%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYO038-1.003.003 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 03:41:46 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 73 ( 25 unt; 9 def)
% Number of atoms : 123 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 93 ( 43 ~; 41 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [N] : f(N,one) = s(one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : f(one,s(X)) = s(s(f(one,X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [N,X] : f(s(N),s(X)) = f(N,f(s(N),X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
d(one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( d(s(X))
| ~ d(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ d(f(s(s(one)),s(s(one)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0] : f(X0,one) = s(one),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0] : f(one,s(X0)) = s(s(f(one,X0))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1] : f(s(X0),s(X1)) = f(X0,f(s(X0),X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
d(one),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
! [X0] :
( d(s(X0))
| ~ d(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
~ d(f(s(s(one)),s(s(one)))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,plain,
f(one,s(one)) = s(s(s(one))),
inference(paramodulation,[status(thm)],[f7,f8]) ).
fof(f14,plain,
! [X0] :
( d(f(one,s(X0)))
| ~ d(s(f(one,X0))) ),
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f15,plain,
f(one,s(s(one))) = s(s(s(s(s(one))))),
inference(paramodulation,[status(thm)],[f13,f8]) ).
fof(f17,plain,
! [X0] : f(s(X0),s(one)) = f(X0,s(one)),
inference(paramodulation,[status(thm)],[f7,f9]) ).
fof(f19,plain,
! [X0] : f(one,s(f(s(one),X0))) = s(s(f(s(one),s(X0)))),
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f22,plain,
! [X0] : f(s(X0),s(s(one))) = f(X0,f(X0,s(one))),
inference(paramodulation,[status(thm)],[f17,f9]) ).
fof(f24,plain,
! [X0] :
( ~ d(f(one,X0))
| d(f(one,s(X0))) ),
inference(resolution,[status(thm)],[f14,f11]) ).
fof(f25,plain,
( d(f(one,s(s(one))))
| ~ d(s(s(s(s(one))))) ),
inference(paramodulation,[status(thm)],[f13,f14]) ).
fof(f27,plain,
( d(f(one,s(one)))
| ~ d(s(s(one))) ),
inference(paramodulation,[status(thm)],[f7,f14]) ).
fof(f28,definition,
( sQ0_spl
<=> d(s(s(s(s(one))))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f30,plain,
( sQ0_spl
| ~ d(s(s(s(s(one))))) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f31,definition,
( sQ1_spl
<=> d(f(one,s(s(one)))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f34,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f25,f28,f31]) ).
fof(f35,definition,
( sQ2_spl
<=> d(s(s(one))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( sQ2_spl
| ~ d(s(s(one))) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,definition,
( sQ3_spl
<=> d(f(one,s(one))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( ~ sQ3_spl
| d(f(one,s(one))) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f27,f35,f38]) ).
fof(f42,plain,
( sQ2_spl
| ~ d(s(one)) ),
inference(resolution,[status(thm)],[f37,f11]) ).
fof(f43,plain,
( sQ2_spl
| ~ d(one) ),
inference(resolution,[status(thm)],[f42,f11]) ).
fof(f44,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f10]) ).
fof(f45,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f44]) ).
fof(f46,plain,
( ~ sQ3_spl
| d(s(s(s(one)))) ),
inference(forward_demodulation,[status(thm)],[f13,f39]) ).
fof(f63,plain,
( sQ0_spl
| ~ d(s(s(s(one)))) ),
inference(resolution,[status(thm)],[f30,f11]) ).
fof(f64,plain,
( sQ0_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f46]) ).
fof(f65,plain,
( sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f64]) ).
fof(f67,plain,
! [X0] :
( ~ d(f(one,s(f(one,X0))))
| d(f(one,f(one,s(X0)))) ),
inference(paramodulation,[status(thm)],[f8,f24]) ).
fof(f77,plain,
! [X0] : f(s(s(X0)),s(s(one))) = f(s(X0),f(X0,s(one))),
inference(paramodulation,[status(thm)],[f17,f22]) ).
fof(f78,plain,
! [X0] : f(s(X0),s(s(s(one)))) = f(X0,f(X0,f(X0,s(one)))),
inference(paramodulation,[status(thm)],[f22,f9]) ).
fof(f85,plain,
( ~ d(f(one,s(s(s(s(one))))))
| d(f(one,f(one,s(s(one))))) ),
inference(paramodulation,[status(thm)],[f15,f24]) ).
fof(f92,definition,
( sQ6_spl
<=> d(f(one,f(one,s(s(one))))) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f95,definition,
( sQ7_spl
<=> d(f(one,s(s(s(s(one)))))) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f85,f92,f95]) ).
fof(f156,plain,
~ d(f(s(one),f(one,s(one)))),
inference(paramodulation,[status(thm)],[f77,f12]) ).
fof(f170,plain,
~ d(f(s(one),s(s(s(one))))),
inference(forward_demodulation,[status(thm)],[f13,f156]) ).
fof(f174,plain,
f(one,s(f(one,s(one)))) = s(s(f(s(one),s(s(one))))),
inference(paramodulation,[status(thm)],[f17,f19]) ).
fof(f180,plain,
! [X0] :
( ~ d(f(one,f(s(one),X0)))
| d(s(s(f(s(one),s(X0))))) ),
inference(paramodulation,[status(thm)],[f19,f24]) ).
fof(f185,plain,
f(one,s(s(s(s(one))))) = s(s(f(s(one),s(s(one))))),
inference(forward_demodulation,[status(thm)],[f13,f174]) ).
fof(f194,plain,
! [X0] :
( ~ d(f(s(one),s(X0)))
| d(s(s(f(s(one),s(X0))))) ),
inference(forward_demodulation,[status(thm)],[f9,f180]) ).
fof(f195,plain,
! [X0] :
( ~ d(f(one,f(one,X0)))
| d(f(one,f(one,s(X0)))) ),
inference(resolution,[status(thm)],[f67,f24]) ).
fof(f199,plain,
( ~ d(f(one,s(s(one))))
| d(f(one,f(one,s(one)))) ),
inference(paramodulation,[status(thm)],[f7,f67]) ).
fof(f203,definition,
( sQ8_spl
<=> d(f(one,f(one,s(one)))) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( ~ sQ8_spl
| d(f(one,f(one,s(one)))) ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,plain,
( ~ sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f199,f203,f31]) ).
fof(f207,plain,
( ~ sQ8_spl
| d(f(one,s(s(s(one))))) ),
inference(forward_demodulation,[status(thm)],[f13,f204]) ).
fof(f231,plain,
f(s(one),s(s(s(one)))) = f(one,f(one,s(s(s(one))))),
inference(paramodulation,[status(thm)],[f13,f78]) ).
fof(f274,definition,
( sQ18_spl
<=> d(f(s(one),s(s(one)))) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f276,plain,
( sQ18_spl
| ~ d(f(s(one),s(s(one)))) ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f530,plain,
( ~ d(f(s(one),s(s(one))))
| d(f(one,s(s(s(s(one)))))) ),
inference(paramodulation,[status(thm)],[f185,f194]) ).
fof(f555,plain,
( ~ sQ18_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f530,f95,f274]) ).
fof(f640,plain,
( sQ18_spl
| ~ d(f(one,f(one,s(one)))) ),
inference(paramodulation,[status(thm)],[f22,f276]) ).
fof(f641,plain,
( sQ18_spl
| ~ d(f(one,s(s(s(one))))) ),
inference(forward_demodulation,[status(thm)],[f13,f640]) ).
fof(f642,plain,
( sQ18_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f641,f207]) ).
fof(f643,plain,
( sQ18_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f642]) ).
fof(f713,plain,
( ~ d(f(one,f(one,s(s(one)))))
| d(f(s(one),s(s(s(one))))) ),
inference(paramodulation,[status(thm)],[f231,f195]) ).
fof(f719,definition,
( sQ33_spl
<=> d(f(s(one),s(s(s(one))))) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f720,plain,
( ~ sQ33_spl
| d(f(s(one),s(s(s(one))))) ),
inference(component_clause,[status(thm)],[f719]) ).
fof(f722,plain,
( ~ sQ6_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f713,f719,f92]) ).
fof(f733,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f720,f170]) ).
fof(f734,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f733]) ).
fof(f735,plain,
$false,
inference(sat_refutation,[status(thm)],[f34,f41,f45,f65,f98,f206,f555,f643,f722,f734]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO038-1.003.003 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 11:36:52 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.048686 seconds
% 0.10/0.41 % CPU time: 0.143381 seconds
% 0.10/0.41 % Total memory used: 33.628 MB
% 0.10/0.41 % Net memory used: 33.481 MB
%------------------------------------------------------------------------------