%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL010-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 02:03:14 PM UTC 2026
% Result : Unsatisfiable 14.42s 2.45s
% Output : CNFRefutation 15.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 16
% Syntax : Number of formulae : 107 ( 107 unt; 0 def)
% Number of atoms : 107 ( 106 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 144 ( 144 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : join(A,B) = join(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : join(A,join(B,C)) = join(join(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : meet(A,B) = complement(join(complement(A),complement(B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : composition(A,composition(B,C)) = composition(composition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : composition(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] : composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] : converse(converse(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] : converse(join(A,B)) = join(converse(A),converse(B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : converse(composition(A,B)) = composition(converse(B),converse(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] : join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : top = join(A,complement(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : zero = meet(A,complement(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C] : join(meet(composition(A,B),C),composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
meet(composition(sk1,sk2),sk3) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
meet(sk2,composition(converse(sk1),sk3)) != zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f29,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f30,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f31,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
meet(composition(sk1,sk2),sk3) = zero,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f36,plain,
meet(sk2,composition(converse(sk1),sk3)) != zero,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f19,f21]) ).
fof(f42,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f22,f41]) ).
fof(f43,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f19,f29]) ).
fof(f44,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f19,f42]) ).
fof(f50,plain,
! [X0,X1] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f51,plain,
! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f52,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f108,plain,
! [X0,X1,X2] : converse(composition(X0,composition(X1,converse(X2)))) = composition(X2,converse(composition(X0,X1))),
inference(paramodulation,[status(thm)],[f23,f51]) ).
fof(f622,plain,
! [X0,X1,X2] : join(meet(composition(converse(X0),X1),X2),composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2)))) = composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(converse(converse(X0)),X2))),
inference(paramodulation,[status(thm)],[f26,f32]) ).
fof(f680,plain,
! [X0,X1,X2] : join(meet(composition(converse(X0),X1),X2),composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2)))) = composition(meet(converse(X0),composition(X2,converse(X1))),meet(X1,composition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f26,f622]) ).
fof(f757,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f24,f52]) ).
fof(f766,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f26,f757]) ).
fof(f774,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f24,f766]) ).
fof(f794,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f774,f766]) ).
fof(f896,plain,
! [X0] : converse(join(X0,one)) = join(converse(X0),one),
inference(paramodulation,[status(thm)],[f774,f50]) ).
fof(f930,plain,
! [X0] : converse(join(X0,one)) = join(one,converse(X0)),
inference(forward_demodulation,[status(thm)],[f19,f896]) ).
fof(f1086,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f30,f22]) ).
fof(f1087,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f1093,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f31,f1086]) ).
fof(f1094,plain,
meet(sk3,composition(sk1,sk2)) = zero,
inference(backward_demodulation,[status(thm)],[f1118,f35]) ).
fof(f1118,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f22,f1087]) ).
fof(f1144,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(paramodulation,[status(thm)],[f1093,f22]) ).
fof(f1148,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f1144]) ).
fof(f1167,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f30,f20]) ).
fof(f1308,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f30,f1167]) ).
fof(f1332,plain,
! [X0,X1] : composition(join(one,X0),X1) = join(X1,composition(X0,X1)),
inference(paramodulation,[status(thm)],[f794,f25]) ).
fof(f1337,plain,
! [X0,X1] : composition(join(X0,one),X1) = join(composition(X0,X1),X1),
inference(paramodulation,[status(thm)],[f794,f25]) ).
fof(f1352,plain,
! [X0,X1] : composition(join(X0,one),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f1337]) ).
fof(f1364,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = complement(top),
inference(paramodulation,[status(thm)],[f1093,f43]) ).
fof(f1367,plain,
! [X0] : join(complement(X0),composition(one,complement(composition(one,X0)))) = complement(X0),
inference(paramodulation,[status(thm)],[f774,f43]) ).
fof(f1388,plain,
! [X0] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f1093,f1364]) ).
fof(f1391,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f794,f1367]) ).
fof(f1392,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f794,f1391]) ).
fof(f1494,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f1392,f22]) ).
fof(f1495,plain,
! [X0] : X0 = join(meet(X0,complement(X0)),complement(complement(X0))),
inference(paramodulation,[status(thm)],[f1392,f44]) ).
fof(f1496,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(paramodulation,[status(thm)],[f1392,f1167]) ).
fof(f1516,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f1495]) ).
fof(f1517,plain,
! [X0] : X0 = join(complement(complement(X0)),zero),
inference(forward_demodulation,[status(thm)],[f31,f1516]) ).
fof(f1518,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f19,f1517]) ).
fof(f1521,plain,
! [X0] : join(X0,top) = top,
inference(backward_demodulation,[status(thm)],[f1523,f1308]) ).
fof(f1523,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[status(thm)],[f30,f1496]) ).
fof(f1536,plain,
! [X0] : join(top,X0) = top,
inference(paramodulation,[status(thm)],[f19,f1521]) ).
fof(f1540,plain,
! [X0] : X0 = join(meet(X0,top),complement(top)),
inference(paramodulation,[status(thm)],[f1521,f44]) ).
fof(f1569,plain,
! [X0] : X0 = join(complement(top),meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f19,f1540]) ).
fof(f1571,plain,
! [X0] : X0 = join(zero,meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f1093,f1569]) ).
fof(f1622,plain,
! [X0] : meet(complement(X0),top) = complement(X0),
inference(paramodulation,[status(thm)],[f1518,f1148]) ).
fof(f1626,plain,
! [X0] : meet(top,complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f1118,f1622]) ).
fof(f1643,plain,
! [X0] : X0 = join(zero,meet(top,X0)),
inference(paramodulation,[status(thm)],[f1118,f1571]) ).
fof(f1695,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(paramodulation,[status(thm)],[f1626,f1643]) ).
fof(f1706,plain,
! [X0] : X0 = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1695,f1518]) ).
fof(f1708,plain,
! [X0] : meet(X0,top) = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1695,f1148]) ).
fof(f1726,plain,
! [X0] : meet(X0,X0) = X0,
inference(backward_demodulation,[status(thm)],[f1706,f1494]) ).
fof(f1740,plain,
! [X0] : X0 = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f1743,f1571]) ).
fof(f1743,plain,
! [X0] : meet(X0,top) = X0,
inference(forward_demodulation,[status(thm)],[f1706,f1708]) ).
fof(f1791,plain,
! [X0] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(backward_demodulation,[status(thm)],[f1740,f1388]) ).
fof(f1814,plain,
! [X0] : X0 = join(X0,complement(join(complement(X0),X0))),
inference(paramodulation,[status(thm)],[f1726,f44]) ).
fof(f1830,plain,
! [X0] : X0 = join(X0,complement(join(X0,complement(X0)))),
inference(forward_demodulation,[status(thm)],[f19,f1814]) ).
fof(f1831,plain,
! [X0] : X0 = join(X0,complement(top)),
inference(forward_demodulation,[status(thm)],[f30,f1830]) ).
fof(f1832,plain,
! [X0] : X0 = join(X0,zero),
inference(forward_demodulation,[status(thm)],[f1093,f1831]) ).
fof(f4217,plain,
! [X0] : composition(join(one,converse(X0)),complement(composition(join(X0,one),top))) = zero,
inference(paramodulation,[status(thm)],[f930,f1791]) ).
fof(f4264,plain,
! [X0] : composition(join(one,converse(X0)),complement(join(top,composition(X0,top)))) = zero,
inference(forward_demodulation,[status(thm)],[f1352,f4217]) ).
fof(f4265,plain,
! [X0] : composition(join(one,converse(X0)),complement(top)) = zero,
inference(forward_demodulation,[status(thm)],[f1536,f4264]) ).
fof(f4266,plain,
! [X0] : composition(join(one,converse(X0)),zero) = zero,
inference(forward_demodulation,[status(thm)],[f1093,f4265]) ).
fof(f4267,plain,
! [X0] : join(zero,composition(converse(X0),zero)) = zero,
inference(forward_demodulation,[status(thm)],[f1332,f4266]) ).
fof(f4270,plain,
! [X0] : composition(converse(X0),zero) = zero,
inference(forward_demodulation,[status(thm)],[f1740,f4267]) ).
fof(f4375,plain,
! [X0,X1,X2] : composition(composition(X0,converse(composition(X1,X2))),zero) = zero,
inference(paramodulation,[status(thm)],[f108,f4270]) ).
fof(f4416,plain,
! [X0,X1,X2] : composition(X0,composition(converse(composition(X1,X2)),zero)) = zero,
inference(forward_demodulation,[status(thm)],[f23,f4375]) ).
fof(f4446,plain,
! [X0] : composition(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f4270,f4416]) ).
fof(f5234,plain,
join(meet(composition(converse(sk1),sk3),sk2),composition(meet(converse(sk1),composition(sk2,converse(sk3))),zero)) = composition(meet(converse(sk1),composition(sk2,converse(sk3))),meet(sk3,composition(sk1,sk2))),
inference(paramodulation,[status(thm)],[f1094,f680]) ).
fof(f5437,plain,
join(meet(sk2,composition(converse(sk1),sk3)),composition(meet(converse(sk1),composition(sk2,converse(sk3))),zero)) = composition(meet(converse(sk1),composition(sk2,converse(sk3))),meet(sk3,composition(sk1,sk2))),
inference(forward_demodulation,[status(thm)],[f1118,f5234]) ).
fof(f5438,plain,
join(meet(sk2,composition(converse(sk1),sk3)),zero) = composition(meet(converse(sk1),composition(sk2,converse(sk3))),meet(sk3,composition(sk1,sk2))),
inference(forward_demodulation,[status(thm)],[f4446,f5437]) ).
fof(f5439,plain,
meet(sk2,composition(converse(sk1),sk3)) = composition(meet(converse(sk1),composition(sk2,converse(sk3))),meet(sk3,composition(sk1,sk2))),
inference(forward_demodulation,[status(thm)],[f1832,f5438]) ).
fof(f5440,plain,
meet(sk2,composition(converse(sk1),sk3)) = composition(meet(converse(sk1),composition(sk2,converse(sk3))),zero),
inference(forward_demodulation,[status(thm)],[f1094,f5439]) ).
fof(f5441,plain,
meet(sk2,composition(converse(sk1),sk3)) = zero,
inference(forward_demodulation,[status(thm)],[f4446,f5440]) ).
fof(f5442,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5441,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL010-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.45 % Computer : n003.cluster.edu
% 0.15/0.45 % Model : x86_64 x86_64
% 0.15/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.45 % Memory : 8046.5625MB
% 0.15/0.45 % OS : Linux 6.8.0-71-generic
% 0.15/0.45 % CPULimit : 300
% 0.15/0.45 % WCLimit : 300
% 0.15/0.45 % DateTime : Mon Sep 21 04:00:15 UTC 2026
% 0.15/0.46 % CPUTime :
% 0.15/0.48 % Drodi V4.1.1
% 14.42/2.45 % Refutation found
% 14.42/2.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 14.42/2.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.79/2.61 % Elapsed time: 2.127536 seconds
% 14.79/2.61 % CPU time: 16.023932 seconds
% 14.79/2.61 % Total memory used: 215.331 MB
% 14.79/2.61 % Net memory used: 204.349 MB
%------------------------------------------------------------------------------