%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:07:28 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C] : ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : ifeq(there_exists(domain(X)),true,there_exists(X),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] : ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] : compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : compose(codomain(X),X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
there_exists(compose(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0,X1,X2] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X0] : ifeq(there_exists(domain(X0)),true,there_exists(X0),true) = true,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0,X1] : ifeq(there_exists(compose(X0,X1)),true,there_exists(domain(X0)),true) = true,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f26,plain,
! [X0,X1] : ifeq2(there_exists(compose(X0,X1)),true,domain(X0),codomain(X1)) = codomain(X1),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
! [X0,X1,X2] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
! [X0] : compose(codomain(X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f31,plain,
there_exists(compose(a,b)) = true,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f32,plain,
codomain(compose(a,b)) != codomain(a),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f39,plain,
! [X0,X1] : compose(codomain(X0),compose(X0,X1)) = compose(X0,X1),
inference(paramodulation,[status(thm)],[f30,f28]) ).
fof(f274,plain,
true = ifeq(true,true,there_exists(domain(a)),true),
inference(paramodulation,[status(thm)],[f31,f25]) ).
fof(f289,plain,
true = there_exists(domain(a)),
inference(forward_demodulation,[status(thm)],[f19,f274]) ).
fof(f296,plain,
! [X0,X1] : codomain(compose(X0,X1)) = ifeq2(there_exists(compose(X0,X1)),true,domain(codomain(X0)),codomain(compose(X0,X1))),
inference(paramodulation,[status(thm)],[f39,f26]) ).
fof(f297,plain,
! [X0] : codomain(X0) = ifeq2(there_exists(X0),true,domain(codomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f30,f26]) ).
fof(f323,plain,
true = ifeq(true,true,there_exists(a),true),
inference(paramodulation,[status(thm)],[f289,f23]) ).
fof(f329,plain,
true = there_exists(a),
inference(forward_demodulation,[status(thm)],[f19,f323]) ).
fof(f606,plain,
codomain(a) = ifeq2(true,true,domain(codomain(a)),codomain(a)),
inference(paramodulation,[status(thm)],[f329,f297]) ).
fof(f617,plain,
codomain(a) = domain(codomain(a)),
inference(forward_demodulation,[status(thm)],[f18,f606]) ).
fof(f1304,plain,
codomain(compose(a,b)) = ifeq2(true,true,domain(codomain(a)),codomain(compose(a,b))),
inference(paramodulation,[status(thm)],[f31,f296]) ).
fof(f1341,plain,
codomain(compose(a,b)) = domain(codomain(a)),
inference(forward_demodulation,[status(thm)],[f18,f1304]) ).
fof(f1342,plain,
codomain(compose(a,b)) = codomain(a),
inference(forward_demodulation,[status(thm)],[f617,f1341]) ).
fof(f1343,plain,
$false,
inference(resolution,[status(thm)],[f1342,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n008.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 13:56:38 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % 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: 0.037401 seconds
% 0.12/0.41 % CPU time: 0.113343 seconds
% 0.12/0.41 % Total memory used: 5.589 MB
% 0.12/0.41 % Net memory used: 5.535 MB
%------------------------------------------------------------------------------