%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP772-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 12:35:18 PM UTC 2026
% Result : Unsatisfiable 228.74s 29.37s
% Output : CNFRefutation 228.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 60 ( 60 unt; 0 def)
% Number of atoms : 60 ( 59 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 132 ( 132 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : product(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] : product(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : product(A,difference(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : difference(A,product(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] : quotient(product(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] : product(quotient(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : i(A) = difference(A,one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : j(A) = quotient(one,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,B] : t(A,B) = quotient(product(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B,C,D,E] : product(a(A,B,C),product(D,E)) = product(product(a(A,B,C),D),E),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A,B,C] : product(a(A,B,C),difference(C,product(a(C,A,B),C))) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B,C] : a(A,i(B),C) = a(A,j(B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A,B,C] : a(j(A),B,C) = a(B,C,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
a(x0,x1,x1) != a(x1,x1,x0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,plain,
! [X0] : product(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f35,plain,
! [X0] : product(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f36,plain,
! [X0,X1] : product(X0,difference(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f37,plain,
! [X0,X1] : difference(X0,product(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f38,plain,
! [X0,X1] : quotient(product(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f39,plain,
! [X0,X1] : product(quotient(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f42,plain,
! [X0] : i(X0) = difference(X0,one),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f43,plain,
! [X0] : j(X0) = quotient(one,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f52,plain,
! [X0,X1] : t(X0,X1) = quotient(product(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f60,plain,
! [X0,X1,X2,X3,X4] : product(a(X0,X1,X2),product(X3,X4)) = product(product(a(X0,X1,X2),X3),X4),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
! [X0,X1,X2] : product(a(X0,X1,X2),difference(X2,product(a(X2,X0,X1),X2))) = one,
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f63,plain,
! [X0,X1,X2] : a(X0,i(X1),X2) = a(X0,j(X1),X2),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
! [X0,X1,X2] : a(j(X0),X1,X2) = a(X1,X2,X0),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f66,plain,
a(x0,x1,x1) != a(x1,x1,x0),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f75,plain,
! [X0] : quotient(X0,one) = X0,
inference(paramodulation,[status(thm)],[f34,f38]) ).
fof(f80,plain,
! [X0,X1] : quotient(X0,difference(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f36,f38]) ).
fof(f89,plain,
! [X0,X1] : t(X0,difference(X0,X1)) = quotient(X1,X0),
inference(paramodulation,[status(thm)],[f36,f52]) ).
fof(f107,plain,
! [X0,X1,X2] : a(j(X0),i(X1),X2) = a(j(X1),X2,X0),
inference(paramodulation,[status(thm)],[f65,f63]) ).
fof(f109,plain,
! [X0,X1,X2] : a(i(X0),X1,X2) = a(j(X0),X1,X2),
inference(forward_demodulation,[status(thm)],[f65,f107]) ).
fof(f110,plain,
! [X0,X1,X2] : a(i(X0),X1,X2) = a(X1,X2,X0),
inference(forward_demodulation,[status(thm)],[f65,f109]) ).
fof(f314,plain,
! [X0] : product(X0,i(X0)) = one,
inference(paramodulation,[status(thm)],[f42,f36]) ).
fof(f346,plain,
! [X0] : product(j(X0),X0) = one,
inference(paramodulation,[status(thm)],[f43,f39]) ).
fof(f358,plain,
! [X0] : difference(j(X0),one) = X0,
inference(paramodulation,[status(thm)],[f346,f37]) ).
fof(f371,plain,
! [X0] : i(j(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f42,f358]) ).
fof(f374,plain,
! [X0,X1,X2] : a(X0,X1,X2) = a(X1,X2,j(X0)),
inference(paramodulation,[status(thm)],[f371,f110]) ).
fof(f381,plain,
! [X0,X1,X2] : a(X0,X1,j(X2)) = a(X1,i(X2),j(X0)),
inference(paramodulation,[status(thm)],[f63,f374]) ).
fof(f390,plain,
! [X0,X1,X2] : a(X0,X1,X2) = a(X2,i(X0),j(X1)),
inference(forward_demodulation,[status(thm)],[f374,f381]) ).
fof(f391,plain,
! [X0,X1,X2] : a(X0,X1,X2) = a(X1,X2,i(X0)),
inference(forward_demodulation,[status(thm)],[f374,f390]) ).
fof(f398,plain,
! [X0,X1,X2] : a(X0,j(X1),X2) = a(X2,i(X0),X1),
inference(paramodulation,[status(thm)],[f65,f391]) ).
fof(f2894,plain,
! [X0,X1,X2,X3] : product(a(X0,X1,X2),product(i(a(X0,X1,X2)),X3)) = product(one,X3),
inference(paramodulation,[status(thm)],[f314,f60]) ).
fof(f2976,plain,
! [X0,X1,X2,X3] : product(a(X0,X1,X2),product(i(a(X0,X1,X2)),X3)) = X3,
inference(forward_demodulation,[status(thm)],[f35,f2894]) ).
fof(f4521,plain,
! [X0,X1,X2,X3] : product(a(X0,X1,X2),X3) = difference(i(a(X0,X1,X2)),X3),
inference(paramodulation,[status(thm)],[f36,f2976]) ).
fof(f6561,plain,
! [X0,X1,X2,X3] : quotient(X0,product(a(X1,X2,X3),X0)) = i(a(X1,X2,X3)),
inference(paramodulation,[status(thm)],[f4521,f80]) ).
fof(f8266,plain,
! [X0,X1,X2] : quotient(difference(X0,product(a(X0,X1,X2),X0)),one) = i(a(X1,X2,X0)),
inference(paramodulation,[status(thm)],[f62,f6561]) ).
fof(f8321,plain,
! [X0,X1,X2] : difference(X0,product(a(X0,X1,X2),X0)) = i(a(X1,X2,X0)),
inference(forward_demodulation,[status(thm)],[f75,f8266]) ).
fof(f10478,plain,
! [X0,X1,X2] : t(X0,i(a(X1,X2,X0))) = quotient(product(a(X0,X1,X2),X0),X0),
inference(paramodulation,[status(thm)],[f8321,f89]) ).
fof(f10598,plain,
! [X0,X1,X2] : t(X0,i(a(X1,X2,X0))) = a(X0,X1,X2),
inference(forward_demodulation,[status(thm)],[f38,f10478]) ).
fof(f10611,plain,
! [X0,X1,X2] : t(X0,i(a(X1,X0,X2))) = a(X0,i(X2),X1),
inference(paramodulation,[status(thm)],[f110,f10598]) ).
fof(f10723,plain,
! [X0,X1] : a(X0,X1,X0) = a(X0,i(X0),X1),
inference(paramodulation,[status(thm)],[f10598,f10611]) ).
fof(f10888,plain,
! [X0,X1] : a(X0,X1,X0) = a(X0,j(X1),X0),
inference(paramodulation,[status(thm)],[f398,f10723]) ).
fof(f10963,plain,
! [X0,X1] : a(X0,X1,X0) = a(X0,i(X1),X0),
inference(forward_demodulation,[status(thm)],[f63,f10888]) ).
fof(f11219,plain,
! [X0,X1] : t(X0,i(a(X0,X1,X0))) = a(X0,X0,i(X1)),
inference(paramodulation,[status(thm)],[f10963,f10598]) ).
fof(f11295,plain,
! [X0,X1] : a(X0,X0,X1) = a(X0,X0,i(X1)),
inference(forward_demodulation,[status(thm)],[f10598,f11219]) ).
fof(f11296,plain,
! [X0,X1] : a(X0,X0,X1) = a(X1,X0,X0),
inference(forward_demodulation,[status(thm)],[f391,f11295]) ).
fof(f11333,plain,
a(x0,x1,x1) != a(x0,x1,x1),
inference(backward_demodulation,[status(thm)],[f11296,f66]) ).
fof(f11494,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f11333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP772-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 20:39:13 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 228.74/29.37 % Refutation found
% 228.74/29.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 228.74/29.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 23.82/30.66 % Elapsed time: 30.067393 seconds
% 23.82/30.66 % CPU time: 225.800334 seconds
% 23.82/30.66 % Total memory used: 1.663 GB
% 23.82/30.66 % Net memory used: 1.610 GB
%------------------------------------------------------------------------------