%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL013-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:03:15 PM UTC 2026
% Result : Unsatisfiable 10.31s 1.77s
% Output : CNFRefutation 10.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 15
% Syntax : Number of formulae : 124 ( 113 unt; 2 def)
% Number of atoms : 135 ( 120 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 9 |; 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 156 ( 156 !; 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(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,negated_conjecture,
( composition(zero,sk1) != zero
| composition(sk1,zero) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f26,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f28,plain,
( composition(zero,sk1) != zero
| composition(sk1,zero) != zero ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f29,definition,
( sQ0_spl
<=> composition(sk1,zero) = zero ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f31,plain,
( sQ0_spl
| composition(sk1,zero) != zero ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,definition,
( sQ1_spl
<=> composition(zero,sk1) = zero ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f34,plain,
( sQ1_spl
| composition(zero,sk1) != zero ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f28,f29,f32]) ).
fof(f36,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(forward_demodulation,[status(thm)],[f15,f17]) ).
fof(f37,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f18,f36]) ).
fof(f38,plain,
! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(forward_demodulation,[status(thm)],[f15,f25]) ).
fof(f39,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(forward_demodulation,[status(thm)],[f15,f37]) ).
fof(f46,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(paramodulation,[status(thm)],[f15,f16]) ).
fof(f49,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f26,f16]) ).
fof(f50,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X1,X0),X2),
inference(paramodulation,[status(thm)],[f15,f16]) ).
fof(f57,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(forward_demodulation,[status(thm)],[f16,f50]) ).
fof(f59,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f26,f18]) ).
fof(f60,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f15,f18]) ).
fof(f66,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f27,f59]) ).
fof(f67,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f18,f60]) ).
fof(f90,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f22,f23]) ).
fof(f91,plain,
! [X0,X1] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(paramodulation,[status(thm)],[f22,f23]) ).
fof(f138,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f22,f24]) ).
fof(f244,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X1,X2),composition(X0,X2)),
inference(paramodulation,[status(thm)],[f15,f21]) ).
fof(f260,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = composition(join(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f21,f244]) ).
fof(f288,plain,
! [X0,X1] : join(X0,top) = join(X1,join(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f26,f57]) ).
fof(f489,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f20,f138]) ).
fof(f508,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f22,f489]) ).
fof(f549,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f20,f508]) ).
fof(f550,plain,
! [X0] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(paramodulation,[status(thm)],[f508,f38]) ).
fof(f556,plain,
! [X0,X1] : composition(join(X0,converse(one)),X1) = join(composition(X0,X1),X1),
inference(paramodulation,[status(thm)],[f508,f21]) ).
fof(f559,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f549,f508]) ).
fof(f563,plain,
! [X0,X1] : composition(join(X0,one),X1) = join(composition(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f549,f556]) ).
fof(f565,plain,
! [X0,X1] : composition(join(X0,one),X1) = join(X1,composition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f15,f563]) ).
fof(f568,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(backward_demodulation,[status(thm)],[f559,f550]) ).
fof(f584,plain,
join(zero,complement(top)) = complement(top),
inference(paramodulation,[status(thm)],[f66,f568]) ).
fof(f585,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),complement(X1)))) = complement(join(complement(X0),complement(X1))),
inference(paramodulation,[status(thm)],[f18,f568]) ).
fof(f588,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f568,f18]) ).
fof(f595,plain,
join(zero,zero) = complement(top),
inference(forward_demodulation,[status(thm)],[f66,f584]) ).
fof(f596,plain,
join(zero,zero) = zero,
inference(forward_demodulation,[status(thm)],[f66,f595]) ).
fof(f597,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,X1)) = complement(join(complement(X0),complement(X1))),
inference(forward_demodulation,[status(thm)],[f18,f585]) ).
fof(f598,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,X1)) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f18,f597]) ).
fof(f610,plain,
! [X0] : join(zero,join(zero,X0)) = join(X0,zero),
inference(paramodulation,[status(thm)],[f596,f46]) ).
fof(f630,plain,
! [X0] : X0 = join(complement(complement(X0)),complement(join(complement(X0),X0))),
inference(paramodulation,[status(thm)],[f588,f39]) ).
fof(f633,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f18,f39]) ).
fof(f641,plain,
! [X0] : X0 = join(meet(X0,complement(complement(X0))),complement(top)),
inference(paramodulation,[status(thm)],[f26,f39]) ).
fof(f654,plain,
! [X0] : X0 = join(complement(complement(X0)),complement(join(X0,complement(X0)))),
inference(forward_demodulation,[status(thm)],[f15,f630]) ).
fof(f655,plain,
! [X0] : X0 = join(complement(complement(X0)),complement(top)),
inference(forward_demodulation,[status(thm)],[f26,f654]) ).
fof(f656,plain,
! [X0] : X0 = join(complement(top),complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f15,f655]) ).
fof(f657,plain,
! [X0] : X0 = join(zero,complement(complement(X0))),
inference(forward_demodulation,[status(thm)],[f66,f656]) ).
fof(f658,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(forward_demodulation,[status(thm)],[f15,f633]) ).
fof(f665,plain,
! [X0] : X0 = join(complement(top),meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f15,f641]) ).
fof(f666,plain,
! [X0] : X0 = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f66,f665]) ).
fof(f736,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
inference(paramodulation,[status(thm)],[f67,f658]) ).
fof(f762,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(paramodulation,[status(thm)],[f568,f49]) ).
fof(f770,plain,
! [X0] : join(X0,top) = join(top,complement(complement(X0))),
inference(paramodulation,[status(thm)],[f26,f49]) ).
fof(f771,plain,
! [X0,X1] : join(X0,join(X1,complement(X0))) = join(top,X1),
inference(paramodulation,[status(thm)],[f15,f49]) ).
fof(f789,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[status(thm)],[f26,f762]) ).
fof(f800,plain,
! [X0] : join(X0,top) = top,
inference(forward_demodulation,[status(thm)],[f789,f770]) ).
fof(f801,plain,
! [X0] : join(X0,top) = join(top,X0),
inference(forward_demodulation,[status(thm)],[f288,f771]) ).
fof(f811,plain,
! [X0] : top = join(top,X0),
inference(forward_demodulation,[status(thm)],[f800,f801]) ).
fof(f862,plain,
! [X0] : X0 = join(meet(X0,top),complement(top)),
inference(paramodulation,[status(thm)],[f800,f39]) ).
fof(f875,plain,
! [X0] : X0 = join(complement(top),meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f15,f862]) ).
fof(f876,plain,
! [X0] : X0 = join(zero,meet(X0,top)),
inference(forward_demodulation,[status(thm)],[f66,f875]) ).
fof(f931,plain,
! [X0] : X0 = join(zero,meet(top,X0)),
inference(paramodulation,[status(thm)],[f67,f876]) ).
fof(f1146,plain,
! [X0] : complement(complement(X0)) = join(meet(complement(complement(X0)),X0),zero),
inference(paramodulation,[status(thm)],[f27,f736]) ).
fof(f1165,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f15,f1146]) ).
fof(f1166,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[status(thm)],[f67,f1165]) ).
fof(f1168,plain,
! [X0] : X0 = join(zero,X0),
inference(backward_demodulation,[status(thm)],[f1180,f657]) ).
fof(f1180,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f666,f1166]) ).
fof(f1189,plain,
! [X0] : X0 = meet(top,X0),
inference(backward_demodulation,[status(thm)],[f1168,f931]) ).
fof(f1203,plain,
! [X0] : join(zero,X0) = join(X0,zero),
inference(backward_demodulation,[status(thm)],[f1168,f610]) ).
fof(f1241,plain,
! [X0] : X0 = join(X0,zero),
inference(forward_demodulation,[status(thm)],[f1168,f1203]) ).
fof(f1390,plain,
! [X0] : converse(converse(X0)) = join(converse(zero),X0),
inference(paramodulation,[status(thm)],[f1168,f91]) ).
fof(f1410,plain,
! [X0] : X0 = join(converse(zero),X0),
inference(forward_demodulation,[status(thm)],[f22,f1390]) ).
fof(f1500,plain,
zero = converse(zero),
inference(paramodulation,[status(thm)],[f1241,f1410]) ).
fof(f2460,plain,
! [X0] : join(X0,meet(top,X0)) = meet(top,X0),
inference(paramodulation,[status(thm)],[f1189,f598]) ).
fof(f2481,plain,
! [X0] : join(X0,X0) = meet(top,X0),
inference(forward_demodulation,[status(thm)],[f1189,f2460]) ).
fof(f2484,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[status(thm)],[f1189,f2481]) ).
fof(f2542,plain,
! [X0,X1] : join(X0,join(X1,X0)) = join(X1,X0),
inference(paramodulation,[status(thm)],[f2484,f57]) ).
fof(f3650,plain,
! [X0] : composition(join(X0,one),zero) = composition(X0,zero),
inference(paramodulation,[status(thm)],[f1168,f565]) ).
fof(f3651,plain,
! [X0] : composition(join(X0,one),top) = top,
inference(paramodulation,[status(thm)],[f811,f565]) ).
fof(f3746,plain,
! [X0] : join(complement(top),composition(converse(join(X0,one)),complement(top))) = complement(top),
inference(paramodulation,[status(thm)],[f3651,f38]) ).
fof(f3756,plain,
! [X0] : composition(join(converse(join(X0,one)),one),complement(top)) = complement(top),
inference(forward_demodulation,[status(thm)],[f565,f3746]) ).
fof(f3757,plain,
! [X0] : composition(join(one,converse(join(X0,one))),complement(top)) = complement(top),
inference(forward_demodulation,[status(thm)],[f260,f3756]) ).
fof(f3758,plain,
! [X0] : composition(join(one,converse(join(X0,one))),zero) = complement(top),
inference(forward_demodulation,[status(thm)],[f66,f3757]) ).
fof(f3759,plain,
! [X0] : composition(join(one,converse(join(X0,one))),zero) = zero,
inference(forward_demodulation,[status(thm)],[f66,f3758]) ).
fof(f6499,plain,
! [X0] : composition(join(one,join(X0,converse(one))),zero) = zero,
inference(paramodulation,[status(thm)],[f90,f3759]) ).
fof(f6523,plain,
! [X0] : composition(join(one,join(X0,one)),zero) = zero,
inference(forward_demodulation,[status(thm)],[f549,f6499]) ).
fof(f6524,plain,
! [X0] : composition(join(X0,one),zero) = zero,
inference(forward_demodulation,[status(thm)],[f2542,f6523]) ).
fof(f6526,plain,
( sQ0_spl
| zero != zero ),
inference(backward_demodulation,[status(thm)],[f6536,f31]) ).
fof(f6536,plain,
! [X0] : composition(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f3650,f6524]) ).
fof(f6578,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f6526]) ).
fof(f6579,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f6578]) ).
fof(f6593,plain,
! [X0] : converse(zero) = composition(converse(zero),X0),
inference(paramodulation,[status(thm)],[f6536,f138]) ).
fof(f6612,plain,
! [X0] : zero = composition(converse(zero),X0),
inference(forward_demodulation,[status(thm)],[f1500,f6593]) ).
fof(f6613,plain,
( sQ1_spl
| zero != zero ),
inference(backward_demodulation,[status(thm)],[f6617,f34]) ).
fof(f6617,plain,
! [X0] : zero = composition(zero,X0),
inference(forward_demodulation,[status(thm)],[f1500,f6612]) ).
fof(f6645,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f6613]) ).
fof(f6646,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f6645]) ).
fof(f6647,plain,
$false,
inference(sat_refutation,[status(thm)],[f35,f6579,f6646]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL013-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 03:58:40 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 10.31/1.77 % Refutation found
% 10.31/1.77 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 10.31/1.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.46/1.82 % Elapsed time: 1.441394 seconds
% 0.46/1.82 % CPU time: 11.111026 seconds
% 0.46/1.82 % Total memory used: 185.990 MB
% 0.46/1.82 % Net memory used: 182.720 MB
%------------------------------------------------------------------------------