%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN982-1 : TPTP v9.3.1. Released v3.1.0.
% 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 03:18:38 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 62 ( 13 unt; 0 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 207 ( 107 ~; 100 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 105 ( 105 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
ssBf(na),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
ssP(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
ssP(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [U,V] :
( ssIm(V)
| ~ ssIm(pair(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
ssM(sent(a,b,pair(a,na))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [U,V,W] :
( ssIm(W)
| ~ ssIm(triple(U,V,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U,V,W] :
( ssIm(V)
| ~ ssIm(triple(U,V,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [U,V,W] :
( ssIm(W)
| ~ ssM(sent(U,V,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U,V] :
( ssIk(key(U,V))
| ~ ssP(V)
| ~ ssIm(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U,V] :
( ssIm(pair(U,V))
| ~ ssIm(V)
| ~ ssIm(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [U,V,W] :
( ssM(sent(V,W,U))
| ~ ssP(W)
| ~ ssP(V)
| ~ ssIm(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [U,V,W] :
( ssIm(encr(U,V))
| ~ ssP(W)
| ~ ssIk(key(V,W))
| ~ ssIm(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [U,V] :
( ssSb(pair(U,V))
| ~ ssBf(V)
| ~ ssM(sent(U,b,pair(U,V))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [U,V] :
( ssM(sent(b,t,triple(b,nb(V),encr(triple(U,V,tb(V)),bt))))
| ~ ssBf(V)
| ~ ssM(sent(U,b,pair(U,V))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [U,V,W] :
( ssBk(key(V,U))
| ~ ssSb(pair(U,W))
| ~ ssM(sent(U,b,pair(encr(triple(U,V,tb(W)),bt),encr(nb(W),V)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
! [U] :
( ~ ssBk(key(U,a))
| ~ ssIk(key(U,b)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,plain,
ssBf(na),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f41,plain,
ssP(b),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f42,plain,
ssP(a),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f51,plain,
! [V] :
( ssIm(V)
| ! [U] : ~ ssIm(pair(U,V)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f52,plain,
! [X0,X1] :
( ssIm(X1)
| ~ ssIm(pair(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f55,plain,
ssM(sent(a,b,pair(a,na))),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f56,plain,
! [W] :
( ssIm(W)
| ! [U,V] : ~ ssIm(triple(U,V,W)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ssIm(X2)
| ~ ssIm(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [V] :
( ssIm(V)
| ! [U,W] : ~ ssIm(triple(U,V,W)) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ssIm(X1)
| ~ ssIm(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f62,plain,
! [W] :
( ssIm(W)
| ! [U,V] : ~ ssM(sent(U,V,W)) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ssIm(X2)
| ~ ssM(sent(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f72,plain,
! [X0,X1] :
( ssIk(key(X0,X1))
| ~ ssP(X1)
| ~ ssIm(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f73,plain,
! [X0,X1] :
( ssIm(pair(X0,X1))
| ~ ssIm(X1)
| ~ ssIm(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ssM(sent(X1,X2,X0))
| ~ ssP(X2)
| ~ ssP(X1)
| ~ ssIm(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f76,plain,
! [U,V] :
( ssIm(encr(U,V))
| ! [W] :
( ~ ssP(W)
| ~ ssIk(key(V,W))
| ~ ssIm(U) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ssIm(encr(X0,X1))
| ~ ssP(X2)
| ~ ssIk(key(X1,X2))
| ~ ssIm(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ssSb(pair(X0,X1))
| ~ ssBf(X1)
| ~ ssM(sent(X0,b,pair(X0,X1))) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f82,plain,
! [X0,X1] :
( ssM(sent(b,t,triple(b,nb(X1),encr(triple(X0,X1,tb(X1)),bt))))
| ~ ssBf(X1)
| ~ ssM(sent(X0,b,pair(X0,X1))) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f83,plain,
! [U,V] :
( ssBk(key(V,U))
| ! [W] :
( ~ ssSb(pair(U,W))
| ~ ssM(sent(U,b,pair(encr(triple(U,V,tb(W)),bt),encr(nb(W),V)))) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ssBk(key(X1,X0))
| ~ ssSb(pair(X0,X2))
| ~ ssM(sent(X0,b,pair(encr(triple(X0,X1,tb(X2)),bt),encr(nb(X2),X1)))) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f88,plain,
! [X0] :
( ~ ssBk(key(X0,a))
| ~ ssIk(key(X0,b)) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f89,plain,
! [X0] :
( ~ ssBk(key(X0,a))
| ~ ssP(b)
| ~ ssIm(X0) ),
inference(resolution,[status(thm)],[f72,f88]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ ssP(X1)
| ~ ssIm(X2)
| ssIm(encr(X0,X2))
| ~ ssP(X1)
| ~ ssIm(X0) ),
inference(resolution,[status(thm)],[f77,f72]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ~ ssIm(X2)
| ssIm(encr(X0,X2))
| ~ ssP(X1)
| ~ ssIm(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f90]) ).
fof(f92,plain,
! [X0] :
( ~ ssBk(key(X0,a))
| ~ ssIm(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f89,f41]) ).
fof(f95,plain,
ssIm(pair(a,na)),
inference(resolution,[status(thm)],[f55,f63]) ).
fof(f97,plain,
ssIm(na),
inference(resolution,[status(thm)],[f95,f52]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ~ ssP(b)
| ~ ssP(X0)
| ~ ssIm(pair(encr(triple(X0,X2,tb(X1)),bt),encr(nb(X1),X2)))
| ssBk(key(X2,X0))
| ~ ssSb(pair(X0,X1)) ),
inference(resolution,[status(thm)],[f84,f74]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ~ ssP(X0)
| ~ ssIm(pair(encr(triple(X0,X2,tb(X1)),bt),encr(nb(X1),X2)))
| ssBk(key(X2,X0))
| ~ ssSb(pair(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f41]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ~ ssIm(encr(nb(X1),X2))
| ~ ssIm(encr(triple(X0,X2,tb(X1)),bt))
| ~ ssP(X0)
| ssBk(key(X2,X0))
| ~ ssSb(pair(X0,X1)) ),
inference(resolution,[status(thm)],[f121,f73]) ).
fof(f132,plain,
! [X0,X1] :
( ssIm(triple(b,nb(X1),encr(triple(X0,X1,tb(X1)),bt)))
| ~ ssBf(X1)
| ~ ssM(sent(X0,b,pair(X0,X1))) ),
inference(resolution,[status(thm)],[f82,f63]) ).
fof(f134,plain,
! [X0,X1] :
( ssIm(nb(X1))
| ~ ssBf(X1)
| ~ ssM(sent(X0,b,pair(X0,X1))) ),
inference(resolution,[status(thm)],[f132,f59]) ).
fof(f135,plain,
! [X0,X1] :
( ssIm(encr(triple(X0,X1,tb(X1)),bt))
| ~ ssBf(X1)
| ~ ssM(sent(X0,b,pair(X0,X1))) ),
inference(resolution,[status(thm)],[f132,f57]) ).
fof(f141,plain,
( ssIm(nb(na))
| ~ ssBf(na) ),
inference(resolution,[status(thm)],[f134,f55]) ).
fof(f143,plain,
ssIm(nb(na)),
inference(forward_subsumption_resolution,[status(thm)],[f141,f40]) ).
fof(f149,plain,
! [X0,X1] :
( ~ ssIm(encr(nb(X1),X1))
| ~ ssP(X0)
| ssBk(key(X1,X0))
| ~ ssSb(pair(X0,X1))
| ~ ssBf(X1)
| ~ ssM(sent(X0,b,pair(X0,X1))) ),
inference(resolution,[status(thm)],[f135,f122]) ).
fof(f150,plain,
! [X0,X1] :
( ~ ssIm(encr(nb(X1),X1))
| ~ ssP(X0)
| ssBk(key(X1,X0))
| ~ ssBf(X1)
| ~ ssM(sent(X0,b,pair(X0,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f78]) ).
fof(f151,plain,
( ~ ssIm(encr(nb(na),na))
| ~ ssP(a)
| ssBk(key(na,a))
| ~ ssBf(na) ),
inference(resolution,[status(thm)],[f150,f55]) ).
fof(f153,plain,
( ~ ssIm(encr(nb(na),na))
| ~ ssP(a)
| ssBk(key(na,a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f40]) ).
fof(f156,plain,
( ~ ssIm(encr(nb(na),na))
| ssBk(key(na,a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f153,f42]) ).
fof(f157,plain,
! [X0] :
( ~ ssIm(na)
| ~ ssP(X0)
| ~ ssIm(nb(na))
| ssBk(key(na,a)) ),
inference(resolution,[status(thm)],[f156,f91]) ).
fof(f158,plain,
! [X0] :
( ~ ssIm(na)
| ~ ssP(X0)
| ~ ssIm(nb(na)) ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f92]) ).
fof(f159,plain,
! [X0] :
( ~ ssIm(na)
| ~ ssP(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f143]) ).
fof(f160,plain,
~ ssIm(na),
inference(resolution,[status(thm)],[f159,f42]) ).
fof(f163,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f160,f97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN982-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n016.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 11:36:54 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.37 % Refutation found
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.39 % Elapsed time: 0.041766 seconds
% 0.11/0.39 % CPU time: 0.110078 seconds
% 0.11/0.39 % Total memory used: 28.784 MB
% 0.11/0.39 % Net memory used: 28.672 MB
%------------------------------------------------------------------------------