%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 03:42:51 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.37s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 10 unt; 0 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 228 ( 123 ~; 105 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 185 ( 185 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [E,A_2,A_0,A_1,A_3,A_4,B_0] :
( ~ 'E'(f(B_0),s(s(s(s(s('0'))))))
| ~ 'E'(f(A_4),'0')
| ~ 'E'(f(A_3),s('0'))
| ~ 'E'(f(A_1),s(s(s('0'))))
| ~ 'E'(f(A_0),s(s(s(s('0')))))
| ~ 'E'(f(A_2),s(s('0'))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [E,B_0] : 'E'(f(B_0),s(s(s(s('0'))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [E,B] : 'E'(f(B),s(s(s(s(s('0')))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [E,A_2,A_0,A_1,A_3,B_0,AP,K] :
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),K)),'0')
| ~ 'E'(f(B_0),s(s(s(s(s('0'))))))
| ~ 'E'(f(A_3),s('0'))
| ~ 'E'(f(A_1),s(s(s('0'))))
| ~ 'E'(f(A_0),s(s(s(s('0')))))
| ~ 'E'(f(A_2),s(s('0'))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [E,A_0,B_0,A_1,A_2,AP,K] :
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),K)),s('0'))
| ~ 'E'(f(A_2),s(s('0')))
| ~ 'E'(f(A_1),s(s(s('0'))))
| ~ 'E'(f(B_0),s(s(s(s(s('0'))))))
| ~ 'E'(f(A_0),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [E,A_0,B_0] :
( 'E'(f(B_0),s(s(s('0'))))
| ~ 'E'(f(B_0),s(s(s(s(s('0'))))))
| ~ 'E'(f(A_0),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [E,A_0,B_0,A_1,AP,K] :
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),K)),s(s('0')))
| ~ 'E'(f(A_1),s(s(s('0'))))
| ~ 'E'(f(B_0),s(s(s(s(s('0'))))))
| ~ 'E'(f(A_0),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,plain,
( ! [B_0] : ~ 'E'(f(B_0),s(s(s(s(s('0'))))))
| ! [A_4] : ~ 'E'(f(A_4),'0')
| ! [A_3] : ~ 'E'(f(A_3),s('0'))
| ! [A_1] : ~ 'E'(f(A_1),s(s(s('0'))))
| ! [A_0] : ~ 'E'(f(A_0),s(s(s(s('0')))))
| ! [A_2] : ~ 'E'(f(A_2),s(s('0'))) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f19,plain,
! [E,X0,X1,X2,X3,X4,X5] :
( ~ 'E'(f(X5),s(s(s(s(s('0'))))))
| ~ 'E'(f(X4),'0')
| ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X1),s(s(s(s('0')))))
| ~ 'E'(f(X0),s(s('0'))) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [B_0] : 'E'(f(B_0),s(s(s(s('0'))))),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f21,plain,
! [E,X0] : 'E'(f(X0),s(s(s(s('0'))))),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [B] : 'E'(f(B),s(s(s(s(s('0')))))),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f23,plain,
! [E,X0] : 'E'(f(X0),s(s(s(s(s('0')))))),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,plain,
( ! [K] : 'E'(f('AP'(s(s(s(s(s(s('0')))))),K)),'0')
| ! [B_0] : ~ 'E'(f(B_0),s(s(s(s(s('0'))))))
| ! [A_3] : ~ 'E'(f(A_3),s('0'))
| ! [A_1] : ~ 'E'(f(A_1),s(s(s('0'))))
| ! [A_0] : ~ 'E'(f(A_0),s(s(s(s('0')))))
| ! [A_2] : ~ 'E'(f(A_2),s(s('0'))) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f27,plain,
! [E,X0,X1,X2,X3,X4,AP,X5] :
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),X5)),'0')
| ~ 'E'(f(X4),s(s(s(s(s('0'))))))
| ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X1),s(s(s(s('0')))))
| ~ 'E'(f(X0),s(s('0'))) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f30,plain,
( ! [K] : 'E'(f('AP'(s(s(s(s(s(s('0')))))),K)),s('0'))
| ! [A_2] : ~ 'E'(f(A_2),s(s('0')))
| ! [A_1] : ~ 'E'(f(A_1),s(s(s('0'))))
| ! [B_0] : ~ 'E'(f(B_0),s(s(s(s(s('0'))))))
| ! [A_0] : ~ 'E'(f(A_0),s(s(s(s('0'))))) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f31,plain,
! [E,X0,X1,X2,X3,AP,X4] :
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),X4)),s('0'))
| ~ 'E'(f(X3),s(s('0')))
| ~ 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| ~ 'E'(f(X0),s(s(s(s('0'))))) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [B_0] :
( 'E'(f(B_0),s(s(s('0'))))
| ~ 'E'(f(B_0),s(s(s(s(s('0'))))))
| ! [A_0] : ~ 'E'(f(A_0),s(s(s(s('0'))))) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f33,plain,
! [E,X0,X1] :
( 'E'(f(X1),s(s(s('0'))))
| ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| ~ 'E'(f(X0),s(s(s(s('0'))))) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,plain,
( ! [K] : 'E'(f('AP'(s(s(s(s(s(s('0')))))),K)),s(s('0')))
| ! [A_1] : ~ 'E'(f(A_1),s(s(s('0'))))
| ! [B_0] : ~ 'E'(f(B_0),s(s(s(s(s('0'))))))
| ! [A_0] : ~ 'E'(f(A_0),s(s(s(s('0'))))) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f37,plain,
! [E,X0,X1,X2,AP,X3] :
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),X3)),s(s('0')))
| ~ 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| ~ 'E'(f(X0),s(s(s(s('0'))))) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f41,plain,
! [E,X0] :
( 'E'(f(X0),s(s(s('0'))))
| ~ 'E'(f(X0),s(s(s(s(s('0')))))) ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f21]) ).
fof(f42,plain,
! [E,X0] : 'E'(f(X0),s(s(s('0')))),
inference(resolution,[status(thm)],[f41,f23]) ).
fof(f47,plain,
! [E,X0,X1,X2,X3,X4] :
( ~ 'E'(f(X4),s(s(s(s(s('0'))))))
| ~ 'E'(f(X3),'0')
| ~ 'E'(f(X2),s('0'))
| ~ 'E'(f(X1),s(s(s('0'))))
| ~ 'E'(f(X0),s(s('0'))) ),
inference(forward_subsumption_resolution,[status(thm)],[f19,f21]) ).
fof(f48,plain,
! [E,X0,X1,AP,X2] :
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),X2)),s(s('0')))
| ~ 'E'(f(X1),s(s(s('0'))))
| ~ 'E'(f(X0),s(s(s(s(s('0')))))) ),
inference(forward_subsumption_resolution,[status(thm)],[f37,f21]) ).
fof(f49,plain,
! [E,X0,X1,X2,X3,X4,X5] :
( ~ 'E'(f(X5),s(s(s(s(s('0'))))))
| ~ 'E'(f(X4),'0')
| ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X1),s(s(s('0'))))
| ~ 'E'(f(X0),s(s(s(s(s('0')))))) ),
inference(resolution,[status(thm)],[f48,f47]) ).
fof(f50,plain,
! [E,X0,X1,X2,X3,X4] :
( ~ 'E'(f(X4),s(s(s(s(s('0'))))))
| ~ 'E'(f(X3),'0')
| ~ 'E'(f(X2),s('0'))
| ~ 'E'(f(X1),s(s(s('0'))))
| ~ 'E'(f(X0),s(s(s('0')))) ),
inference(forward_subsumption_resolution,[status(thm)],[f49,f23]) ).
fof(f51,plain,
! [E,X0,X1,X2,X3] :
( ~ 'E'(f(X3),s(s(s(s(s('0'))))))
| ~ 'E'(f(X2),'0')
| ~ 'E'(f(X1),s('0'))
| ~ 'E'(f(X0),s(s(s('0')))) ),
inference(forward_subsumption_resolution,[status(thm)],[f50,f42]) ).
fof(f52,plain,
! [E,X0,X1,X2,AP,X3] :
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),X3)),s('0'))
| ~ 'E'(f(X2),s(s('0')))
| ~ 'E'(f(X1),s(s(s('0'))))
| ~ 'E'(f(X0),s(s(s(s(s('0')))))) ),
inference(forward_subsumption_resolution,[status(thm)],[f31,f21]) ).
fof(f53,plain,
! [E,X0,X1,X2,X3,X4,X5] :
( ~ 'E'(f(X5),s(s(s(s(s('0'))))))
| ~ 'E'(f(X4),'0')
| ~ 'E'(f(X3),s(s(s('0'))))
| ~ 'E'(f(X2),s(s('0')))
| ~ 'E'(f(X1),s(s(s('0'))))
| ~ 'E'(f(X0),s(s(s(s(s('0')))))) ),
inference(resolution,[status(thm)],[f52,f51]) ).
fof(f54,plain,
! [E,X0,X1,X2,X3,X4] :
( ~ 'E'(f(X4),s(s(s(s(s('0'))))))
| ~ 'E'(f(X3),'0')
| ~ 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X1),s(s('0')))
| ~ 'E'(f(X0),s(s(s('0')))) ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f23]) ).
fof(f55,plain,
! [E,X0,X1,X2,X3,AP,X4] :
( 'E'(f('AP'(s(s(s(s(s(s('0')))))),X4)),'0')
| ~ 'E'(f(X3),s(s(s(s(s('0'))))))
| ~ 'E'(f(X2),s('0'))
| ~ 'E'(f(X1),s(s(s('0'))))
| ~ 'E'(f(X0),s(s('0'))) ),
inference(forward_subsumption_resolution,[status(thm)],[f27,f21]) ).
fof(f56,plain,
! [E,X0,X1,X2,X3] :
( ~ 'E'(f(X3),s(s(s(s(s('0'))))))
| ~ 'E'(f(X2),s('0'))
| ~ 'E'(f(X1),s(s(s('0'))))
| ~ 'E'(f(X0),s(s('0'))) ),
inference(backward_subsumption_resolution,[status(thm)],[f55,f57]) ).
fof(f57,plain,
! [E,X0,X1,X2,X3] :
( ~ 'E'(f(X3),s(s(s(s(s('0'))))))
| ~ 'E'(f(X2),'0')
| ~ 'E'(f(X1),s(s(s('0'))))
| ~ 'E'(f(X0),s(s('0'))) ),
inference(forward_subsumption_resolution,[status(thm)],[f54,f42]) ).
fof(f60,plain,
! [E,X0,X1,X2] :
( ~ 'E'(f(X2),s(s(s(s(s('0'))))))
| ~ 'E'(f(X1),s('0'))
| ~ 'E'(f(X0),s(s('0'))) ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f42]) ).
fof(f63,plain,
! [E,X0,X1,X2] :
( ~ 'E'(f(X2),s(s('0')))
| ~ 'E'(f(X1),s(s(s('0'))))
| ~ 'E'(f(X0),s(s(s(s(s('0')))))) ),
inference(backward_subsumption_resolution,[status(thm)],[f52,f64]) ).
fof(f64,plain,
! [E,X0,X1] :
( ~ 'E'(f(X1),s('0'))
| ~ 'E'(f(X0),s(s('0'))) ),
inference(forward_subsumption_resolution,[status(thm)],[f60,f23]) ).
fof(f66,plain,
! [E,X0,X1] :
( ~ 'E'(f(X1),s(s('0')))
| ~ 'E'(f(X0),s(s(s('0')))) ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f23]) ).
fof(f69,plain,
! [E,X0,X1] :
( ~ 'E'(f(X1),s(s(s('0'))))
| ~ 'E'(f(X0),s(s(s(s(s('0')))))) ),
inference(backward_subsumption_resolution,[status(thm)],[f48,f70]) ).
fof(f70,plain,
! [E,X0] : ~ 'E'(f(X0),s(s('0'))),
inference(forward_subsumption_resolution,[status(thm)],[f66,f42]) ).
fof(f71,plain,
! [E,X0] : ~ 'E'(f(X0),s(s(s('0')))),
inference(forward_subsumption_resolution,[status(thm)],[f69,f23]) ).
fof(f72,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f71,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 12:06:19 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.11/0.37 % Refutation found
% 0.11/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.39 % Elapsed time: 0.036533 seconds
% 0.11/0.39 % CPU time: 0.086294 seconds
% 0.11/0.39 % Total memory used: 2.013 MB
% 0.11/0.39 % Net memory used: 1.929 MB
%------------------------------------------------------------------------------