%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL144-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 01:06:55 PM UTC 2026
% Result : Unsatisfiable 1.04s 0.59s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 7 unt; 2 def)
% Number of atoms : 81 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 72 ( 34 ~; 36 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : implies(truth,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( implies(X,Y) = truth
| ~ ordered(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( ordered(X,Y)
| implies(X,Y) != truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( ordered(y,implies(x,z))
| ordered(x,implies(y,z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( ~ ordered(y,implies(x,z))
| ~ ordered(x,implies(y,z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0] : implies(truth,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0,X1] :
( implies(X0,X1) = truth
| ~ ordered(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f18,plain,
! [X0,X1] :
( ordered(X0,X1)
| implies(X0,X1) != truth ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f19,plain,
( ordered(y,implies(x,z))
| ordered(x,implies(y,z)) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
( ~ ordered(y,implies(x,z))
| ~ ordered(x,implies(y,z)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f21,definition,
( sQ0_spl
<=> ordered(x,implies(y,z)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f22,plain,
( ~ sQ0_spl
| ordered(x,implies(y,z)) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f23,plain,
( sQ0_spl
| ~ ordered(x,implies(y,z)) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,definition,
( sQ1_spl
<=> ordered(y,implies(x,z)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f25,plain,
( ~ sQ1_spl
| ordered(y,implies(x,z)) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f26,plain,
( sQ1_spl
| ~ ordered(y,implies(x,z)) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f21,f24]) ).
fof(f28,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f21,f24]) ).
fof(f35,plain,
( ~ sQ1_spl
| implies(y,implies(x,z)) = truth ),
inference(resolution,[status(thm)],[f17,f25]) ).
fof(f36,plain,
! [X0,X1,X2,X3] : implies(truth,implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3))) = truth,
inference(paramodulation,[status(thm)],[f12,f12]) ).
fof(f37,plain,
! [X0] :
( ~ sQ1_spl
| implies(truth,implies(implies(implies(x,z),X0),implies(y,X0))) = truth ),
inference(paramodulation,[status(thm)],[f35,f12]) ).
fof(f46,plain,
! [X0,X1,X2,X3] : implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3)) = truth,
inference(forward_demodulation,[status(thm)],[f11,f36]) ).
fof(f47,plain,
! [X0] :
( ~ sQ1_spl
| implies(implies(implies(x,z),X0),implies(y,X0)) = truth ),
inference(forward_demodulation,[status(thm)],[f11,f37]) ).
fof(f158,plain,
( sQ0_spl
| implies(x,implies(y,z)) != truth ),
inference(resolution,[status(thm)],[f18,f23]) ).
fof(f161,plain,
! [X0] :
( ~ sQ1_spl
| implies(truth,implies(implies(X0,x),implies(y,implies(X0,z)))) = truth ),
inference(paramodulation,[status(thm)],[f47,f46]) ).
fof(f210,plain,
! [X0] :
( ~ sQ1_spl
| implies(implies(X0,x),implies(y,implies(X0,z))) = truth ),
inference(forward_demodulation,[status(thm)],[f11,f161]) ).
fof(f938,plain,
( ~ sQ1_spl
| implies(x,implies(y,implies(truth,z))) = truth ),
inference(paramodulation,[status(thm)],[f11,f210]) ).
fof(f959,plain,
( ~ sQ1_spl
| implies(x,implies(y,z)) = truth ),
inference(forward_demodulation,[status(thm)],[f11,f938]) ).
fof(f960,plain,
( ~ sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f959,f158]) ).
fof(f961,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f960]) ).
fof(f962,plain,
( ~ sQ0_spl
| implies(x,implies(y,z)) = truth ),
inference(resolution,[status(thm)],[f22,f17]) ).
fof(f963,plain,
( sQ1_spl
| implies(y,implies(x,z)) != truth ),
inference(resolution,[status(thm)],[f26,f18]) ).
fof(f975,plain,
! [X0] :
( ~ sQ0_spl
| implies(truth,implies(implies(implies(y,z),X0),implies(x,X0))) = truth ),
inference(paramodulation,[status(thm)],[f962,f12]) ).
fof(f992,plain,
! [X0] :
( ~ sQ0_spl
| implies(implies(implies(y,z),X0),implies(x,X0)) = truth ),
inference(forward_demodulation,[status(thm)],[f11,f975]) ).
fof(f1198,plain,
! [X0] :
( ~ sQ0_spl
| implies(truth,implies(implies(X0,y),implies(x,implies(X0,z)))) = truth ),
inference(paramodulation,[status(thm)],[f992,f46]) ).
fof(f1221,plain,
! [X0] :
( ~ sQ0_spl
| implies(implies(X0,y),implies(x,implies(X0,z))) = truth ),
inference(forward_demodulation,[status(thm)],[f11,f1198]) ).
fof(f2315,plain,
( ~ sQ0_spl
| implies(y,implies(x,implies(truth,z))) = truth ),
inference(paramodulation,[status(thm)],[f11,f1221]) ).
fof(f2338,plain,
( ~ sQ0_spl
| implies(y,implies(x,z)) = truth ),
inference(forward_demodulation,[status(thm)],[f11,f2315]) ).
fof(f2339,plain,
( ~ sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2338,f963]) ).
fof(f2340,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f2339]) ).
fof(f2341,plain,
$false,
inference(sat_refutation,[status(thm)],[f27,f28,f961,f2340]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL144-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 00:02:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 1.04/0.59 % Refutation found
% 1.04/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.04/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.04/0.60 % Elapsed time: 0.228094 seconds
% 1.04/0.60 % CPU time: 1.534181 seconds
% 1.04/0.60 % Total memory used: 142.485 MB
% 1.04/0.60 % Net memory used: 140.490 MB
%------------------------------------------------------------------------------