%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX222-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 03:13:29 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 38 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 6 con; 0-4 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Z,X3,Tx3] : aux(X,Z,X3,just(Tx3)) = eq(Tx3,Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
notb(btrue) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Z,Xs] : index(cons(Z,Xs),zero) = just(Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Q] : andb(btrue,Q) = Q,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [E] : nf(lam(E)) = nf(E),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X4] : nf(var(X4)) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,E,Tx2,T1] : tc(X,lam(E),arr(Tx2,T1)) = tc(cons(Tx2,X),E,T1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,X3,Z] : tc(X,var(X3),Z) = aux(X,Z,X3,index(X,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] : sat_synth_nf_k(X) = notb(andb(nf(X),tc(nil,X,arr(a,arr(b,b))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [X] : eq(X,X) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [X] : eq4(X,X) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
! [X] : eq4(sat_synth_nf_k(X),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,plain,
! [X0,X1,X2,X3] : aux(X0,X1,X2,just(X3)) = eq(X3,X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f59,plain,
notb(btrue) = bfalse,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f62,plain,
! [X0,X1] : index(cons(X0,X1),zero) = just(X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f64,plain,
! [X0] : andb(btrue,X0) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f69,plain,
! [X0] : nf(lam(X0)) = nf(X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f70,plain,
! [X0] : nf(var(X0)) = btrue,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f72,plain,
! [X0,X1,X2,X3] : tc(X0,lam(X1),arr(X2,X3)) = tc(cons(X2,X0),X1,X3),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f76,plain,
! [X0,X1,X2] : tc(X0,var(X1),X2) = aux(X0,X2,X1,index(X0,X1)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f77,plain,
! [X0] : sat_synth_nf_k(X0) = notb(andb(nf(X0),tc(nil,X0,arr(a,arr(b,b))))),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f113,plain,
! [X0] : eq(X0,X0) = btrue,
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f116,plain,
! [X0] : eq4(X0,X0) = btrue,
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f117,plain,
! [X0] : eq4(sat_synth_nf_k(X0),bfalse) != btrue,
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f129,plain,
! [X0] : sat_synth_nf_k(lam(X0)) = notb(andb(nf(X0),tc(nil,lam(X0),arr(a,arr(b,b))))),
inference(paramodulation,[status(thm)],[f69,f77]) ).
fof(f130,plain,
! [X0] : sat_synth_nf_k(lam(X0)) = notb(andb(nf(X0),tc(cons(a,nil),X0,arr(b,b)))),
inference(forward_demodulation,[status(thm)],[f72,f129]) ).
fof(f137,plain,
! [X0] : sat_synth_nf_k(lam(lam(X0))) = notb(andb(nf(X0),tc(cons(a,nil),lam(X0),arr(b,b)))),
inference(paramodulation,[status(thm)],[f69,f130]) ).
fof(f141,plain,
! [X0] : sat_synth_nf_k(lam(lam(X0))) = notb(andb(nf(X0),tc(cons(b,cons(a,nil)),X0,b))),
inference(forward_demodulation,[status(thm)],[f72,f137]) ).
fof(f147,plain,
! [X0] : sat_synth_nf_k(lam(lam(var(X0)))) = notb(andb(btrue,tc(cons(b,cons(a,nil)),var(X0),b))),
inference(paramodulation,[status(thm)],[f70,f141]) ).
fof(f152,plain,
! [X0] : sat_synth_nf_k(lam(lam(var(X0)))) = notb(tc(cons(b,cons(a,nil)),var(X0),b)),
inference(forward_demodulation,[status(thm)],[f64,f147]) ).
fof(f269,plain,
! [X0,X1,X2] : tc(cons(X0,X1),var(zero),X2) = aux(cons(X0,X1),X2,zero,just(X0)),
inference(paramodulation,[status(thm)],[f62,f76]) ).
fof(f271,plain,
! [X0,X1,X2] : tc(cons(X0,X1),var(zero),X2) = eq(X0,X2),
inference(forward_demodulation,[status(thm)],[f58,f269]) ).
fof(f281,plain,
sat_synth_nf_k(lam(lam(var(zero)))) = notb(eq(b,b)),
inference(paramodulation,[status(thm)],[f271,f152]) ).
fof(f285,plain,
sat_synth_nf_k(lam(lam(var(zero)))) = notb(btrue),
inference(forward_demodulation,[status(thm)],[f113,f281]) ).
fof(f286,plain,
sat_synth_nf_k(lam(lam(var(zero)))) = bfalse,
inference(forward_demodulation,[status(thm)],[f59,f285]) ).
fof(f299,plain,
eq4(bfalse,bfalse) != btrue,
inference(paramodulation,[status(thm)],[f286,f117]) ).
fof(f300,plain,
btrue != btrue,
inference(forward_demodulation,[status(thm)],[f116,f299]) ).
fof(f301,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX222-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 10:35:19 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.059205 seconds
% 0.14/0.42 % CPU time: 0.195594 seconds
% 0.14/0.42 % Total memory used: 70.425 MB
% 0.14/0.42 % Net memory used: 70.395 MB
%------------------------------------------------------------------------------