%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL048+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:03:28 PM UTC 2026
% Result : Theorem 1.03s 0.86s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 86 ( 80 unt; 0 def)
% Number of atoms : 96 ( 95 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 4 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 114 ( 111 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [X0,X1,X2] :
( join(join(X0,X1),X2) = X2
=> ( join(X1,X2) = X2
& join(X0,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] :
( join(join(X0,X1),X2) = X2
=> ( join(X1,X2) = X2
& join(X0,X2) = X2 ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f25,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,plain,
? [X0,X1,X2] :
( ( join(X1,X2) != X2
| join(X0,X2) != X2 )
& join(join(X0,X1),X2) = X2 ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f30,plain,
( ( join(sK1_skl,sK2_skl) != sK2_skl
| join(sK0_skl,sK2_skl) != sK2_skl )
& join(join(sK0_skl,sK1_skl),sK2_skl) = sK2_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X2,sK2_skl)],[f29]) ).
fof(f31,plain,
join(join(sK0_skl,sK1_skl),sK2_skl) = sK2_skl,
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
( join(sK1_skl,sK2_skl) != sK2_skl
| join(sK0_skl,sK2_skl) != sK2_skl ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f16,f18]) ).
fof(f34,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f19,f33]) ).
fof(f35,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f16,f26]) ).
fof(f36,plain,
join(sK0_skl,join(sK1_skl,sK2_skl)) = sK2_skl,
inference(forward_demodulation,[status(thm)],[f17,f31]) ).
fof(f37,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f16,f34]) ).
fof(f48,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f27,f17]) ).
fof(f59,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f27,f19]) ).
fof(f60,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f16,f19]) ).
fof(f66,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f28,f59]) ).
fof(f67,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f19,f60]) ).
fof(f71,plain,
! [X0] : meet(X0,top) = complement(join(complement(X0),zero)),
inference(paramodulation,[status(thm)],[f66,f19]) ).
fof(f75,plain,
! [X0] : meet(X0,top) = complement(join(zero,complement(X0))),
inference(forward_demodulation,[status(thm)],[f16,f71]) ).
fof(f84,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f21,f20]) ).
fof(f172,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f323,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f27,f48]) ).
fof(f723,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f21,f172]) ).
fof(f744,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f23,f723]) ).
fof(f758,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f84,f744]) ).
fof(f760,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f744,f35]) ).
fof(f773,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f744,f758]) ).
fof(f775,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f773,f760]) ).
fof(f821,plain,
! [X0] : X0 = join(zero,complement(join(complement(X0),complement(X0)))),
inference(paramodulation,[status(thm)],[f28,f37]) ).
fof(f826,plain,
! [X0,X1] : X0 = join(meet(X0,join(complement(complement(X0)),X1)),complement(join(top,X1))),
inference(paramodulation,[status(thm)],[f48,f37]) ).
fof(f847,plain,
! [X0] : X0 = join(zero,meet(X0,X0)),
inference(forward_demodulation,[status(thm)],[f19,f821]) ).
fof(f850,plain,
! [X0,X1] : X0 = join(complement(join(top,X1)),meet(X0,join(complement(complement(X0)),X1))),
inference(forward_demodulation,[status(thm)],[f16,f826]) ).
fof(f878,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f775,f19]) ).
fof(f879,plain,
! [X0] : X0 = join(meet(X0,complement(X0)),complement(complement(X0))),
inference(paramodulation,[status(thm)],[f775,f37]) ).
fof(f880,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(paramodulation,[status(thm)],[f775,f48]) ).
fof(f904,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,complement(X0))),
inference(forward_demodulation,[status(thm)],[f16,f879]) ).
fof(f905,plain,
! [X0] : X0 = join(complement(complement(X0)),zero),
inference(forward_demodulation,[status(thm)],[f28,f904]) ).
fof(f906,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f16,f905]) ).
fof(f908,plain,
! [X0] : join(X0,top) = top,
inference(backward_demodulation,[status(thm)],[f909,f323]) ).
fof(f909,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[status(thm)],[f27,f880]) ).
fof(f925,plain,
! [X0] : join(top,X0) = top,
inference(paramodulation,[status(thm)],[f16,f908]) ).
fof(f929,plain,
! [X0] : X0 = join(meet(X0,top),complement(top)),
inference(paramodulation,[status(thm)],[f908,f37]) ).
fof(f957,plain,
! [X0,X1] : X0 = join(complement(top),meet(X0,join(complement(complement(X0)),X1))),
inference(backward_demodulation,[status(thm)],[f925,f850]) ).
fof(f963,plain,
! [X0] : X0 = join(complement(top),meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f16,f929]) ).
fof(f965,plain,
! [X0] : X0 = join(zero,meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f66,f963]) ).
fof(f983,plain,
! [X0,X1] : X0 = join(zero,meet(X0,join(complement(complement(X0)),X1))),
inference(forward_demodulation,[status(thm)],[f66,f957]) ).
fof(f1050,plain,
! [X0] : meet(complement(X0),top) = complement(join(zero,meet(X0,X0))),
inference(paramodulation,[status(thm)],[f878,f75]) ).
fof(f1060,plain,
! [X0] : meet(top,complement(X0)) = complement(join(zero,meet(X0,X0))),
inference(forward_demodulation,[status(thm)],[f67,f1050]) ).
fof(f1061,plain,
! [X0] : meet(top,complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f847,f1060]) ).
fof(f1129,plain,
! [X0] : X0 = join(zero,meet(top,X0)),
inference(paramodulation,[status(thm)],[f67,f965]) ).
fof(f1159,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(paramodulation,[status(thm)],[f1061,f1129]) ).
fof(f1173,plain,
! [X0] : X0 = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1159,f906]) ).
fof(f1174,plain,
! [X0] : meet(X0,top) = complement(complement(X0)),
inference(backward_demodulation,[status(thm)],[f1159,f75]) ).
fof(f1192,plain,
! [X0,X1] : X0 = join(zero,meet(X0,join(X0,X1))),
inference(backward_demodulation,[status(thm)],[f1173,f983]) ).
fof(f1196,plain,
! [X0] : X0 = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f1199,f965]) ).
fof(f1199,plain,
! [X0] : meet(X0,top) = X0,
inference(forward_demodulation,[status(thm)],[f1173,f1174]) ).
fof(f1233,plain,
! [X0,X1] : X0 = meet(X0,join(X0,X1)),
inference(backward_demodulation,[status(thm)],[f1196,f1192]) ).
fof(f1548,plain,
! [X0,X1] : X0 = meet(X0,join(X1,X0)),
inference(paramodulation,[status(thm)],[f16,f1233]) ).
fof(f1712,plain,
join(sK1_skl,sK2_skl) = meet(join(sK1_skl,sK2_skl),sK2_skl),
inference(paramodulation,[status(thm)],[f36,f1548]) ).
fof(f1735,plain,
join(sK1_skl,sK2_skl) = meet(sK2_skl,join(sK1_skl,sK2_skl)),
inference(forward_demodulation,[status(thm)],[f67,f1712]) ).
fof(f1736,plain,
( sK2_skl != sK2_skl
| join(sK0_skl,sK2_skl) != sK2_skl ),
inference(backward_demodulation,[status(thm)],[f1740,f32]) ).
fof(f1737,plain,
join(sK0_skl,sK2_skl) = sK2_skl,
inference(backward_demodulation,[status(thm)],[f1740,f36]) ).
fof(f1740,plain,
join(sK1_skl,sK2_skl) = sK2_skl,
inference(forward_demodulation,[status(thm)],[f1548,f1735]) ).
fof(f1745,plain,
join(sK0_skl,sK2_skl) != sK2_skl,
inference(trivial_equality_resolution,[status(thm)],[f1736]) ).
fof(f1746,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1737,f1745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n006.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 04:08:29 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 1.03/0.86 % Refutation found
% 1.03/0.86 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.03/0.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.39/0.89 % Elapsed time: 0.448672 seconds
% 0.39/0.89 % CPU time: 3.237085 seconds
% 0.39/0.89 % Total memory used: 92.594 MB
% 0.39/0.89 % Net memory used: 91.978 MB
%------------------------------------------------------------------------------