%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN349+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 : n003.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 03:15:50 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 2
% Syntax : Number of formulae : 42 ( 6 unt; 1 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 158 ( 46 ~; 75 |; 18 &)
% ( 15 <=>; 2 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% Number of variables : 85 ( 75 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X1] :
! [X2] :
? [X3] :
! [X4] :
( ( big_f(X1,X4)
<=> big_f(X2,X4) )
=> ( ( ( big_f(X1,X4)
<=> big_f(X4,X3) )
<=> big_f(X3,X4) )
<=> big_f(X4,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ? [X1] :
! [X2] :
? [X3] :
! [X4] :
( ( big_f(X1,X4)
<=> big_f(X2,X4) )
=> ( ( ( big_f(X1,X4)
<=> big_f(X4,X3) )
<=> big_f(X3,X4) )
<=> big_f(X4,X2) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X1] :
? [X2] :
! [X3] :
? [X4] :
( ( ( ( big_f(X1,X4)
<=> big_f(X4,X3) )
<=> big_f(X3,X4) )
<~> big_f(X4,X2) )
& ( big_f(X1,X4)
<=> big_f(X2,X4) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X1,X3,X4] :
( sP0_prd(X4,X3,X1)
<=> ( big_f(X1,X4)
<=> big_f(X4,X3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
! [X1] :
? [X2] :
! [X3] :
? [X4] :
( ( ( sP0_prd(X4,X3,X1)
<=> big_f(X3,X4) )
<~> big_f(X4,X2) )
& ( big_f(X1,X4)
<=> big_f(X2,X4) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
! [X1] :
? [X2] :
! [X3] :
? [X4] :
( ( ~ big_f(X4,X2)
| ( ( big_f(X3,X4)
| sP0_prd(X4,X3,X1) )
& ( ~ big_f(X3,X4)
| ~ sP0_prd(X4,X3,X1) ) ) )
& ( big_f(X4,X2)
| ( ( ~ big_f(X3,X4)
| sP0_prd(X4,X3,X1) )
& ( big_f(X3,X4)
| ~ sP0_prd(X4,X3,X1) ) ) )
& ( ~ big_f(X2,X4)
| big_f(X1,X4) )
& ( big_f(X2,X4)
| ~ big_f(X1,X4) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [X1,X3] :
( ( ~ big_f(sK1_skl(X3,X1),sK0_skl(X1))
| ( ( big_f(X3,sK1_skl(X3,X1))
| sP0_prd(sK1_skl(X3,X1),X3,X1) )
& ( ~ big_f(X3,sK1_skl(X3,X1))
| ~ sP0_prd(sK1_skl(X3,X1),X3,X1) ) ) )
& ( big_f(sK1_skl(X3,X1),sK0_skl(X1))
| ( ( ~ big_f(X3,sK1_skl(X3,X1))
| sP0_prd(sK1_skl(X3,X1),X3,X1) )
& ( big_f(X3,sK1_skl(X3,X1))
| ~ sP0_prd(sK1_skl(X3,X1),X3,X1) ) ) )
& ( ~ big_f(sK0_skl(X1),sK1_skl(X3,X1))
| big_f(X1,sK1_skl(X3,X1)) )
& ( big_f(sK0_skl(X1),sK1_skl(X3,X1))
| ~ big_f(X1,sK1_skl(X3,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X2,sK0_skl(X1)),skolemize(X4,sK1_skl(X3,X1))],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( big_f(sK0_skl(X0),sK1_skl(X1,X0))
| ~ big_f(X0,sK1_skl(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( ~ big_f(sK0_skl(X0),sK1_skl(X1,X0))
| big_f(X0,sK1_skl(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( big_f(sK1_skl(X0,X1),sK0_skl(X1))
| big_f(X0,sK1_skl(X0,X1))
| ~ sP0_prd(sK1_skl(X0,X1),X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [X0,X1] :
( big_f(sK1_skl(X0,X1),sK0_skl(X1))
| ~ big_f(X0,sK1_skl(X0,X1))
| sP0_prd(sK1_skl(X0,X1),X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( ~ big_f(sK1_skl(X0,X1),sK0_skl(X1))
| ~ big_f(X0,sK1_skl(X0,X1))
| ~ sP0_prd(sK1_skl(X0,X1),X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f13,plain,
! [X0,X1] :
( ~ big_f(sK1_skl(X0,X1),sK0_skl(X1))
| big_f(X0,sK1_skl(X0,X1))
| sP0_prd(sK1_skl(X0,X1),X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f14,plain,
! [X1,X3,X4] :
( ( ( ( big_f(X4,X3)
| big_f(X1,X4) )
& ( ~ big_f(X4,X3)
| ~ big_f(X1,X4) ) )
| sP0_prd(X4,X3,X1) )
& ( ( ( ~ big_f(X4,X3)
| big_f(X1,X4) )
& ( big_f(X4,X3)
| ~ big_f(X1,X4) ) )
| ~ sP0_prd(X4,X3,X1) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f15,plain,
( ! [X1,X3,X4] :
( ( ( big_f(X4,X3)
| big_f(X1,X4) )
& ( ~ big_f(X4,X3)
| ~ big_f(X1,X4) ) )
| sP0_prd(X4,X3,X1) )
& ! [X1,X3,X4] :
( ( ( ~ big_f(X4,X3)
| big_f(X1,X4) )
& ( big_f(X4,X3)
| ~ big_f(X1,X4) ) )
| ~ sP0_prd(X4,X3,X1) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( big_f(X0,X1)
| ~ big_f(X2,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ big_f(X0,X1)
| big_f(X2,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ big_f(X0,X1)
| ~ big_f(X2,X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
! [X0,X1,X2] :
( big_f(X0,X1)
| big_f(X2,X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f20,plain,
! [X0,X1] :
( big_f(sK1_skl(X0,X1),X0)
| big_f(X1,sK1_skl(X0,X1))
| big_f(sK1_skl(X0,X1),sK0_skl(X1))
| big_f(X0,sK1_skl(X0,X1)) ),
inference(resolution,[status(thm)],[f10,f19]) ).
fof(f21,plain,
! [X0] :
( big_f(sK0_skl(X0),sK1_skl(sK0_skl(X0),X0))
| sP0_prd(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0),X0)
| big_f(X0,sK1_skl(sK0_skl(X0),X0))
| big_f(sK0_skl(X0),sK1_skl(sK0_skl(X0),X0)) ),
inference(resolution,[status(thm)],[f20,f13]) ).
fof(f27,plain,
! [X0,X1] :
( big_f(X1,sK1_skl(sK0_skl(X0),X0))
| ~ sP0_prd(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0),X1)
| big_f(X0,sK1_skl(sK0_skl(X0),X0))
| big_f(sK0_skl(X0),sK1_skl(sK0_skl(X0),X0)) ),
inference(resolution,[status(thm)],[f20,f17]) ).
fof(f36,plain,
! [X0] :
( sP0_prd(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0),X0)
| big_f(X0,sK1_skl(sK0_skl(X0),X0))
| big_f(sK0_skl(X0),sK1_skl(sK0_skl(X0),X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f21]) ).
fof(f37,plain,
! [X0] :
( sP0_prd(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0),X0)
| big_f(X0,sK1_skl(sK0_skl(X0),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f36,f9]) ).
fof(f40,plain,
! [X0,X1] :
( big_f(X1,sK1_skl(sK0_skl(X0),X0))
| ~ sP0_prd(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0),X1)
| big_f(X0,sK1_skl(sK0_skl(X0),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f27,f9]) ).
fof(f43,plain,
! [X0] :
( big_f(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0))
| big_f(sK0_skl(X0),sK1_skl(sK0_skl(X0),X0))
| big_f(X0,sK1_skl(sK0_skl(X0),X0)) ),
inference(resolution,[status(thm)],[f37,f10]) ).
fof(f44,plain,
! [X0] :
( big_f(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0))
| big_f(sK0_skl(X0),sK1_skl(sK0_skl(X0),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f8]) ).
fof(f45,plain,
! [X0] :
( big_f(sK0_skl(X0),sK1_skl(sK0_skl(X0),X0))
| sP0_prd(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0),X0)
| big_f(sK0_skl(X0),sK1_skl(sK0_skl(X0),X0)) ),
inference(resolution,[status(thm)],[f44,f13]) ).
fof(f50,plain,
! [X0] :
( sP0_prd(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0),X0)
| big_f(sK0_skl(X0),sK1_skl(sK0_skl(X0),X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f45]) ).
fof(f83,plain,
! [X0] :
( big_f(sK0_skl(X0),sK1_skl(sK0_skl(X0),X0))
| big_f(X0,sK1_skl(sK0_skl(X0),X0))
| big_f(X0,sK1_skl(sK0_skl(X0),X0)) ),
inference(resolution,[status(thm)],[f40,f50]) ).
fof(f84,plain,
! [X0] :
( big_f(X0,sK1_skl(sK0_skl(X0),X0))
| big_f(X0,sK1_skl(sK0_skl(X0),X0))
| big_f(X0,sK1_skl(sK0_skl(X0),X0)) ),
inference(resolution,[status(thm)],[f40,f37]) ).
fof(f86,plain,
! [X0] :
( big_f(sK0_skl(X0),sK1_skl(sK0_skl(X0),X0))
| big_f(X0,sK1_skl(sK0_skl(X0),X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f83]) ).
fof(f87,plain,
! [X0] : big_f(sK0_skl(X0),sK1_skl(sK0_skl(X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[f86,f8]) ).
fof(f88,plain,
! [X0] : big_f(X0,sK1_skl(sK0_skl(X0),X0)),
inference(duplicate_literals_removal,[status(thm)],[f84]) ).
fof(f103,plain,
! [X0,X1] :
( ~ big_f(sK1_skl(sK0_skl(X0),X0),X1)
| sP0_prd(sK1_skl(sK0_skl(X0),X0),X1,X0) ),
inference(resolution,[status(thm)],[f88,f18]) ).
fof(f105,plain,
! [X0,X1] :
( big_f(sK1_skl(sK0_skl(X0),X0),X1)
| ~ sP0_prd(sK1_skl(sK0_skl(X0),X0),X1,X0) ),
inference(resolution,[status(thm)],[f88,f16]) ).
fof(f108,plain,
! [X0] :
( big_f(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0))
| sP0_prd(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0),X0) ),
inference(resolution,[status(thm)],[f87,f11]) ).
fof(f139,plain,
! [X0] : big_f(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f108,f105]) ).
fof(f140,plain,
! [X0] : sP0_prd(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0),X0),
inference(resolution,[status(thm)],[f139,f103]) ).
fof(f142,plain,
! [X0] :
( ~ big_f(sK0_skl(X0),sK1_skl(sK0_skl(X0),X0))
| ~ sP0_prd(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0),X0) ),
inference(resolution,[status(thm)],[f139,f12]) ).
fof(f147,plain,
! [X0] : ~ sP0_prd(sK1_skl(sK0_skl(X0),X0),sK0_skl(X0),X0),
inference(forward_subsumption_resolution,[status(thm)],[f142,f87]) ).
fof(f154,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f147,f140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN349+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n003.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 10:52:32 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.044932 seconds
% 0.13/0.40 % CPU time: 0.166767 seconds
% 0.13/0.40 % Total memory used: 17.781 MB
% 0.13/0.40 % Net memory used: 17.225 MB
%------------------------------------------------------------------------------