%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN728+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 03:17:11 PM UTC 2026
% Result : Theorem 0.14s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 2 unt; 4 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 109 ( 44 ~; 35 |; 20 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 46 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [W] :
( q(W)
=> ~ m(g(W)) )
& ! [R] :
? [S] :
( ( q(f(R,S))
& m(R) )
| p(R,S) )
& ! [X] :
( ? [Y] : p(X,Y)
=> ! [Z] : p(Z,Z) ) )
=> ! [U] :
? [V] :
( p(U,U)
& p(g(U),V) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ! [W] :
( q(W)
=> ~ m(g(W)) )
& ! [R] :
? [S] :
( ( q(f(R,S))
& m(R) )
| p(R,S) )
& ! [X] :
( ? [Y] : p(X,Y)
=> ! [Z] : p(Z,Z) ) )
=> ! [U] :
? [V] :
( p(U,U)
& p(g(U),V) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [U] :
! [V] :
( ~ p(U,U)
| ~ p(g(U),V) )
& ! [W] :
( ~ m(g(W))
| ~ q(W) )
& ! [R] :
? [S] :
( ( q(f(R,S))
& m(R) )
| p(R,S) )
& ! [X] :
( ! [Z] : p(Z,Z)
| ! [Y] : ~ p(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ( ? [U] : ~ p(U,U)
| ? [U] :
! [V] : ~ p(g(U),V) )
& ! [W] :
( ~ m(g(W))
| ~ q(W) )
& ! [R] :
( ( ? [S] : q(f(R,S))
& m(R) )
| ? [S] : p(R,S) )
& ( ! [Z] : p(Z,Z)
| ! [X,Y] : ~ p(X,Y) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f5,plain,
( ( ~ p(sK3_skl,sK3_skl)
| ! [V] : ~ p(g(sK2_skl),V) )
& ! [W] :
( ~ m(g(W))
| ~ q(W) )
& ! [R] :
( ( q(f(R,sK1_skl(R)))
& m(R) )
| p(R,sK0_skl(R)) )
& ( ! [Z] : p(Z,Z)
| ! [X,Y] : ~ p(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(S,sK0_skl(R)),skolemize(S,sK1_skl(R)),skolemize(U,sK2_skl),skolemize(U,sK3_skl)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2] :
( p(X2,X2)
| ~ p(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [X0] :
( m(X0)
| p(X0,sK0_skl(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f8,plain,
! [X0] :
( q(f(X0,sK1_skl(X0)))
| p(X0,sK0_skl(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f9,plain,
! [X0] :
( ~ m(g(X0))
| ~ q(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f10,plain,
! [X0] :
( ~ p(sK3_skl,sK3_skl)
| ~ p(g(sK2_skl),X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
! [X0,X1] :
( sQ0_spl
<=> ~ p(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f12,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ p(X0,X1) ),
inference(component_clause,[status(thm)],[f11]) ).
fof(f14,definition,
! [X2] :
( sQ1_spl
<=> p(X2,X2) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f15,plain,
! [X0] :
( ~ sQ1_spl
| p(X0,X0) ),
inference(component_clause,[status(thm)],[f14]) ).
fof(f17,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f6,f11,f14]) ).
fof(f18,definition,
! [X0] :
( sQ2_spl
<=> ~ p(g(sK2_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f19,plain,
! [X0] :
( ~ sQ2_spl
| ~ p(g(sK2_skl),X0) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,definition,
( sQ3_spl
<=> p(sK3_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f23,plain,
( sQ3_spl
| ~ p(sK3_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f10,f18,f21]) ).
fof(f25,plain,
! [X0] :
( ~ sQ0_spl
| ~ q(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f9,f26]) ).
fof(f26,plain,
! [X0] :
( ~ sQ0_spl
| m(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f7,f12]) ).
fof(f27,plain,
! [X0] :
( ~ sQ0_spl
| q(f(X0,sK1_skl(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f8,f12]) ).
fof(f28,plain,
( ~ sQ0_spl
| $false ),
inference(resolution,[status(thm)],[f27,f25]) ).
fof(f29,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f28]) ).
fof(f30,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(resolution,[status(thm)],[f19,f15]) ).
fof(f31,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f30]) ).
fof(f32,plain,
( sQ3_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23,f15]) ).
fof(f33,plain,
( sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f32]) ).
fof(f34,plain,
$false,
inference(sat_refutation,[status(thm)],[f17,f24,f29,f31,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN728+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n006.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 11:13:19 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.14/5.40 % Refutation found
% 0.14/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.42 % Elapsed time: 0.039605 seconds
% 0.14/5.42 % CPU time: 0.109801 seconds
% 0.14/5.42 % Total memory used: 16.581 MB
% 0.14/5.42 % Net memory used: 15.990 MB
%------------------------------------------------------------------------------