
inference(paramodulation,[status(thm)],[f2171,f2948]) ).
fof(f3611,plain,
$false,
inference(resolution,[status(thm)],[f3579,f2468]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT168+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.39 % Computer : n019.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Mon Sep 21 04:36:01 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.15/10.46 % Drodi V4.1.1
% 0.15/10.66 % Refutation found
% 0.15/10.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/10.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/10.69 % Elapsed time: 0.283214 seconds
% 0.15/10.69 % CPU time: 1.556121 seconds
% 0.15/10.69 % Total memory used: 204.353 MB
% 0.15/10.69 % Net memory used: 202.776 MB
%------------------------------------------------------------------------------