%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL077-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 01:06:45 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 13 unt; 4 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 95 ( 48 ~; 43 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 5 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X1,X2,X3] :
( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ is_a_theorem(implies(not(not(a)),a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [X1,X3] :
( is_a_theorem(implies(X1,X3))
| ! [X2] :
( ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(X1,X2)) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
~ is_a_theorem(implies(not(not(a)),a)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f8,f9]) ).
fof(f16,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f15,f9]) ).
fof(f17,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f10,f8]) ).
fof(f19,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f16,f8]) ).
fof(f21,definition,
! [X0] :
( sQ0_spl
<=> ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f22,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,definition,
! [X1,X2] :
( sQ1_spl
<=> is_a_theorem(implies(X1,implies(X2,X1))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f25,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f21,f24]) ).
fof(f28,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f10,f22]) ).
fof(f31,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f28]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f13,f25]) ).
fof(f52,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(not(X0),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f35,f11]) ).
fof(f57,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(not(X0),not(X1)),X1),implies(implies(not(X0),not(X1)),X0))),
inference(resolution,[status(thm)],[f17,f11]) ).
fof(f61,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,X1),implies(X0,X0))) ),
inference(resolution,[status(thm)],[f17,f25]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(not(X0),X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f52,f13]) ).
fof(f78,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,X1))) ),
inference(resolution,[status(thm)],[f61,f35]) ).
fof(f86,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X1,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f78,f8]) ).
fof(f89,definition,
! [X1] :
( sQ3_spl
<=> is_a_theorem(implies(X1,X1)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f90,plain,
! [X0] :
( ~ sQ3_spl
| is_a_theorem(implies(X0,X0)) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( ~ sQ1_spl
| sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f86,f21,f89,f24]) ).
fof(f263,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(implies(not(X1),not(X0)),X1))) ),
inference(resolution,[status(thm)],[f57,f35]) ).
fof(f335,definition,
! [X1] :
( sQ11_spl
<=> is_a_theorem(X1) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f336,plain,
! [X0] :
( ~ sQ11_spl
| is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f460,plain,
( ~ sQ11_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f14,f336]) ).
fof(f461,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f460]) ).
fof(f923,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(not(X1),not(X0)),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f263,f8]) ).
fof(f1115,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ1_spl
| is_a_theorem(implies(implies(not(X0),not(implies(X1,X1))),X0)) ),
inference(resolution,[status(thm)],[f923,f90]) ).
fof(f1203,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ1_spl
| is_a_theorem(implies(not(not(X0)),X0)) ),
inference(resolution,[status(thm)],[f64,f1115]) ).
fof(f1233,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f14,f1203]) ).
fof(f1247,plain,
( ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1233]) ).
fof(f1248,plain,
$false,
inference(sat_refutation,[status(thm)],[f27,f31,f92,f461,f1247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL077-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.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 00:03:55 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
% 0.13/0.43 % Elapsed time: 0.060955 seconds
% 0.13/0.43 % CPU time: 0.158315 seconds
% 0.13/0.43 % Total memory used: 15.894 MB
% 0.13/0.43 % Net memory used: 15.404 MB
%------------------------------------------------------------------------------