%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN066+1 : TPTP v9.3.1. Bugfixed v3.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 03:15:06 PM UTC 2026
% Result : Theorem 0.10s 0.55s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 8 unt; 2 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 52 ( 22 ~; 18 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 54 ( 40 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Z] :
? [W] :
! [X] :
? [Y] :
( ( big_p(Y,W)
=> ? [U] : big_q(U,W) )
& big_p(Y,Z)
& ( big_p(X,Z)
=> big_p(Y,W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Z] :
( ~ big_p(X,Z)
=> ? [Y] : big_q(Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( ? [X,Y] : big_q(X,Y)
=> ! [Z] : big_r(Z,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
! [X] :
? [Y] : big_r(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ! [X] :
? [Y] : big_r(X,Y),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [Z] :
? [W] :
! [X] :
? [Y] :
( ( ? [U] : big_q(U,W)
| ~ big_p(Y,W) )
& big_p(Y,Z)
& ( big_p(Y,W)
| ~ big_p(X,Z) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [Z,X] :
( ( big_q(sK2_skl(X,Z),sK0_skl(Z))
| ~ big_p(sK1_skl(X,Z),sK0_skl(Z)) )
& big_p(sK1_skl(X,Z),Z)
& ( big_p(sK1_skl(X,Z),sK0_skl(Z))
| ~ big_p(X,Z) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(W,sK0_skl(Z)),skolemize(Y,sK1_skl(X,Z)),skolemize(U,sK2_skl(X,Z))],[f6]) ).
fof(f10,plain,
! [X0,X1] :
( big_q(sK2_skl(X0,X1),sK0_skl(X1))
| ~ big_p(sK1_skl(X0,X1),sK0_skl(X1)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [X,Z] :
( ? [Y] : big_q(Y,Z)
| big_p(X,Z) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [Z] :
( ? [Y] : big_q(Y,Z)
| ! [X] : big_p(X,Z) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f13,plain,
! [Z] :
( big_q(sK3_skl(Z),Z)
| ! [X] : big_p(X,Z) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y,sK3_skl(Z))],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( big_q(sK3_skl(X1),X1)
| big_p(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
( ! [Z] : big_r(Z,Z)
| ! [X,Y] : ~ big_q(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [X0,X1,X2] :
( big_r(X2,X2)
| ~ big_q(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
? [X] :
! [Y] : ~ big_r(X,Y),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
! [Y] : ~ big_r(sK4_skl,Y),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(X,sK4_skl)],[f17]) ).
fof(f19,plain,
! [X0] : ~ big_r(sK4_skl,X0),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,definition,
! [X0,X1] :
( sQ0_spl
<=> ~ big_q(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f21,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ big_q(X0,X1) ),
inference(component_clause,[status(thm)],[f20]) ).
fof(f23,definition,
! [X2] :
( sQ1_spl
<=> big_r(X2,X2) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f24,plain,
! [X0] :
( ~ sQ1_spl
| big_r(X0,X0) ),
inference(component_clause,[status(thm)],[f23]) ).
fof(f26,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f20,f23]) ).
fof(f27,plain,
! [X0,X1] :
( ~ sQ0_spl
| big_p(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f14,f21]) ).
fof(f28,plain,
! [X0,X1] :
( ~ sQ0_spl
| big_q(sK2_skl(X0,X1),sK0_skl(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f10,f27]) ).
fof(f29,plain,
( ~ sQ0_spl
| $false ),
inference(resolution,[status(thm)],[f28,f21]) ).
fof(f30,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f29]) ).
fof(f31,plain,
( ~ sQ1_spl
| $false ),
inference(resolution,[status(thm)],[f24,f19]) ).
fof(f32,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f31]) ).
fof(f33,plain,
$false,
inference(sat_refutation,[status(thm)],[f26,f30,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN066+1 : TPTP v9.3.1. Bugfixed v3.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.52 % Computer : n009.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Mon Sep 21 10:41:44 UTC 2026
% 0.10/0.52 % CPUTime :
% 0.10/0.53 % Drodi V4.1.1
% 0.10/0.55 % Refutation found
% 0.10/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.57 % Elapsed time: 0.043642 seconds
% 0.17/0.57 % CPU time: 0.113305 seconds
% 0.17/0.57 % Total memory used: 16.559 MB
% 0.17/0.57 % Net memory used: 16.006 MB
%------------------------------------------------------------------------------