%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN077+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 : n010.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 03:15:09 PM UTC 2026
% Result : Theorem 0.10s 5.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of formulae : 41 ( 6 unt; 0 def)
% Number of atoms : 132 ( 10 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 148 ( 57 ~; 65 |; 20 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 74 ( 55 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Y] :
? [Z] :
! [X] :
( big_f(X,Z)
<=> X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,conjecture,
~ ? [W] :
! [X] :
( big_f(X,W)
<=> ! [U] :
( big_f(X,U)
=> ? [Y] :
( ~ ? [Z] :
( big_f(Z,Y)
& big_f(Z,U) )
& big_f(Y,U) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ ~ ? [W] :
! [X] :
( big_f(X,W)
<=> ! [U] :
( big_f(X,U)
=> ? [Y] :
( ~ ? [Z] :
( big_f(Z,Y)
& big_f(Z,U) )
& big_f(Y,U) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
! [Y] :
? [Z] :
! [X] :
( ( X != Y
| big_f(X,Z) )
& ( X = Y
| ~ big_f(X,Z) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [Y] :
? [Z] :
( ! [X] :
( X != Y
| big_f(X,Z) )
& ! [X] :
( X = Y
| ~ big_f(X,Z) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
! [Y] :
( ! [X] :
( X != Y
| big_f(X,sK0_skl(Y)) )
& ! [X] :
( X = Y
| ~ big_f(X,sK0_skl(Y)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Z,sK0_skl(Y))],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( X0 = X1
| ~ big_f(X0,sK0_skl(X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( X0 != X1
| big_f(X0,sK0_skl(X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
? [W] :
! [X] :
( big_f(X,W)
<=> ! [U] :
( ? [Y] :
( ! [Z] :
( ~ big_f(Z,Y)
| ~ big_f(Z,U) )
& big_f(Y,U) )
| ~ big_f(X,U) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
? [W] :
! [X] :
( ( ? [U] :
( ! [Y] :
( ? [Z] :
( big_f(Z,Y)
& big_f(Z,U) )
| ~ big_f(Y,U) )
& big_f(X,U) )
| big_f(X,W) )
& ( ! [U] :
( ? [Y] :
( ! [Z] :
( ~ big_f(Z,Y)
| ~ big_f(Z,U) )
& big_f(Y,U) )
| ~ big_f(X,U) )
| ~ big_f(X,W) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
? [W] :
( ! [X] :
( ? [U] :
( ! [Y] :
( ? [Z] :
( big_f(Z,Y)
& big_f(Z,U) )
| ~ big_f(Y,U) )
& big_f(X,U) )
| big_f(X,W) )
& ! [X] :
( ! [U] :
( ? [Y] :
( ! [Z] :
( ~ big_f(Z,Y)
| ~ big_f(Z,U) )
& big_f(Y,U) )
| ~ big_f(X,U) )
| ~ big_f(X,W) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f12,plain,
( ! [X] :
( ( ! [Y] :
( ( big_f(sK4_skl(Y,X),Y)
& big_f(sK4_skl(Y,X),sK3_skl(X)) )
| ~ big_f(Y,sK3_skl(X)) )
& big_f(X,sK3_skl(X)) )
| big_f(X,sK1_skl) )
& ! [X] :
( ! [U] :
( ( ! [Z] :
( ~ big_f(Z,sK2_skl(U,X))
| ~ big_f(Z,U) )
& big_f(sK2_skl(U,X),U) )
| ~ big_f(X,U) )
| ~ big_f(X,sK1_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(W,sK1_skl),skolemize(Y,sK2_skl(U,X)),skolemize(U,sK3_skl(X)),skolemize(Z,sK4_skl(Y,X))],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( big_f(sK2_skl(X1,X0),X1)
| ~ big_f(X0,X1)
| ~ big_f(X0,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ big_f(X2,sK2_skl(X1,X0))
| ~ big_f(X2,X1)
| ~ big_f(X0,X1)
| ~ big_f(X0,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f15,plain,
! [X0] :
( big_f(X0,sK3_skl(X0))
| big_f(X0,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,plain,
! [X0,X1] :
( big_f(sK4_skl(X1,X0),sK3_skl(X0))
| ~ big_f(X1,sK3_skl(X0))
| big_f(X0,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f17,plain,
! [X0,X1] :
( big_f(sK4_skl(X1,X0),X1)
| ~ big_f(X1,sK3_skl(X0))
| big_f(X0,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f18,plain,
! [X0] : big_f(X0,sK0_skl(X0)),
inference(destructive_equality_resolution,[status(thm)],[f8]) ).
fof(f19,plain,
! [X0] :
( big_f(X0,sK1_skl)
| big_f(sK4_skl(X0,X0),X0)
| big_f(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f17,f15]) ).
fof(f20,plain,
! [X0] :
( big_f(sK4_skl(X0,X0),X0)
| big_f(X0,sK1_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f19]) ).
fof(f22,plain,
! [X0] :
( big_f(sK2_skl(X0,sK4_skl(sK1_skl,sK1_skl)),X0)
| ~ big_f(sK4_skl(sK1_skl,sK1_skl),X0)
| big_f(sK1_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f20,f13]) ).
fof(f25,plain,
! [X0] :
( big_f(X0,sK1_skl)
| big_f(sK4_skl(X0,X0),sK3_skl(X0))
| big_f(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f16,f15]) ).
fof(f26,plain,
! [X0] :
( big_f(sK4_skl(X0,X0),sK3_skl(X0))
| big_f(X0,sK1_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f25]) ).
fof(f47,plain,
( big_f(sK1_skl,sK1_skl)
| big_f(sK2_skl(sK3_skl(sK1_skl),sK4_skl(sK1_skl,sK1_skl)),sK3_skl(sK1_skl))
| big_f(sK1_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f22,f26]) ).
fof(f50,plain,
( big_f(sK2_skl(sK3_skl(sK1_skl),sK4_skl(sK1_skl,sK1_skl)),sK3_skl(sK1_skl))
| big_f(sK1_skl,sK1_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f47]) ).
fof(f53,plain,
( big_f(sK4_skl(sK2_skl(sK3_skl(sK1_skl),sK4_skl(sK1_skl,sK1_skl)),sK1_skl),sK3_skl(sK1_skl))
| big_f(sK1_skl,sK1_skl)
| big_f(sK1_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f50,f16]) ).
fof(f54,plain,
( big_f(sK4_skl(sK2_skl(sK3_skl(sK1_skl),sK4_skl(sK1_skl,sK1_skl)),sK1_skl),sK2_skl(sK3_skl(sK1_skl),sK4_skl(sK1_skl,sK1_skl)))
| big_f(sK1_skl,sK1_skl)
| big_f(sK1_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f50,f17]) ).
fof(f55,plain,
( big_f(sK4_skl(sK2_skl(sK3_skl(sK1_skl),sK4_skl(sK1_skl,sK1_skl)),sK1_skl),sK3_skl(sK1_skl))
| big_f(sK1_skl,sK1_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f53]) ).
fof(f56,plain,
( big_f(sK4_skl(sK2_skl(sK3_skl(sK1_skl),sK4_skl(sK1_skl,sK1_skl)),sK1_skl),sK2_skl(sK3_skl(sK1_skl),sK4_skl(sK1_skl,sK1_skl)))
| big_f(sK1_skl,sK1_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f54]) ).
fof(f117,plain,
( ~ big_f(sK4_skl(sK2_skl(sK3_skl(sK1_skl),sK4_skl(sK1_skl,sK1_skl)),sK1_skl),sK3_skl(sK1_skl))
| ~ big_f(sK4_skl(sK1_skl,sK1_skl),sK3_skl(sK1_skl))
| ~ big_f(sK4_skl(sK1_skl,sK1_skl),sK1_skl)
| big_f(sK1_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f56,f14]) ).
fof(f118,plain,
( ~ big_f(sK4_skl(sK2_skl(sK3_skl(sK1_skl),sK4_skl(sK1_skl,sK1_skl)),sK1_skl),sK3_skl(sK1_skl))
| ~ big_f(sK4_skl(sK1_skl,sK1_skl),sK3_skl(sK1_skl))
| big_f(sK1_skl,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f117,f20]) ).
fof(f167,plain,
big_f(sK1_skl,sK1_skl),
inference(backward_subsumption_resolution,[status(thm)],[f55,f168]) ).
fof(f168,plain,
( ~ big_f(sK4_skl(sK2_skl(sK3_skl(sK1_skl),sK4_skl(sK1_skl,sK1_skl)),sK1_skl),sK3_skl(sK1_skl))
| big_f(sK1_skl,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f26]) ).
fof(f170,plain,
! [X0] :
( big_f(sK2_skl(X0,sK1_skl),X0)
| ~ big_f(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f167,f13]) ).
fof(f172,plain,
big_f(sK2_skl(sK0_skl(sK1_skl),sK1_skl),sK0_skl(sK1_skl)),
inference(resolution,[status(thm)],[f170,f18]) ).
fof(f175,plain,
sK2_skl(sK0_skl(sK1_skl),sK1_skl) = sK1_skl,
inference(resolution,[status(thm)],[f172,f7]) ).
fof(f180,plain,
! [X0] :
( ~ big_f(X0,sK1_skl)
| ~ big_f(X0,sK0_skl(sK1_skl))
| ~ big_f(sK1_skl,sK0_skl(sK1_skl))
| ~ big_f(sK1_skl,sK1_skl) ),
inference(paramodulation,[status(thm)],[f175,f14]) ).
fof(f183,plain,
! [X0] :
( ~ big_f(X0,sK1_skl)
| ~ big_f(X0,sK0_skl(sK1_skl))
| ~ big_f(sK1_skl,sK0_skl(sK1_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f180,f167]) ).
fof(f184,plain,
! [X0] :
( ~ big_f(X0,sK1_skl)
| ~ big_f(X0,sK0_skl(sK1_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f183,f18]) ).
fof(f186,plain,
~ big_f(sK1_skl,sK1_skl),
inference(resolution,[status(thm)],[f184,f18]) ).
fof(f187,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f186,f167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN077+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n010.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 10:42:34 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.10/5.40 % Refutation found
% 0.10/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.42 % Elapsed time: 0.045838 seconds
% 0.13/5.42 % CPU time: 0.154557 seconds
% 0.13/5.42 % Total memory used: 58.612 MB
% 0.13/5.42 % Net memory used: 58.143 MB
%------------------------------------------------------------------------------