%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL026-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 01:06:37 PM UTC 2026
% Result : Unsatisfiable 24.04s 3.43s
% Output : CNFRefutation 24.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 79 ( 28 unt; 2 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 127 ( 65 ~; 60 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 180 ( 180 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : is_a_theorem(implies(implies(implies(X,falsehood),falsehood),X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0] : is_a_theorem(implies(implies(implies(X0,falsehood),falsehood),X0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
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)],[f4]) ).
fof(f11,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f7,f8]) ).
fof(f13,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f14,plain,
! [X0] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(implies(X0,falsehood),falsehood)) ),
inference(resolution,[status(thm)],[f9,f7]) ).
fof(f15,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(implies(X1,falsehood),falsehood),X1))),
inference(resolution,[status(thm)],[f9,f12]) ).
fof(f16,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f13,f7]) ).
fof(f18,definition,
! [X0] :
( sQ0_spl
<=> ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f19,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,definition,
! [X1,X2] :
( sQ1_spl
<=> is_a_theorem(implies(X1,implies(X2,X1))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f22,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f18,f21]) ).
fof(f25,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f9,f19]) ).
fof(f28,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f25]) ).
fof(f29,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(X0,implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3))))),
inference(resolution,[status(thm)],[f12,f10]) ).
fof(f31,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)],[f7,f10]) ).
fof(f36,plain,
is_a_theorem(implies(falsehood,falsehood)),
inference(resolution,[status(thm)],[f9,f14]) ).
fof(f40,plain,
! [X0] : is_a_theorem(implies(X0,implies(falsehood,falsehood))),
inference(resolution,[status(thm)],[f36,f12]) ).
fof(f58,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,implies(X1,X2)),implies(X0,X1)),implies(implies(X0,implies(X1,X2)),implies(X0,X2)))),
inference(resolution,[status(thm)],[f31,f10]) ).
fof(f61,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(X0,implies(X2,X1)))),
inference(resolution,[status(thm)],[f31,f13]) ).
fof(f62,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,X1),implies(X0,X0))) ),
inference(resolution,[status(thm)],[f31,f22]) ).
fof(f64,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f62,f7]) ).
fof(f70,plain,
! [X0] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f64,f40]) ).
fof(f74,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,X1),X0),implies(implies(X0,X1),X1))) ),
inference(resolution,[status(thm)],[f70,f31]) ).
fof(f76,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,X1))) ),
inference(resolution,[status(thm)],[f70,f12]) ).
fof(f77,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(implies(X1,falsehood),falsehood)),implies(X0,X1))),
inference(resolution,[status(thm)],[f15,f31]) ).
fof(f84,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(X0,implies(X1,implies(X2,X3))),implies(X0,implies(implies(X1,X2),implies(X1,X3))))),
inference(resolution,[status(thm)],[f29,f31]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,implies(X2,X2)))) ),
inference(resolution,[status(thm)],[f76,f12]) ).
fof(f116,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,implies(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f61,f7]) ).
fof(f126,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X0,X2)))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f58,f7]) ).
fof(f127,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(X0,implies(implies(implies(X1,implies(X2,X3)),implies(X1,X2)),implies(implies(X1,implies(X2,X3)),implies(X1,X3))))),
inference(resolution,[status(thm)],[f58,f12]) ).
fof(f140,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,implies(X2,X0)))) ),
inference(resolution,[status(thm)],[f116,f22]) ).
fof(f145,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,implies(X2,implies(X3,X1))))) ),
inference(resolution,[status(thm)],[f140,f12]) ).
fof(f163,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(implies(X1,falsehood),falsehood))) ),
inference(resolution,[status(thm)],[f77,f7]) ).
fof(f223,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f74,f7]) ).
fof(f347,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,implies(X1,X2)),implies(implies(implies(X0,X1),implies(X0,X2)),X3)),implies(implies(X0,implies(X1,X2)),X3))),
inference(resolution,[status(thm)],[f126,f29]) ).
fof(f358,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,implies(implies(X1,X1),X2)),implies(X0,X2))) ),
inference(resolution,[status(thm)],[f126,f93]) ).
fof(f359,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(implies(X1,X0),X2)),implies(X0,X2))),
inference(resolution,[status(thm)],[f126,f13]) ).
fof(f393,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(X0,implies(implies(X1,implies(X2,X3)),implies(X1,X2))),implies(X0,implies(implies(X1,implies(X2,X3)),implies(X1,X3))))),
inference(resolution,[status(thm)],[f127,f31]) ).
fof(f415,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,implies(X1,implies(X2,X0))),X3),X3)) ),
inference(resolution,[status(thm)],[f223,f145]) ).
fof(f419,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),X2),X2)) ),
inference(resolution,[status(thm)],[f223,f13]) ).
fof(f485,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[f419,f7]) ).
fof(f565,plain,
! [X0] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,falsehood),X0),X0)) ),
inference(resolution,[status(thm)],[f163,f74]) ).
fof(f572,plain,
! [X0] :
( ~ sQ1_spl
| is_a_theorem(implies(falsehood,X0)) ),
inference(resolution,[status(thm)],[f163,f22]) ).
fof(f581,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(falsehood,X1))) ),
inference(resolution,[status(thm)],[f572,f12]) ).
fof(f592,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,falsehood),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f581,f31]) ).
fof(f627,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(implies(implies(X1,falsehood),X1),X1))) ),
inference(resolution,[status(thm)],[f565,f12]) ).
fof(f1068,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))) ),
inference(resolution,[status(thm)],[f84,f485]) ).
fof(f1162,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,implies(implies(X1,falsehood),X1)),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f627,f31]) ).
fof(f1569,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,implies(implies(X1,X1),X2))) ),
inference(resolution,[status(thm)],[f358,f7]) ).
fof(f1583,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,implies(implies(X1,X0),X2))) ),
inference(resolution,[status(thm)],[f359,f7]) ).
fof(f1587,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(X0,implies(implies(X1,implies(implies(X2,X1),X3)),implies(X1,X3)))),
inference(resolution,[status(thm)],[f359,f12]) ).
fof(f1663,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| is_a_theorem(X3)
| ~ is_a_theorem(implies(implies(X0,implies(X1,implies(X2,X0))),X3)) ),
inference(resolution,[status(thm)],[f415,f7]) ).
fof(f2633,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X2,X0),implies(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1068,f7]) ).
fof(f2660,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X0,implies(X1,X2)),X3))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(implies(X0,X1),implies(X0,X2)),X3))) ),
inference(resolution,[status(thm)],[f347,f7]) ).
fof(f3597,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(implies(X1,implies(X0,X2)),implies(X1,X2)))) ),
inference(resolution,[status(thm)],[f393,f1663]) ).
fof(f3695,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(implies(X0,X1),X1))) ),
inference(resolution,[status(thm)],[f3597,f1569]) ).
fof(f3725,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,X1),implies(X0,implies(implies(X1,X2),X2)))) ),
inference(resolution,[status(thm)],[f3695,f2633]) ).
fof(f4505,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(implies(X1,X2),X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f3725,f7]) ).
fof(f4866,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(X0,falsehood),implies(implies(implies(X0,X1),X2),X2))) ),
inference(resolution,[status(thm)],[f4505,f592]) ).
fof(f6044,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(implies(X1,falsehood),X1))) ),
inference(resolution,[status(thm)],[f1162,f7]) ).
fof(f14109,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))),
inference(resolution,[status(thm)],[f1587,f1583]) ).
fof(f14211,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X3),implies(X2,X3)))),
inference(resolution,[status(thm)],[f14109,f12]) ).
fof(f36108,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))),
inference(resolution,[status(thm)],[f2660,f14211]) ).
fof(f36233,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f36108,f7]) ).
fof(f36560,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X0,falsehood),X2))) ),
inference(resolution,[status(thm)],[f36233,f4866]) ).
fof(f50739,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,X1),X0),X0)) ),
inference(resolution,[status(thm)],[f36560,f6044]) ).
fof(f50800,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f11,f50739]) ).
fof(f50898,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f50800]) ).
fof(f50899,plain,
$false,
inference(sat_refutation,[status(thm)],[f24,f28,f50898]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL026-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Mon Sep 21 00:00:06 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 24.04/3.43 % Refutation found
% 24.04/3.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 24.04/3.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 24.04/3.47 % Elapsed time: 3.161699 seconds
% 24.04/3.47 % CPU time: 24.859416 seconds
% 24.04/3.47 % Total memory used: 324.028 MB
% 24.04/3.47 % Net memory used: 276.300 MB
%------------------------------------------------------------------------------