%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 03:14:58 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 89 ( 1 unt; 10 def)
% Number of atoms : 263 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 329 ( 155 ~; 164 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 203 ( 203 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,negated_conjecture,
! [X,X1,Z1] :
( q(f1(X,X1),Z1)
| ~ s(X,f1(X,X1))
| p(f1(X,X1),f1(X,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
! [X,X1,Z,Z1] :
( q(f1(X,X1),Z1)
| s(f1(X,X1),Z)
| p(f1(X,X1),f1(X,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
! [X,X1,Z1] :
( ~ q(X1,f1(X,X1))
| ~ q(Z1,Z1)
| p(f1(X,X1),f1(X,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [X,X1,Z1] :
( ~ s(X1,X1)
| ~ q(Z1,Z1)
| p(f1(X,X1),f1(X,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
! [X,X1] :
( ~ s(X1,X1)
| ~ s(X,f1(X,X1))
| ~ p(X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
! [X,X1,Z,Z1] :
( q(f1(X,X1),Z1)
| s(f1(X,X1),Z)
| ~ p(X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
! [X,Z1,X1] :
( ~ q(X1,f1(X,X1))
| ~ q(Z1,Z1)
| ~ p(X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
! [X,Z1,X1] :
( ~ s(X1,X1)
| ~ q(Z1,Z1)
| ~ p(X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
! [Z,X,X1] :
( ~ s(X1,X1)
| ~ s(X,f1(X,X1))
| s(Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
! [Z,X,Z1,X1] :
( ~ q(X1,f1(X,X1))
| ~ q(Z1,Z1)
| s(Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
! [Z,X,Z1,X1] :
( ~ s(X1,X1)
| ~ q(Z1,Z1)
| s(Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,plain,
! [X,X1] :
( ! [Z1] : q(f1(X,X1),Z1)
| ~ s(X,f1(X,X1))
| p(f1(X,X1),f1(X,X1)) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f30,plain,
! [X0,X1,X2] :
( q(f1(X0,X1),X2)
| ~ s(X0,f1(X0,X1))
| p(f1(X0,X1),f1(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f35,plain,
! [X,X1] :
( ! [Z1] : q(f1(X,X1),Z1)
| ! [Z] : s(f1(X,X1),Z)
| p(f1(X,X1),f1(X,X1)) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( q(f1(X0,X1),X3)
| s(f1(X0,X1),X2)
| p(f1(X0,X1),f1(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f39,plain,
! [X,X1] :
( ~ q(X1,f1(X,X1))
| ! [Z1] : ~ q(Z1,Z1)
| p(f1(X,X1),f1(X,X1)) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ q(X1,f1(X0,X1))
| ~ q(X2,X2)
| p(f1(X0,X1),f1(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f42,plain,
! [X1] :
( ~ s(X1,X1)
| ! [Z1] : ~ q(Z1,Z1)
| ! [X] : p(f1(X,X1),f1(X,X1)) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ s(X1,X1)
| ~ q(X2,X2)
| p(f1(X0,X1),f1(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f47,plain,
! [X1] :
( ~ s(X1,X1)
| ! [X] :
( ~ s(X,f1(X,X1))
| ~ p(X,X) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f48,plain,
! [X0,X1] :
( ~ s(X1,X1)
| ~ s(X0,f1(X0,X1))
| ~ p(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
! [X,X1] :
( ! [Z1] : q(f1(X,X1),Z1)
| ! [Z] : s(f1(X,X1),Z)
| ~ p(X,X) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( q(f1(X0,X1),X3)
| s(f1(X0,X1),X2)
| ~ p(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f55,plain,
! [X] :
( ! [X1] : ~ q(X1,f1(X,X1))
| ! [Z1] : ~ q(Z1,Z1)
| ~ p(X,X) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ q(X2,f1(X0,X2))
| ~ q(X1,X1)
| ~ p(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f59,plain,
( ! [X1] : ~ s(X1,X1)
| ! [Z1] : ~ q(Z1,Z1)
| ! [X] : ~ p(X,X) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ s(X2,X2)
| ~ q(X1,X1)
| ~ p(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f65,plain,
! [X1] :
( ~ s(X1,X1)
| ! [X] :
( ~ s(X,f1(X,X1))
| ! [Z] : s(Z,X) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ s(X2,X2)
| ~ s(X1,f1(X1,X2))
| s(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f73,plain,
! [X] :
( ! [X1] : ~ q(X1,f1(X,X1))
| ! [Z1] : ~ q(Z1,Z1)
| ! [Z] : s(Z,X) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( ~ q(X3,f1(X1,X3))
| ~ q(X2,X2)
| s(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f77,plain,
( ! [X1] : ~ s(X1,X1)
| ! [Z1] : ~ q(Z1,Z1)
| ! [Z,X] : s(Z,X) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ~ s(X3,X3)
| ~ q(X2,X2)
| s(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f79,definition,
! [X0,X1] :
( sQ0_spl
<=> ( ~ q(X1,f1(X0,X1))
| p(f1(X0,X1),f1(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f82,definition,
! [X2] :
( sQ1_spl
<=> ~ q(X2,X2) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f83,plain,
! [X0] :
( ~ sQ1_spl
| ~ q(X0,X0) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f79,f82]) ).
fof(f86,definition,
! [X0,X1] :
( sQ2_spl
<=> ( ~ s(X1,X1)
| p(f1(X0,X1),f1(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f87,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ s(X1,X1)
| p(f1(X0,X1),f1(X0,X1)) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f43,f86,f82]) ).
fof(f90,definition,
! [X0,X2] :
( sQ3_spl
<=> ( ~ q(X2,f1(X0,X2))
| ~ p(X0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f91,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ q(X1,f1(X0,X1))
| ~ p(X0,X0) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f56,f90,f82]) ).
fof(f94,definition,
! [X0] :
( sQ4_spl
<=> ~ p(X0,X0) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f95,plain,
! [X0] :
( ~ sQ4_spl
| ~ p(X0,X0) ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
! [X2] :
( sQ5_spl
<=> ~ s(X2,X2) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f98,plain,
! [X0] :
( ~ sQ5_spl
| ~ s(X0,X0) ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ5_spl
| sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f60,f94,f82,f97]) ).
fof(f101,definition,
! [X0,X1,X3] :
( sQ6_spl
<=> ( ~ q(X3,f1(X1,X3))
| s(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| ~ q(X2,f1(X1,X2))
| s(X0,X1) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f74,f101,f82]) ).
fof(f105,definition,
! [X0,X1] :
( sQ7_spl
<=> s(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f106,plain,
! [X0,X1] :
( ~ sQ7_spl
| s(X0,X1) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ5_spl
| sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f78,f105,f82,f97]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| s(f1(X0,X1),X2)
| p(f1(X0,X1),f1(X0,X1)) ),
inference(resolution,[status(thm)],[f36,f83]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| q(f1(X0,X1),X2)
| p(f1(X0,X1),f1(X0,X1)) ),
inference(resolution,[status(thm)],[f98,f36]) ).
fof(f157,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ1_spl
| p(f1(X0,X1),f1(X0,X1)) ),
inference(resolution,[status(thm)],[f142,f98]) ).
fof(f158,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ5_spl
| ~ sQ1_spl
| q(f1(f1(X0,X1),X2),X4)
| s(f1(f1(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[f157,f52]) ).
fof(f161,plain,
! [X0,X1,X2,X3] :
( ~ sQ5_spl
| ~ sQ1_spl
| q(f1(f1(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[f158,f98]) ).
fof(f170,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| $false ),
inference(resolution,[status(thm)],[f161,f83]) ).
fof(f171,plain,
( ~ sQ1_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f170]) ).
fof(f174,plain,
! [X0,X1,X2,X3] :
( ~ sQ6_spl
| ~ sQ5_spl
| s(X2,X3)
| p(f1(X0,X1),f1(X0,X1)) ),
inference(resolution,[status(thm)],[f151,f102]) ).
fof(f175,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ5_spl
| ~ p(X2,X2)
| p(f1(X0,X1),f1(X0,X1)) ),
inference(resolution,[status(thm)],[f151,f91]) ).
fof(f178,definition,
! [X0,X1] :
( sQ10_spl
<=> p(f1(X0,X1),f1(X0,X1)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f179,plain,
! [X0,X1] :
( ~ sQ10_spl
| p(f1(X0,X1),f1(X0,X1)) ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f174,f178,f105,f97,f101]) ).
fof(f182,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f175,f178,f94,f97,f90]) ).
fof(f189,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ s(X3,X3)
| s(X2,f1(X0,X1))
| p(f1(X0,X1),f1(X0,X1)) ),
inference(resolution,[status(thm)],[f142,f66]) ).
fof(f192,definition,
! [X0,X1,X2] :
( sQ11_spl
<=> ( s(X2,f1(X0,X1))
| p(f1(X0,X1),f1(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f193,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| s(X2,f1(X0,X1))
| p(f1(X0,X1),f1(X0,X1)) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( ~ sQ1_spl
| sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f189,f192,f97,f82]) ).
fof(f209,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| q(f1(X0,X1),X2)
| p(f1(X0,X1),f1(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f193]) ).
fof(f217,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ11_spl
| p(f1(X0,X1),f1(X0,X1)) ),
inference(resolution,[status(thm)],[f209,f83]) ).
fof(f223,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ11_spl
| ~ s(X2,X2)
| ~ s(f1(X0,X1),f1(f1(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f217,f48]) ).
fof(f224,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ11_spl
| q(f1(f1(X0,X1),X2),X4)
| s(f1(f1(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[f217,f52]) ).
fof(f235,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ11_spl
| s(f1(f1(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[f224,f83]) ).
fof(f245,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ11_spl
| ~ s(X0,X0) ),
inference(resolution,[status(thm)],[f235,f223]) ).
fof(f249,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f245,f97,f192,f82]) ).
fof(f256,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ4_spl
| ~ s(X0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f95]) ).
fof(f257,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ4_spl
| $false ),
inference(resolution,[status(thm)],[f256,f106]) ).
fof(f258,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f257]) ).
fof(f270,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ10_spl
| q(f1(f1(X0,X1),X2),X4)
| s(f1(f1(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[f52,f179]) ).
fof(f283,plain,
! [X0,X1,X2,X3] :
( ~ sQ5_spl
| ~ sQ10_spl
| q(f1(f1(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[f270,f98]) ).
fof(f294,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ10_spl
| ~ p(X0,X0) ),
inference(resolution,[status(thm)],[f283,f91]) ).
fof(f295,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ10_spl
| s(X0,X1) ),
inference(resolution,[status(thm)],[f283,f102]) ).
fof(f298,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ10_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f294,f94,f178,f97,f90]) ).
fof(f300,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f98,f295]) ).
fof(f301,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f300]) ).
fof(f302,plain,
$false,
inference(sat_refutation,[status(thm)],[f85,f89,f93,f100,f104,f108,f171,f181,f182,f195,f249,f258,f298,f301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.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 10:39:34 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.044358 seconds
% 0.13/0.42 % CPU time: 0.146093 seconds
% 0.13/0.42 % Total memory used: 18.100 MB
% 0.13/0.42 % Net memory used: 17.710 MB
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