%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN353-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 13
% Syntax : Number of formulae : 72 ( 8 unt; 0 def)
% Number of atoms : 192 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 200 ( 80 ~; 120 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-3 aty)
% Number of variables : 153 ( 153 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [Y1,Y2,Y3] :
( f(Y3,Y1,Y2)
| f(Y2,Y3,Y1)
| ~ f(a,a,z(Y1,Y2,Y3))
| ~ f(Y1,Y2,Y3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [Y3,Y1,Y2] :
( ~ f(Y2,Y1,z(Y1,Y2,Y3))
| f(Y1,Y2,Y3)
| ~ f(Y3,Y1,Y2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [Y3,Y1,Y2] :
( ~ f(Y2,Y1,z(Y1,Y2,Y3))
| f(Y2,Y3,Y1)
| ~ f(Y3,Y1,Y2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [Y3,Y1,Y2] :
( f(Y2,Y1,z(Y1,Y2,Y3))
| f(Y3,Y1,Y2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
! [Y1,Y2,Y3] :
( f(Y2,Y1,z(Y1,Y2,Y3))
| ~ f(Y2,Y3,Y1)
| ~ f(Y1,Y2,Y3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [Y2,Y3,Y1] :
( ~ f(Y1,z(Y1,Y2,Y3),Y2)
| f(Y1,Y2,Y3)
| ~ f(Y2,Y3,Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
! [Y2,Y3,Y1] :
( ~ f(Y1,z(Y1,Y2,Y3),Y2)
| f(Y3,Y1,Y2)
| ~ f(Y2,Y3,Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
! [Y2,Y3,Y1] :
( f(Y1,z(Y1,Y2,Y3),Y2)
| f(Y2,Y3,Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [Y1,Y2,Y3] :
( f(Y1,z(Y1,Y2,Y3),Y2)
| ~ f(Y3,Y1,Y2)
| ~ f(Y1,Y2,Y3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
! [Y3,Y1,Y2] :
( ~ f(z(Y1,Y2,Y3),Y2,Y1)
| f(Y1,Y2,Y3)
| f(Y3,Y1,Y2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
! [Y2,Y3,Y1] :
( ~ f(z(Y1,Y2,Y3),Y2,Y1)
| f(Y1,Y2,Y3)
| f(Y2,Y3,Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
! [Y3,Y1,Y2] :
( f(z(Y1,Y2,Y3),Y2,Y1)
| ~ f(Y2,Y3,Y1)
| ~ f(Y3,Y1,Y2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
! [Y1,Y2,Y3] :
( ~ f(z(Y1,Y2,Y3),z(Y1,Y2,Y3),z(Y1,Y2,Y3))
| ~ f(Y3,Y1,Y2)
| ~ f(Y2,Y3,Y1)
| ~ f(Y1,Y2,Y3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0,X1,X2] :
( f(X2,X0,X1)
| f(X1,X2,X0)
| ~ f(a,a,z(X0,X1,X2))
| ~ f(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ f(X2,X1,z(X1,X2,X0))
| f(X1,X2,X0)
| ~ f(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ f(X2,X1,z(X1,X2,X0))
| f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0,X1,X2] :
( f(X2,X1,z(X1,X2,X0))
| f(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [X0,X1,X2] :
( f(X1,X0,z(X0,X1,X2))
| ~ f(X1,X2,X0)
| ~ f(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ f(X2,z(X2,X0,X1),X0)
| f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ f(X2,z(X2,X0,X1),X0)
| f(X1,X2,X0)
| ~ f(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0,X1,X2] :
( f(X2,z(X2,X0,X1),X0)
| f(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
! [X0,X1,X2] :
( f(X0,z(X0,X1,X2),X1)
| ~ f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ f(z(X1,X2,X0),X2,X1)
| f(X1,X2,X0)
| f(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ f(z(X2,X0,X1),X0,X2)
| f(X2,X0,X1)
| f(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
! [X0,X1,X2] :
( f(z(X1,X2,X0),X2,X1)
| ~ f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ f(z(X0,X1,X2),z(X0,X1,X2),z(X0,X1,X2))
| ~ f(X2,X0,X1)
| ~ f(X1,X2,X0)
| ~ f(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f35,plain,
! [X0] :
( f(X0,a,a)
| f(X0,a,a)
| f(a,X0,a)
| ~ f(a,a,X0) ),
inference(resolution,[status(thm)],[f18,f21]) ).
fof(f36,plain,
! [X0] :
( f(X0,a,a)
| f(a,X0,a)
| ~ f(a,a,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f35]) ).
fof(f51,plain,
! [X0] :
( f(X0,a,a)
| f(z(a,a,X0),a,a)
| f(a,z(a,a,X0),a) ),
inference(resolution,[status(thm)],[f36,f21]) ).
fof(f56,plain,
! [X0] :
( f(a,a,X0)
| f(X0,a,a)
| f(X0,a,a)
| f(a,z(a,a,X0),a) ),
inference(resolution,[status(thm)],[f51,f27]) ).
fof(f57,plain,
! [X0] :
( f(a,a,X0)
| f(X0,a,a)
| f(a,z(a,a,X0),a) ),
inference(duplicate_literals_removal,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0] :
( f(X0,a,a)
| ~ f(a,X0,a)
| f(a,a,X0)
| f(X0,a,a) ),
inference(resolution,[status(thm)],[f57,f24]) ).
fof(f60,plain,
! [X0] :
( ~ f(a,X0,a)
| f(a,a,X0)
| f(X0,a,a) ),
inference(duplicate_literals_removal,[status(thm)],[f58]) ).
fof(f64,plain,
! [X0] :
( f(a,X0,a)
| f(a,a,z(a,a,X0))
| f(z(a,a,X0),a,a) ),
inference(resolution,[status(thm)],[f60,f25]) ).
fof(f65,plain,
! [X0] :
( f(a,a,X0)
| f(a,X0,a)
| f(a,X0,a)
| f(a,a,z(a,a,X0)) ),
inference(resolution,[status(thm)],[f64,f28]) ).
fof(f67,plain,
! [X0] :
( f(a,a,X0)
| f(a,X0,a)
| f(a,a,z(a,a,X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f65]) ).
fof(f70,plain,
! [X0] :
( f(a,X0,a)
| ~ f(X0,a,a)
| f(a,a,X0)
| f(a,X0,a) ),
inference(resolution,[status(thm)],[f67,f20]) ).
fof(f72,plain,
! [X0] :
( ~ f(X0,a,a)
| f(a,a,X0)
| f(a,X0,a) ),
inference(duplicate_literals_removal,[status(thm)],[f70]) ).
fof(f76,plain,
! [X0] :
( ~ f(a,X0,a)
| ~ f(X0,a,a)
| f(a,a,z(a,a,X0))
| f(a,z(a,a,X0),a) ),
inference(resolution,[status(thm)],[f72,f29]) ).
fof(f80,plain,
! [X0] :
( ~ f(X0,a,a)
| f(a,a,z(a,a,X0))
| f(a,z(a,a,X0),a) ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f25]) ).
fof(f81,plain,
! [X0] :
( f(a,a,z(a,a,X0))
| f(a,z(a,a,X0),a) ),
inference(forward_subsumption_resolution,[status(thm)],[f80,f21]) ).
fof(f84,plain,
! [X0] :
( f(a,a,X0)
| ~ f(a,X0,a)
| f(a,a,z(a,a,X0)) ),
inference(resolution,[status(thm)],[f81,f23]) ).
fof(f86,plain,
! [X0] :
( ~ f(a,X0,a)
| f(a,a,z(a,a,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f22]) ).
fof(f92,plain,
! [X0] :
( f(a,a,X0)
| ~ f(X0,a,a)
| ~ f(a,X0,a) ),
inference(resolution,[status(thm)],[f86,f19]) ).
fof(f94,plain,
! [X0] :
( f(a,a,X0)
| ~ f(X0,a,a) ),
inference(forward_subsumption_resolution,[status(thm)],[f92,f72]) ).
fof(f95,plain,
! [X0] :
( ~ f(a,X0,a)
| f(a,a,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f60,f94]) ).
fof(f100,plain,
! [X0] : f(a,a,z(a,a,X0)),
inference(backward_subsumption_resolution,[status(thm)],[f81,f95]) ).
fof(f107,plain,
! [X0] :
( f(a,X0,a)
| ~ f(X0,a,a) ),
inference(resolution,[status(thm)],[f100,f20]) ).
fof(f109,plain,
! [X0] :
( f(X0,a,a)
| f(a,z(a,a,X0),a) ),
inference(backward_subsumption_resolution,[status(thm)],[f51,f107]) ).
fof(f110,plain,
! [X0] :
( f(a,X0,a)
| ~ f(a,a,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f36,f107]) ).
fof(f114,plain,
! [X0] : f(a,z(a,a,X0),a),
inference(resolution,[status(thm)],[f110,f100]) ).
fof(f119,plain,
! [X0] :
( f(X0,a,a)
| ~ f(a,X0,a)
| f(X0,a,a) ),
inference(resolution,[status(thm)],[f109,f24]) ).
fof(f121,plain,
! [X0] :
( ~ f(a,X0,a)
| f(X0,a,a) ),
inference(duplicate_literals_removal,[status(thm)],[f119]) ).
fof(f125,plain,
! [X0] : f(z(a,a,X0),a,a),
inference(resolution,[status(thm)],[f121,f114]) ).
fof(f128,plain,
! [X0] :
( f(a,a,X0)
| f(a,X0,a) ),
inference(resolution,[status(thm)],[f125,f28]) ).
fof(f132,plain,
! [X0] : f(a,a,X0),
inference(forward_subsumption_resolution,[status(thm)],[f128,f95]) ).
fof(f134,plain,
! [X0,X1,X2] :
( f(X2,X0,X1)
| f(X1,X2,X0)
| ~ f(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f18,f132]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ~ f(X0,X2,X1)
| ~ f(X2,X1,X0)
| f(X1,z(X1,X0,X2),X0)
| f(X0,X1,z(X1,X0,X2)) ),
inference(resolution,[status(thm)],[f134,f29]) ).
fof(f161,plain,
! [X0,X1,X2] :
( ~ f(X2,X1,X0)
| f(X1,z(X1,X0,X2),X0)
| f(X0,X1,z(X1,X0,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f25]) ).
fof(f162,plain,
! [X0,X1,X2] :
( f(X1,z(X1,X0,X2),X0)
| f(X0,X1,z(X1,X0,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f21]) ).
fof(f164,plain,
! [X0,X1,X2] :
( f(X0,X1,X2)
| ~ f(X2,X0,X1)
| f(X0,z(X0,X1,X2),X1) ),
inference(resolution,[status(thm)],[f162,f19]) ).
fof(f169,plain,
! [X0,X1,X2] :
( ~ f(X2,X0,X1)
| f(X0,z(X0,X1,X2),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f164,f26]) ).
fof(f174,plain,
! [X0,X1,X2] :
( f(X1,X2,X0)
| ~ f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
inference(resolution,[status(thm)],[f169,f23]) ).
fof(f176,plain,
! [X0,X1,X2] :
( f(X1,X2,X0)
| ~ f(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f174,f134]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ~ f(z(X2,X0,X1),X0,X2)
| f(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f28,f176]) ).
fof(f180,plain,
! [X0,X1,X2] : f(X0,z(X0,X1,X2),X1),
inference(backward_subsumption_resolution,[status(thm)],[f162,f176]) ).
fof(f181,plain,
! [X0,X1,X2] :
( ~ f(z(X0,X1,X2),z(X0,X1,X2),z(X0,X1,X2))
| ~ f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f34,f176]) ).
fof(f186,plain,
! [X0,X1,X2] :
( ~ f(z(X1,X2,X0),z(X1,X2,X0),z(X1,X2,X0))
| ~ f(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f176]) ).
fof(f190,plain,
! [X0,X1,X2] :
( ~ f(X2,z(X2,X0,X1),X0)
| f(X0,X1,X2) ),
inference(resolution,[status(thm)],[f178,f176]) ).
fof(f191,plain,
! [X0,X1,X2] : f(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f190,f180]) ).
fof(f192,plain,
! [X0,X1,X2] : ~ f(z(X0,X1,X2),z(X0,X1,X2),z(X0,X1,X2)),
inference(forward_subsumption_resolution,[status(thm)],[f186,f191]) ).
fof(f193,plain,
$false,
inference(resolution,[status(thm)],[f192,f191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN353-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 10:52:04 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.052464 seconds
% 0.13/0.41 % CPU time: 0.176361 seconds
% 0.13/0.41 % Total memory used: 17.687 MB
% 0.13/0.41 % Net memory used: 17.140 MB
%------------------------------------------------------------------------------