%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL128-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 01:06:53 PM UTC 2026
% Result : Unsatisfiable 157.39s 20.57s
% Output : CNFRefutation 157.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 63 ( 7 unt; 5 def)
% Number of atoms : 167 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 220 ( 116 ~; 99 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 147 ( 147 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z,U] : is_a_theorem(equivalent(X,equivalent(X,equivalent(equivalent(equivalent(Y,Z),equivalent(U,Z)),equivalent(Y,U))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2,X3] : is_a_theorem(equivalent(X0,equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3))))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f6,f5]) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3)))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f8,f5]) ).
fof(f10,definition,
! [X0] :
( sQ0_spl
<=> ( ~ is_a_theorem(X0)
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f11,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f10]) ).
fof(f13,definition,
! [X1,X2,X3] :
( sQ1_spl
<=> is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),equivalent(X0,X2))) ),
inference(component_clause,[status(thm)],[f13]) ).
fof(f16,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f10,f13]) ).
fof(f17,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f11]) ).
fof(f18,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6,f17]) ).
fof(f19,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(equivalent(X0,X2))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,X1))) ),
inference(resolution,[status(thm)],[f14,f5]) ).
fof(f21,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),equivalent(X0,X2)),equivalent(equivalent(equivalent(X3,X4),equivalent(X5,X4)),equivalent(X3,X5)))) ),
inference(resolution,[status(thm)],[f8,f14]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),equivalent(equivalent(X0,X3),equivalent(X2,X3)))) ),
inference(resolution,[status(thm)],[f21,f20]) ).
fof(f28,definition,
! [X0,X1,X2] :
( sQ2_spl
<=> ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),equivalent(X0,X2))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),equivalent(X0,X2))) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f32,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X0,X1))) ),
inference(resolution,[status(thm)],[f25,f20]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(X0,X3),equivalent(X2,X3)))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,X1))) ),
inference(resolution,[status(thm)],[f25,f5]) ).
fof(f35,plain,
! [X0] :
( ~ sQ1_spl
| is_a_theorem(equivalent(X0,X0)) ),
inference(resolution,[status(thm)],[f32,f20]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(X0,X0),equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3)))) ),
inference(resolution,[status(thm)],[f35,f8]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X0,X2),equivalent(X1,X2)))) ),
inference(resolution,[status(thm)],[f40,f20]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(X0,X2),equivalent(X1,X2)))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f44,f5]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X0,X2))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f51,f5]) ).
fof(f59,definition,
! [X0,X1,X2,X3] :
( sQ4_spl
<=> ~ is_a_theorem(equivalent(X0,equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3))))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| ~ is_a_theorem(equivalent(X0,equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3))))) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,X2))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f54,f5]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(equivalent(X0,X2))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X3)) ),
inference(resolution,[status(thm)],[f72,f14]) ).
fof(f85,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f72,f35]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ is_a_theorem(equivalent(X2,X0))
| is_a_theorem(equivalent(X2,X1))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f85,f51]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3)))) ),
inference(resolution,[status(thm)],[f85,f6]) ).
fof(f127,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f14]) ).
fof(f128,plain,
( ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(equivalent(X3,X1))
| ~ is_a_theorem(equivalent(equivalent(X3,X2),X0))
| ~ is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(resolution,[status(thm)],[f109,f20]) ).
fof(f132,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(X2,X3))
| ~ is_a_theorem(equivalent(X2,X0))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f109,f72]) ).
fof(f321,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X3),equivalent(equivalent(X0,X2),X3))) ),
inference(resolution,[status(thm)],[f111,f14]) ).
fof(f325,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X3),equivalent(X2,X3))))
| is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
inference(resolution,[status(thm)],[f111,f51]) ).
fof(f337,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ is_a_theorem(equivalent(equivalent(a,X1),X0))
| ~ is_a_theorem(equivalent(X0,equivalent(equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))),X1))) ),
inference(resolution,[status(thm)],[f129,f7]) ).
fof(f392,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X3,X4),equivalent(X5,X4)),equivalent(X3,X5)))
| ~ is_a_theorem(equivalent(equivalent(X2,X2),X0))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f132,f40]) ).
fof(f423,definition,
! [X0,X1,X2] :
( sQ25_spl
<=> ( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,X2),X0))
| ~ is_a_theorem(equivalent(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f424,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,X2),X0))
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f426,plain,
( ~ sQ1_spl
| sQ2_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f392,f423,f28,f13]) ).
fof(f428,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ25_spl
| is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f424,f14]) ).
fof(f449,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ25_spl
| ~ is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X0,X2)))
| is_a_theorem(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[f428,f33]) ).
fof(f565,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f60,f6]) ).
fof(f566,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f1594,plain,
! [X0] :
( ~ sQ1_spl
| ~ is_a_theorem(equivalent(equivalent(a,equivalent(X0,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e))))),equivalent(a,X0))) ),
inference(resolution,[status(thm)],[f337,f44]) ).
fof(f1614,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ is_a_theorem(equivalent(X0,equivalent(a,X1)))
| ~ is_a_theorem(equivalent(X0,equivalent(a,equivalent(X1,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e))))))) ),
inference(resolution,[status(thm)],[f1594,f54]) ).
fof(f2167,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(X0,X3),X2))
| ~ is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X2,equivalent(X1,X3)))) ),
inference(resolution,[status(thm)],[f321,f77]) ).
fof(f2228,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X0,equivalent(equivalent(X1,X3),equivalent(X2,X3))))) ),
inference(resolution,[status(thm)],[f325,f6]) ).
fof(f8609,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X1)),X0)) ),
inference(resolution,[status(thm)],[f2228,f2167]) ).
fof(f8635,plain,
! [X0] :
( ~ sQ1_spl
| ~ is_a_theorem(equivalent(equivalent(a,equivalent(X0,equivalent(b,c))),equivalent(a,equivalent(X0,equivalent(equivalent(b,e),equivalent(c,e)))))) ),
inference(resolution,[status(thm)],[f2228,f1614]) ).
fof(f8761,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ25_spl
| is_a_theorem(equivalent(X0,equivalent(X0,equivalent(X1,X1)))) ),
inference(resolution,[status(thm)],[f8609,f449]) ).
fof(f9784,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ is_a_theorem(equivalent(X0,equivalent(a,equivalent(X1,equivalent(equivalent(b,e),equivalent(c,e))))))
| ~ is_a_theorem(equivalent(X0,equivalent(a,equivalent(X1,equivalent(b,c))))) ),
inference(resolution,[status(thm)],[f8635,f54]) ).
fof(f20929,plain,
( ~ sQ1_spl
| ~ sQ25_spl
| ~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(equivalent(b,e),equivalent(c,e)),equivalent(b,c))))) ),
inference(resolution,[status(thm)],[f9784,f8761]) ).
fof(f20931,plain,
( ~ sQ1_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20929,f6]) ).
fof(f20932,plain,
( ~ sQ1_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f20931]) ).
fof(f20933,plain,
$false,
inference(sat_refutation,[status(thm)],[f16,f19,f128,f426,f566,f20932]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL128-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n006.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 00:06:13 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 157.39/20.57 % Refutation found
% 157.39/20.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 157.39/20.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.62/21.25 % Elapsed time: 20.797304 seconds
% 5.62/21.25 % CPU time: 160.257553 seconds
% 5.62/21.25 % Total memory used: 477.701 MB
% 5.62/21.25 % Net memory used: 431.586 MB
%------------------------------------------------------------------------------