%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN075-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 5 unt; 0 def)
% Number of atoms : 75 ( 47 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 84 ( 41 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( X = a
| ~ big_f(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( big_f(X,Y)
| Y != b
| X != a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [Y,X] :
( f(X) = X
| Y != g(X)
| ~ big_f(Y,f(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [Y,X] :
( f(X) = X
| big_f(Y,f(X))
| Y != g(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [X,Z] :
( h(X,Z) = Z
| big_f(h(X,Z),f(X))
| f(X) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
! [X,Z] :
( ~ big_f(h(X,Z),f(X))
| h(X,Z) != Z
| f(X) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X] :
( X = a
| ! [Y] : ~ big_f(X,Y) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1] :
( X0 = a
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( big_f(X0,X1)
| X1 != b
| X0 != a ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [X] :
( f(X) = X
| ! [Y] :
( Y != g(X)
| ~ big_f(Y,f(X)) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f17,plain,
! [X0,X1] :
( f(X1) = X1
| X0 != g(X1)
| ~ big_f(X0,f(X1)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,plain,
! [X] :
( f(X) = X
| ! [Y] :
( big_f(Y,f(X))
| Y != g(X) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0,X1] :
( f(X1) = X1
| big_f(X0,f(X1))
| X0 != g(X1) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f26,plain,
! [X0,X1] :
( h(X0,X1) = X1
| big_f(h(X0,X1),f(X0))
| f(X0) != X0 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f27,plain,
! [X0,X1] :
( ~ big_f(h(X0,X1),f(X0))
| h(X0,X1) != X1
| f(X0) != X0 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
big_f(a,b),
inference(destructive_equality_resolution,[status(thm)],[f15]) ).
fof(f29,plain,
! [X0] :
( f(X0) = X0
| ~ big_f(g(X0),f(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f17]) ).
fof(f30,plain,
! [X0] :
( f(X0) = X0
| big_f(g(X0),f(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f21]) ).
fof(f34,plain,
! [X0] : f(X0) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f30,f29]) ).
fof(f35,plain,
! [X0,X1] :
( h(X0,X1) = X1
| big_f(h(X0,X1),f(X0))
| X0 != X0 ),
inference(forward_demodulation,[status(thm)],[f34,f26]) ).
fof(f36,plain,
! [X0,X1] :
( h(X0,X1) = X1
| big_f(h(X0,X1),X0)
| X0 != X0 ),
inference(forward_demodulation,[status(thm)],[f34,f35]) ).
fof(f37,plain,
! [X0,X1] :
( h(X0,X1) = X1
| big_f(h(X0,X1),X0) ),
inference(trivial_equality_resolution,[status(thm)],[f36]) ).
fof(f40,plain,
! [X0,X1] :
( ~ big_f(h(X0,X1),f(X0))
| h(X0,X1) != X1
| X0 != X0 ),
inference(forward_demodulation,[status(thm)],[f34,f27]) ).
fof(f41,plain,
! [X0,X1] :
( ~ big_f(h(X0,X1),X0)
| h(X0,X1) != X1
| X0 != X0 ),
inference(forward_demodulation,[status(thm)],[f34,f40]) ).
fof(f42,plain,
! [X0,X1] :
( ~ big_f(h(X0,X1),X0)
| h(X0,X1) != X1 ),
inference(trivial_equality_resolution,[status(thm)],[f41]) ).
fof(f47,plain,
! [X0,X1] :
( h(X0,X1) = X1
| h(X0,X1) = a ),
inference(resolution,[status(thm)],[f12,f37]) ).
fof(f50,plain,
! [X0,X1] :
( h(X1,X0) = X0
| a != X0 ),
inference(equality_factoring,[status(thm)],[f47]) ).
fof(f52,plain,
! [X0] : h(X0,a) = a,
inference(destructive_equality_resolution,[status(thm)],[f50]) ).
fof(f55,plain,
! [X0] :
( ~ big_f(a,X0)
| h(X0,a) != a ),
inference(paramodulation,[status(thm)],[f52,f42]) ).
fof(f65,plain,
! [X0] :
( ~ big_f(a,X0)
| a != a ),
inference(forward_demodulation,[status(thm)],[f52,f55]) ).
fof(f66,plain,
! [X0] : ~ big_f(a,X0),
inference(trivial_equality_resolution,[status(thm)],[f65]) ).
fof(f73,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f28,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN075-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 10:42:13 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.056885 seconds
% 0.12/0.41 % CPU time: 0.153347 seconds
% 0.12/0.41 % Total memory used: 79.913 MB
% 0.12/0.41 % Net memory used: 79.444 MB
%------------------------------------------------------------------------------