%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG011-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 11:47:44 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 7 unt; 5 def)
% Number of atoms : 117 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 158 ( 85 ~; 68 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 61 ( 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] :
( d(X)
| c(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,hypothesis,
! [X] :
( ~ d(X)
| ~ c(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,hypothesis,
c(a1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [X,Y] :
( ~ c(Y)
| ~ c(X)
| d(f(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
! [X,Y] :
( ~ d(Y)
| ~ d(X)
| c(f(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [X0,X1,X2] : f(X0,f(X1,X2)) = f(f(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0] :
( d(X0)
| c(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0] :
( ~ d(X0)
| ~ c(X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
c(a1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [Y] :
( ~ c(Y)
| ! [X] :
( ~ c(X)
| d(f(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f14,plain,
! [X0,X1] :
( ~ c(X1)
| ~ c(X0)
| d(f(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [Y] :
( ~ d(Y)
| ! [X] :
( ~ d(X)
| c(f(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f16,plain,
! [X0,X1] :
( ~ d(X1)
| ~ d(X0)
| c(f(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ~ d(X1)
| ~ d(X0)
| ~ d(f(X0,X1)) ),
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ d(X2)
| ~ d(f(X0,X1))
| ~ d(f(X0,f(X1,X2))) ),
inference(paramodulation,[status(thm)],[f8,f17]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ c(f(X1,X2))
| ~ c(X0)
| ~ d(X2)
| ~ d(f(X0,X1)) ),
inference(resolution,[status(thm)],[f25,f14]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ d(X2)
| ~ d(X1)
| ~ c(X0)
| ~ d(X2)
| ~ d(f(X0,X1)) ),
inference(resolution,[status(thm)],[f30,f16]) ).
fof(f49,plain,
! [X0,X1,X2] :
( d(f(X1,X2))
| ~ c(X0)
| ~ d(X2)
| ~ d(f(X0,X1)) ),
inference(resolution,[status(thm)],[f30,f9]) ).
fof(f51,definition,
! [X0,X1] :
( sQ2_spl
<=> ( ~ d(X1)
| ~ c(X0)
| ~ d(f(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f52,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ d(X1)
| ~ c(X0)
| ~ d(f(X0,X1)) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
! [X2] :
( sQ3_spl
<=> ( ~ d(X2)
| ~ d(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f55,plain,
! [X0] :
( ~ sQ3_spl
| ~ d(X0)
| ~ d(X0) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f48,f51,f54]) ).
fof(f61,definition,
! [X0] :
( sQ4_spl
<=> ( ~ c(X0)
| ~ c(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f62,plain,
! [X0] :
( ~ sQ4_spl
| ~ c(X0)
| ~ c(X0) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f65,plain,
! [X0] :
( ~ sQ3_spl
| ~ d(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f55]) ).
fof(f68,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ c(X1)
| ~ c(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f14,f65]) ).
fof(f72,definition,
! [X2] :
( sQ6_spl
<=> ~ c(X2) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f73,plain,
! [X0] :
( ~ sQ6_spl
| ~ c(X0) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f76,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f68,f72,f54]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ~ c(X2)
| ~ c(X1)
| d(f(X2,X0))
| ~ c(X1)
| ~ d(X0) ),
inference(resolution,[status(thm)],[f49,f14]) ).
fof(f102,definition,
! [X0,X2] :
( sQ8_spl
<=> ( ~ c(X2)
| d(f(X2,X0))
| ~ d(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f103,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ c(X1)
| d(f(X1,X0))
| ~ d(X0) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f100,f102,f61]) ).
fof(f106,plain,
! [X0] :
( ~ sQ4_spl
| ~ c(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f62]) ).
fof(f107,plain,
( ~ sQ4_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f11,f106]) ).
fof(f110,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f107]) ).
fof(f116,plain,
( ~ sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f11,f73]) ).
fof(f118,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f130,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ sQ2_spl
| ~ c(X1)
| ~ c(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f14,f132]) ).
fof(f132,plain,
! [X0,X1] :
( ~ sQ8_spl
| ~ sQ2_spl
| ~ c(X1)
| ~ d(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f52]) ).
fof(f133,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f130,f72,f51,f102]) ).
fof(f138,plain,
$false,
inference(sat_refutation,[status(thm)],[f57,f76,f105,f110,f118,f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG011-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n005.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 12:52:18 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.041828 seconds
% 0.12/0.41 % CPU time: 0.091845 seconds
% 0.12/0.41 % Total memory used: 19.257 MB
% 0.12/0.41 % Net memory used: 19.175 MB
%------------------------------------------------------------------------------