%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN967+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 03:18:36 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 4 unt; 3 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 84 ( 30 ~; 27 |; 16 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 44 ( 36 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A,B] :
( ! [Y] :
( q(Y)
=> p(Y) )
=> ? [X] :
( ( q(X)
=> p(B) )
& ( p(X)
=> p(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A,B] :
( ! [Y] :
( q(Y)
=> p(Y) )
=> ? [X] :
( ( q(X)
=> p(B) )
& ( p(X)
=> p(A) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [A,B] :
( ! [X] :
( ( ~ p(B)
& q(X) )
| ( ~ p(A)
& p(X) ) )
& ! [Y] :
( p(Y)
| ~ q(Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [A,X] :
( sP0_prd(X,A)
<=> ( ~ p(A)
& p(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
? [A,B] :
( ! [X] :
( ( ~ p(B)
& q(X) )
| sP0_prd(X,A) )
& ! [Y] :
( p(Y)
| ~ q(Y) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ? [A,B] :
! [X] :
( ( ~ p(B)
& q(X) )
| sP0_prd(X,A) )
& ! [Y] :
( p(Y)
| ~ q(Y) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f7,plain,
( ! [X] :
( ( ~ p(sK1_skl)
& q(X) )
| sP0_prd(X,sK0_skl) )
& ! [Y] :
( p(Y)
| ~ q(Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl)],[f6]) ).
fof(f8,plain,
! [X0] :
( p(X0)
| ~ q(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0] :
( q(X0)
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X0] :
( ~ p(sK1_skl)
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [A,X] :
( ( p(A)
| ~ p(X)
| sP0_prd(X,A) )
& ( ( ~ p(A)
& p(X) )
| ~ sP0_prd(X,A) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
( ! [A,X] :
( p(A)
| ~ p(X)
| sP0_prd(X,A) )
& ! [A,X] :
( ( ~ p(A)
& p(X) )
| ~ sP0_prd(X,A) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( p(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ~ p(X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(X0,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f17,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f16]) ).
fof(f19,definition,
( sQ1_spl
<=> p(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f21,plain,
( sQ1_spl
| ~ p(sK1_skl) ),
inference(component_clause,[status(thm)],[f19]) ).
fof(f22,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f16,f19]) ).
fof(f23,plain,
! [X0] :
( ~ sQ0_spl
| p(X0) ),
inference(resolution,[status(thm)],[f13,f17]) ).
fof(f24,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f17,f25]) ).
fof(f25,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sP0_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f14,f23]) ).
fof(f26,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f24]) ).
fof(f27,plain,
! [X0] :
( p(X0)
| q(X0) ),
inference(resolution,[status(thm)],[f9,f13]) ).
fof(f28,plain,
! [X0] : p(X0),
inference(forward_subsumption_resolution,[status(thm)],[f27,f8]) ).
fof(f29,plain,
( sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f21,f28]) ).
fof(f31,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f29]) ).
fof(f32,plain,
$false,
inference(sat_refutation,[status(thm)],[f22,f26,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN967+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 11:31:12 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.048078 seconds
% 0.13/0.41 % CPU time: 0.116349 seconds
% 0.13/0.41 % Total memory used: 16.527 MB
% 0.13/0.41 % Net memory used: 15.927 MB
%------------------------------------------------------------------------------