%------------------------------------------------------------------------------
% 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/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 02:03:29 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.58s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 74 ( 60 unt; 2 def)
% Number of atoms : 89 ( 70 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 14 ~; 13 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 82 ( 82 !; 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(f8,axiom,
! [A] : converse(converse(A)) = A,
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,negated_conjecture,
join(join(sk1,sk2),sk3) = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( join(sk2,sk3) != sk3
| join(sk1,sk3) != sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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,
join(join(sk1,sk2),sk3) = sk3,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f30,plain,
( join(sk2,sk3) != sk3
| join(sk1,sk3) != sk3 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f31,definition,
( sQ0_spl
<=> join(sk1,sk3) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f32,plain,
( ~ sQ0_spl
| join(sk1,sk3) = sk3 ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f33,plain,
( sQ0_spl
| join(sk1,sk3) != sk3 ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,definition,
( sQ1_spl
<=> join(sk2,sk3) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( sQ1_spl
| join(sk2,sk3) != sk3 ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f30,f31,f34]) ).
fof(f46,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f50,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X1,X0),X2),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f57,plain,
join(sk1,join(sk2,sk3)) = sk3,
inference(forward_demodulation,[status(thm)],[f17,f29]) ).
fof(f58,plain,
join(sk1,join(sk3,sk2)) = sk3,
inference(paramodulation,[status(thm)],[f16,f57]) ).
fof(f64,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f27,f19]) ).
fof(f65,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f16,f19]) ).
fof(f71,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f28,f64]) ).
fof(f73,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f19,f18]) ).
fof(f75,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f73]) ).
fof(f91,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f16,f75]) ).
fof(f102,plain,
! [X0] : X0 = join(zero,meet(X0,complement(complement(X0)))),
inference(paramodulation,[status(thm)],[f28,f91]) ).
fof(f109,plain,
! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(paramodulation,[status(thm)],[f21,f20]) ).
fof(f170,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f306,plain,
join(sk3,join(sk2,sk1)) = sk3,
inference(paramodulation,[status(thm)],[f58,f46]) ).
fof(f553,plain,
! [X0] : meet(complement(X0),X0) = complement(top),
inference(paramodulation,[status(thm)],[f27,f65]) ).
fof(f563,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X1,X0)),
inference(paramodulation,[status(thm)],[f65,f73]) ).
fof(f578,plain,
! [X0] : meet(complement(X0),X0) = zero,
inference(forward_demodulation,[status(thm)],[f71,f553]) ).
fof(f639,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(paramodulation,[status(thm)],[f578,f563]) ).
fof(f660,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f102,f639]) ).
fof(f3707,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f21,f170]) ).
fof(f3731,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f23,f3707]) ).
fof(f3743,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f109,f3731]) ).
fof(f3765,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[status(thm)],[f3731,f3743]) ).
fof(f3788,plain,
! [X0] : join(composition(converse(one),complement(X0)),complement(X0)) = complement(X0),
inference(paramodulation,[status(thm)],[f3765,f26]) ).
fof(f3797,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(forward_demodulation,[status(thm)],[f3731,f3788]) ).
fof(f4042,plain,
! [X0] : join(X0,complement(complement(X0))) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f660,f3797]) ).
fof(f4069,plain,
! [X0] : join(X0,X0) = complement(complement(X0)),
inference(forward_demodulation,[status(thm)],[f660,f4042]) ).
fof(f4070,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[status(thm)],[f660,f4069]) ).
fof(f4106,plain,
! [X0,X1] : join(X0,join(join(X1,X0),X1)) = join(X1,X0),
inference(paramodulation,[status(thm)],[f46,f4070]) ).
fof(f4140,plain,
! [X0,X1] : join(X0,join(X0,join(X1,X1))) = join(X1,X0),
inference(forward_demodulation,[status(thm)],[f50,f4106]) ).
fof(f4141,plain,
! [X0,X1] : join(X0,join(X0,X1)) = join(X1,X0),
inference(forward_demodulation,[status(thm)],[f4070,f4140]) ).
fof(f5179,plain,
join(sk1,sk3) = join(join(sk2,sk3),sk1),
inference(paramodulation,[status(thm)],[f57,f4141]) ).
fof(f5304,plain,
join(sk1,sk3) = join(sk3,join(sk2,sk1)),
inference(forward_demodulation,[status(thm)],[f50,f5179]) ).
fof(f5305,plain,
join(sk1,sk3) = sk3,
inference(forward_demodulation,[status(thm)],[f306,f5304]) ).
fof(f5306,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5305,f33]) ).
fof(f5307,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f5306]) ).
fof(f5404,plain,
( sQ1_spl
| join(sk3,sk2) != sk3 ),
inference(paramodulation,[status(thm)],[f16,f36]) ).
fof(f5415,plain,
! [X0] :
( ~ sQ0_spl
| join(sk1,join(sk3,X0)) = join(sk3,X0) ),
inference(paramodulation,[status(thm)],[f32,f17]) ).
fof(f5607,plain,
( ~ sQ0_spl
| join(sk3,sk2) = sk3 ),
inference(backward_demodulation,[status(thm)],[f5415,f58]) ).
fof(f5645,plain,
( ~ sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5607,f5404]) ).
fof(f5646,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f5645]) ).
fof(f5647,plain,
$false,
inference(sat_refutation,[status(thm)],[f37,f5307,f5646]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL048-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n020.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 04:09:39 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.14/5.58 % Refutation found
% 0.14/5.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.59 % Elapsed time: 0.204836 seconds
% 0.14/5.59 % CPU time: 1.387123 seconds
% 0.14/5.59 % Total memory used: 85.667 MB
% 0.14/5.59 % Net memory used: 85.166 MB
%------------------------------------------------------------------------------