%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:07:25 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.55s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 18 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 74 ( 38 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X,Y] :
( codomain(compose(X,Y)) = codomain(Y)
| codomain(X) != domain(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] :
( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z)
| codomain(Y) != domain(Z)
| codomain(X) != domain(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
! [X,Y,Z] :
( X = Z
| compose(compose(a,b),Z) != Y
| codomain(compose(a,b)) != domain(Z)
| compose(compose(a,b),X) != Y
| codomain(compose(a,b)) != domain(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
codomain(a) = domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
codomain(b) = domain(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
codomain(b) = domain(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
compose(b,h) = compose(b,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
g != h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0,X1] :
( codomain(compose(X0,X1)) = codomain(X1)
| codomain(X0) != domain(X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f20,plain,
! [X0,X1,X2] :
( compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2)
| codomain(X1) != domain(X2)
| codomain(X0) != domain(X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f21,plain,
! [X,Z] :
( X = Z
| ! [Y] :
( compose(compose(a,b),Z) != Y
| codomain(compose(a,b)) != domain(Z)
| compose(compose(a,b),X) != Y
| codomain(compose(a,b)) != domain(X) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f22,plain,
! [X0,X1,X2] :
( X0 = X2
| compose(compose(a,b),X2) != X1
| codomain(compose(a,b)) != domain(X2)
| compose(compose(a,b),X0) != X1
| codomain(compose(a,b)) != domain(X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
codomain(a) = domain(b),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
codomain(b) = domain(h),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
codomain(b) = domain(g),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f26,plain,
compose(b,h) = compose(b,g),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
g != h,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f28,plain,
! [X0,X1] :
( X0 = X1
| compose(compose(a,b),X1) != compose(compose(a,b),X0)
| codomain(compose(a,b)) != domain(X1)
| codomain(compose(a,b)) != domain(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f22]) ).
fof(f29,plain,
domain(h) = domain(g),
inference(forward_demodulation,[status(thm)],[f24,f25]) ).
fof(f90,plain,
codomain(compose(a,b)) = codomain(b),
inference(resolution,[status(thm)],[f19,f23]) ).
fof(f100,plain,
! [X0,X1] :
( X0 = X1
| compose(compose(a,b),X1) != compose(compose(a,b),X0)
| domain(h) != domain(X1)
| codomain(compose(a,b)) != domain(X0) ),
inference(backward_demodulation,[status(thm)],[f101,f28]) ).
fof(f101,plain,
codomain(compose(a,b)) = domain(h),
inference(forward_demodulation,[status(thm)],[f24,f90]) ).
fof(f105,plain,
! [X0,X1] :
( X0 = X1
| compose(compose(a,b),X1) != compose(compose(a,b),X0)
| domain(h) != domain(X1)
| domain(h) != domain(X0) ),
inference(forward_demodulation,[status(thm)],[f101,f100]) ).
fof(f108,plain,
! [X0] :
( compose(X0,compose(b,h)) = compose(compose(X0,b),h)
| codomain(X0) != domain(b) ),
inference(resolution,[status(thm)],[f20,f24]) ).
fof(f113,plain,
! [X0,X1] :
( compose(X0,compose(b,X1)) = compose(compose(X0,b),X1)
| domain(h) != domain(X1)
| codomain(X0) != domain(b) ),
inference(paramodulation,[status(thm)],[f24,f20]) ).
fof(f151,plain,
! [X0] :
( X0 = g
| compose(compose(a,b),g) != compose(compose(a,b),X0)
| domain(h) != domain(X0) ),
inference(resolution,[status(thm)],[f105,f29]) ).
fof(f224,plain,
compose(a,compose(b,h)) = compose(compose(a,b),h),
inference(resolution,[status(thm)],[f108,f23]) ).
fof(f477,plain,
! [X0] :
( compose(a,compose(b,X0)) = compose(compose(a,b),X0)
| domain(h) != domain(X0) ),
inference(resolution,[status(thm)],[f113,f23]) ).
fof(f3493,plain,
compose(a,compose(b,g)) = compose(compose(a,b),g),
inference(resolution,[status(thm)],[f477,f29]) ).
fof(f3506,plain,
! [X0] :
( X0 = g
| compose(a,compose(b,h)) != compose(compose(a,b),X0)
| domain(h) != domain(X0) ),
inference(backward_demodulation,[status(thm)],[f3574,f151]) ).
fof(f3574,plain,
compose(a,compose(b,h)) = compose(compose(a,b),g),
inference(forward_demodulation,[status(thm)],[f26,f3493]) ).
fof(f3620,plain,
( h = g
| domain(h) != domain(h) ),
inference(resolution,[status(thm)],[f3506,f224]) ).
fof(f3624,plain,
h = g,
inference(trivial_equality_resolution,[status(thm)],[f3620]) ).
fof(f3625,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3624,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n017.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 13:50:43 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.13/0.55 % Refutation found
% 0.13/0.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.58 % Elapsed time: 0.233647 seconds
% 0.13/0.58 % CPU time: 1.632824 seconds
% 0.13/0.58 % Total memory used: 96.942 MB
% 0.13/0.58 % Net memory used: 95.132 MB
%------------------------------------------------------------------------------