%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN069+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 03:15:07 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 8 unt; 4 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 149 ( 57 ~; 48 |; 36 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 62 ( 51 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] :
( ( ! [Y] :
( ( big_h(X,Y)
& big_g(Y) )
=> big_j(X,Y) )
& big_f(X) )
=> ! [Y1] :
( big_k(Y1)
& big_h(X,Y1)
& big_g(Y1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
~ ? [Y] :
( big_k(Y)
& big_l(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
? [X] :
( ! [Y1] :
( ( big_h(X,Y1)
& big_g(Y1) )
=> big_j(X,Y1) )
& ! [Y] :
( big_h(X,Y)
=> big_l(Y) )
& big_f(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
? [X] :
( ~ ? [Y] :
( big_h(X,Y)
& big_g(Y) )
& big_f(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ? [X] :
( ~ ? [Y] :
( big_h(X,Y)
& big_g(Y) )
& big_f(X) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X] :
( ! [Y1] :
( big_k(Y1)
& big_h(X,Y1)
& big_g(Y1) )
| ? [Y] :
( ~ big_j(X,Y)
& big_h(X,Y)
& big_g(Y) )
| ~ big_f(X) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f7,definition,
! [X,Y] :
( sP0_prd(Y,X)
<=> ( ~ big_j(X,Y)
& big_h(X,Y)
& big_g(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f8,plain,
! [X] :
( ! [Y1] :
( big_k(Y1)
& big_h(X,Y1)
& big_g(Y1) )
| ? [Y] : sP0_prd(Y,X)
| ~ big_f(X) ),
inference(formula_renaming,[status(thm)],[f6,f7]) ).
fof(f9,plain,
! [X] :
( ( ! [Y1] : big_k(Y1)
& ! [Y1] : big_h(X,Y1)
& ! [Y1] : big_g(Y1) )
| ? [Y] : sP0_prd(Y,X)
| ~ big_f(X) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f10,plain,
! [X] :
( ( ! [Y1] : big_k(Y1)
& ! [Y1] : big_h(X,Y1)
& ! [Y1] : big_g(Y1) )
| sP0_prd(sK0_skl(X),X)
| ~ big_f(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y,sK0_skl(X))],[f9]) ).
fof(f13,plain,
! [X0,X1] :
( big_k(X1)
| sP0_prd(sK0_skl(X0),X0)
| ~ big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f14,plain,
! [Y] :
( ~ big_k(Y)
| ~ big_l(Y) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
! [X0] :
( ~ big_k(X0)
| ~ big_l(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
? [X] :
( ! [Y1] :
( big_j(X,Y1)
| ~ big_h(X,Y1)
| ~ big_g(Y1) )
& ! [Y] :
( big_l(Y)
| ~ big_h(X,Y) )
& big_f(X) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
( ! [Y1] :
( big_j(sK1_skl,Y1)
| ~ big_h(sK1_skl,Y1)
| ~ big_g(Y1) )
& ! [Y] :
( big_l(Y)
| ~ big_h(sK1_skl,Y) )
& big_f(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X,sK1_skl)],[f16]) ).
fof(f18,plain,
big_f(sK1_skl),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0] :
( big_l(X0)
| ~ big_h(sK1_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0] :
( big_j(sK1_skl,X0)
| ~ big_h(sK1_skl,X0)
| ~ big_g(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [X] :
( ? [Y] :
( big_h(X,Y)
& big_g(Y) )
| ~ big_f(X) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X] :
( ( big_h(X,sK2_skl(X))
& big_g(sK2_skl(X)) )
| ~ big_f(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(X))],[f21]) ).
fof(f24,plain,
! [X0] :
( big_h(X0,sK2_skl(X0))
| ~ big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X,Y] :
( ( big_j(X,Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| sP0_prd(Y,X) )
& ( ( ~ big_j(X,Y)
& big_h(X,Y)
& big_g(Y) )
| ~ sP0_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
( ! [X,Y] :
( big_j(X,Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| sP0_prd(Y,X) )
& ! [X,Y] :
( ( ~ big_j(X,Y)
& big_h(X,Y)
& big_g(Y) )
| ~ sP0_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( big_g(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( big_h(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,plain,
! [X0,X1] :
( ~ big_j(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f31,definition,
! [X0] :
( sQ0_spl
<=> ( sP0_prd(sK0_skl(X0),X0)
| ~ big_f(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f32,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(sK0_skl(X0),X0)
| ~ big_f(X0) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f38,definition,
! [X1] :
( sQ2_spl
<=> big_k(X1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f39,plain,
! [X0] :
( ~ sQ2_spl
| big_k(X0) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f13,f31,f38]) ).
fof(f42,plain,
big_h(sK1_skl,sK2_skl(sK1_skl)),
inference(resolution,[status(thm)],[f18,f24]) ).
fof(f43,plain,
big_l(sK2_skl(sK1_skl)),
inference(resolution,[status(thm)],[f19,f42]) ).
fof(f45,plain,
~ big_k(sK2_skl(sK1_skl)),
inference(resolution,[status(thm)],[f43,f15]) ).
fof(f47,definition,
( sQ3_spl
<=> sP0_prd(sK0_skl(sK1_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f48,plain,
( ~ sQ3_spl
| sP0_prd(sK0_skl(sK1_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f57,plain,
( ~ sQ0_spl
| sP0_prd(sK0_skl(sK1_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f32,f18]) ).
fof(f58,plain,
! [X0] :
( ~ sP0_prd(X0,sK1_skl)
| ~ big_h(sK1_skl,X0)
| ~ big_g(X0) ),
inference(resolution,[status(thm)],[f20,f29]) ).
fof(f59,plain,
! [X0] :
( ~ sP0_prd(X0,sK1_skl)
| ~ big_h(sK1_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f27]) ).
fof(f60,plain,
( ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f48,f61]) ).
fof(f61,plain,
! [X0] : ~ sP0_prd(X0,sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f59,f28]) ).
fof(f62,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( ~ sQ0_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f57,f47,f31]) ).
fof(f68,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f45,f39]) ).
fof(f69,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f68]) ).
fof(f70,plain,
$false,
inference(sat_refutation,[status(thm)],[f41,f62,f63,f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN069+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 10:41:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.041783 seconds
% 0.09/0.42 % CPU time: 0.111201 seconds
% 0.09/0.42 % Total memory used: 16.750 MB
% 0.09/0.42 % Net memory used: 16.280 MB
%------------------------------------------------------------------------------