%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN941+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 03:18:32 PM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 3 unt; 6 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 111 ( 46 ~; 38 |; 15 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 33 ( 25 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [B,C] :
( q(f(B))
=> ? [X,Y] :
( q(X)
& ( p(f(Y))
=> ( ( r(Y)
=> ( r(C)
& r(B) ) )
& p(X) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [B,C] :
( q(f(B))
=> ? [X,Y] :
( q(X)
& ( p(f(Y))
=> ( ( r(Y)
=> ( r(C)
& r(B) ) )
& p(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [B,C] :
( ! [X,Y] :
( ~ q(X)
| ( ( ( ( ~ r(C)
| ~ r(B) )
& r(Y) )
| ~ p(X) )
& p(f(Y)) ) )
& q(f(B)) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
? [B] :
( ? [C] :
! [X] :
( ~ q(X)
| ( ( ( ( ~ r(C)
| ~ r(B) )
& ! [Y] : r(Y) )
| ~ p(X) )
& ! [Y] : p(f(Y)) ) )
& q(f(B)) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f5,plain,
( ! [X] :
( ~ q(X)
| ( ( ( ( ~ r(sK1_skl)
| ~ r(sK0_skl) )
& ! [Y] : r(Y) )
| ~ p(X) )
& ! [Y] : p(f(Y)) ) )
& q(f(sK0_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(B,sK0_skl),skolemize(C,sK1_skl)],[f4]) ).
fof(f6,plain,
q(f(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ~ q(X1)
| p(f(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f8,plain,
! [X0,X1] :
( ~ q(X0)
| r(X1)
| ~ p(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f9,plain,
! [X0] :
( ~ q(X0)
| ~ r(sK1_skl)
| ~ r(sK0_skl)
| ~ p(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f10,definition,
! [X0] :
( sQ0_spl
<=> p(f(X0)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f11,plain,
! [X0] :
( ~ sQ0_spl
| p(f(X0)) ),
inference(component_clause,[status(thm)],[f10]) ).
fof(f13,definition,
! [X1] :
( sQ1_spl
<=> ~ q(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f14,plain,
! [X0] :
( ~ sQ1_spl
| ~ q(X0) ),
inference(component_clause,[status(thm)],[f13]) ).
fof(f16,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f10,f13]) ).
fof(f17,definition,
! [X0] :
( sQ2_spl
<=> ( ~ q(X0)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f18,plain,
! [X0] :
( ~ sQ2_spl
| ~ q(X0)
| ~ p(X0) ),
inference(component_clause,[status(thm)],[f17]) ).
fof(f20,definition,
! [X1] :
( sQ3_spl
<=> r(X1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f21,plain,
! [X0] :
( ~ sQ3_spl
| r(X0) ),
inference(component_clause,[status(thm)],[f20]) ).
fof(f23,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f8,f17,f20]) ).
fof(f24,definition,
( sQ4_spl
<=> r(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f26,plain,
( sQ4_spl
| ~ r(sK0_skl) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,definition,
( sQ5_spl
<=> r(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f29,plain,
( sQ5_spl
| ~ r(sK1_skl) ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f30,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f9,f17,f24,f27]) ).
fof(f31,plain,
( ~ sQ2_spl
| ~ p(f(sK0_skl)) ),
inference(resolution,[status(thm)],[f18,f6]) ).
fof(f32,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f31,f11]) ).
fof(f33,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f32]) ).
fof(f34,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6,f14]) ).
fof(f35,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f34]) ).
fof(f36,plain,
( sQ4_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26,f21]) ).
fof(f37,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f36]) ).
fof(f38,plain,
( sQ5_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f21]) ).
fof(f39,plain,
( sQ5_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f38]) ).
fof(f40,plain,
$false,
inference(sat_refutation,[status(thm)],[f16,f23,f30,f33,f35,f37,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN941+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n006.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 11:30:27 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.050171 seconds
% 0.13/0.40 % CPU time: 0.140520 seconds
% 0.13/0.40 % Total memory used: 55.297 MB
% 0.13/0.40 % Net memory used: 54.706 MB
%------------------------------------------------------------------------------