%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN351+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 03:15:51 PM UTC 2026
% Result : Theorem 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 3 unt; 1 def)
% Number of atoms : 86 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 95 ( 25 ~; 23 |; 28 &)
% ( 7 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 43 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,Y2,X1,Z)
=> ( ( big_f(X1,Y1,X1,Y2)
<=> big_f(Y1,X2,Y1,Y2) )
=> ( big_f(X1,Y1,X1,Y2)
=> ( ( big_f(X1,Z,Y1,Z)
=> ( big_f(X1,Y1,X1,Y2)
<=> big_f(X1,Y2,Y1,Y2) ) )
& ( big_f(X1,Y2,Y1,Y2)
=> big_f(X1,Z,Y1,Z) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,Y2,X1,Z)
=> ( ( big_f(X1,Y1,X1,Y2)
<=> big_f(Y1,X2,Y1,Y2) )
=> ( big_f(X1,Y1,X1,Y2)
=> ( ( big_f(X1,Z,Y1,Z)
=> ( big_f(X1,Y1,X1,Y2)
<=> big_f(X1,Y2,Y1,Y2) ) )
& ( big_f(X1,Y2,Y1,Y2)
=> big_f(X1,Z,Y1,Z) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ( ( big_f(X1,Y1,X1,Y2)
<~> big_f(X1,Y2,Y1,Y2) )
& big_f(X1,Z,Y1,Z) )
| ( ~ big_f(X1,Z,Y1,Z)
& big_f(X1,Y2,Y1,Y2) ) )
& big_f(X1,Y1,X1,Y2)
& ( big_f(X1,Y1,X1,Y2)
<=> big_f(Y1,X2,Y1,Y2) )
& big_f(X1,Y2,X1,Z) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X1,Y1,Y2,Z] :
( sP0_prd(Z,Y2,Y1,X1)
<=> ( ~ big_f(X1,Z,Y1,Z)
& big_f(X1,Y2,Y1,Y2) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ( ( big_f(X1,Y1,X1,Y2)
<~> big_f(X1,Y2,Y1,Y2) )
& big_f(X1,Z,Y1,Z) )
| sP0_prd(Z,Y2,Y1,X1) )
& big_f(X1,Y1,X1,Y2)
& ( big_f(X1,Y1,X1,Y2)
<=> big_f(Y1,X2,Y1,Y2) )
& big_f(X1,Y2,X1,Z) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ( ( ~ big_f(X1,Y2,Y1,Y2)
| ~ big_f(X1,Y1,X1,Y2) )
& ( big_f(X1,Y2,Y1,Y2)
| big_f(X1,Y1,X1,Y2) )
& big_f(X1,Z,Y1,Z) )
| sP0_prd(Z,Y2,Y1,X1) )
& big_f(X1,Y1,X1,Y2)
& ( ~ big_f(Y1,X2,Y1,Y2)
| big_f(X1,Y1,X1,Y2) )
& ( big_f(Y1,X2,Y1,Y2)
| ~ big_f(X1,Y1,X1,Y2) )
& big_f(X1,Y2,X1,Z) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [Y1,Y2] :
( ( ( ( ~ big_f(sK0_skl,Y2,Y1,Y2)
| ~ big_f(sK0_skl,Y1,sK0_skl,Y2) )
& ( big_f(sK0_skl,Y2,Y1,Y2)
| big_f(sK0_skl,Y1,sK0_skl,Y2) )
& big_f(sK0_skl,sK2_skl(Y2,Y1),Y1,sK2_skl(Y2,Y1)) )
| sP0_prd(sK2_skl(Y2,Y1),Y2,Y1,sK0_skl) )
& big_f(sK0_skl,Y1,sK0_skl,Y2)
& ( ~ big_f(Y1,sK1_skl,Y1,Y2)
| big_f(sK0_skl,Y1,sK0_skl,Y2) )
& ( big_f(Y1,sK1_skl,Y1,Y2)
| ~ big_f(sK0_skl,Y1,sK0_skl,Y2) )
& big_f(sK0_skl,Y2,sK0_skl,sK2_skl(Y2,Y1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X1,sK0_skl),skolemize(X2,sK1_skl),skolemize(Z,sK2_skl(Y2,Y1))],[f6]) ).
fof(f11,plain,
! [X0,X1] : big_f(sK0_skl,X0,sK0_skl,X1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f14,plain,
! [X0,X1] :
( ~ big_f(sK0_skl,X0,X1,X0)
| ~ big_f(sK0_skl,X1,sK0_skl,X0)
| sP0_prd(sK2_skl(X0,X1),X0,X1,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f15,plain,
! [X1,Y1,Y2,Z] :
( ( big_f(X1,Z,Y1,Z)
| ~ big_f(X1,Y2,Y1,Y2)
| sP0_prd(Z,Y2,Y1,X1) )
& ( ( ~ big_f(X1,Z,Y1,Z)
& big_f(X1,Y2,Y1,Y2) )
| ~ sP0_prd(Z,Y2,Y1,X1) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
( ! [X1,Y1,Y2,Z] :
( big_f(X1,Z,Y1,Z)
| ~ big_f(X1,Y2,Y1,Y2)
| sP0_prd(Z,Y2,Y1,X1) )
& ! [X1,Y1,Y2,Z] :
( ( ~ big_f(X1,Z,Y1,Z)
& big_f(X1,Y2,Y1,Y2) )
| ~ sP0_prd(Z,Y2,Y1,X1) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( ~ big_f(X3,X0,X2,X0)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ~ big_f(sK0_skl,X0,X1,X0)
| sP0_prd(sK2_skl(X0,X1),X0,X1,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f14,f11]) ).
fof(f22,plain,
! [X0,X1] :
( ~ big_f(sK0_skl,sK2_skl(X0,X1),X1,sK2_skl(X0,X1))
| ~ big_f(sK0_skl,X0,X1,X0) ),
inference(resolution,[status(thm)],[f21,f18]) ).
fof(f24,plain,
! [X0] : ~ big_f(sK0_skl,X0,sK0_skl,X0),
inference(resolution,[status(thm)],[f22,f11]) ).
fof(f27,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f24,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN351+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.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 10:45:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.37 % Refutation found
% 0.09/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.026680 seconds
% 0.13/0.39 % CPU time: 0.045157 seconds
% 0.13/0.39 % Total memory used: 2.634 MB
% 0.13/0.39 % Net memory used: 2.573 MB
%------------------------------------------------------------------------------