%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : REL004-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 02:03:10 PM UTC 2026
% Result : Unsatisfiable 7.17s 1.60s
% Output : CNFRefutation 7.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 12
% Syntax : Number of formulae : 123 ( 123 unt; 0 def)
% Number of atoms : 123 ( 122 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 170 ( 170 !; 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(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,
converse(complement(sk1)) != complement(converse(sk1)),
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(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,
converse(complement(sk1)) != complement(converse(sk1)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f34,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(backward_demodulation,[status(thm)],[f18,f17]) ).
fof(f36,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(paramodulation,[status(thm)],[f22,f23]) ).
fof(f39,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(paramodulation,[status(thm)],[f22,f24]) ).
fof(f55,plain,
! [X0,X1] : join(composition(X0,complement(composition(converse(X0),X1))),complement(X1)) = complement(X1),
inference(paramodulation,[status(thm)],[f22,f25]) ).
fof(f545,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(paramodulation,[status(thm)],[f20,f39]) ).
fof(f549,plain,
! [X0] : X0 = composition(converse(one),X0),
inference(forward_demodulation,[status(thm)],[f22,f545]) ).
fof(f555,plain,
! [X0] : converse(top) = join(X0,converse(complement(converse(X0)))),
inference(paramodulation,[status(thm)],[f26,f36]) ).
fof(f561,plain,
one = converse(one),
inference(paramodulation,[status(thm)],[f20,f549]) ).
fof(f567,plain,
! [X0] : join(composition(one,complement(X0)),complement(X0)) = complement(X0),
inference(paramodulation,[status(thm)],[f549,f55]) ).
fof(f580,plain,
! [X0] : X0 = composition(one,X0),
inference(backward_demodulation,[status(thm)],[f561,f549]) ).
fof(f599,plain,
! [X0] : join(complement(X0),complement(X0)) = complement(X0),
inference(backward_demodulation,[status(thm)],[f580,f567]) ).
fof(f686,plain,
! [X0] : meet(X0,X0) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f599,f18]) ).
fof(f687,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(paramodulation,[status(thm)],[f26,f18]) ).
fof(f690,plain,
! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f18,f34]) ).
fof(f699,plain,
! [X0,X1,X2] : join(complement(X0),complement(X1)) = join(meet(join(complement(X0),complement(X1)),X2),complement(join(meet(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f18,f34]) ).
fof(f701,plain,
zero = complement(top),
inference(forward_demodulation,[status(thm)],[f27,f687]) ).
fof(f715,plain,
top = join(top,zero),
inference(paramodulation,[status(thm)],[f701,f26]) ).
fof(f737,plain,
! [X0] : join(complement(complement(X0)),meet(X0,X0)) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f686,f599]) ).
fof(f738,plain,
! [X0] : join(meet(X0,X0),complement(complement(X0))) = complement(complement(X0)),
inference(paramodulation,[status(thm)],[f686,f599]) ).
fof(f739,plain,
! [X0] : top = join(complement(X0),meet(X0,X0)),
inference(paramodulation,[status(thm)],[f686,f26]) ).
fof(f807,plain,
! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f690,f15]) ).
fof(f834,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(paramodulation,[status(thm)],[f15,f18]) ).
fof(f835,plain,
! [X0,X1] : X0 = join(meet(X0,X1),complement(join(X1,complement(X0)))),
inference(paramodulation,[status(thm)],[f15,f34]) ).
fof(f918,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(paramodulation,[status(thm)],[f26,f16]) ).
fof(f962,plain,
! [X0] : X0 = join(complement(complement(X0)),meet(X0,complement(X0))),
inference(paramodulation,[status(thm)],[f686,f807]) ).
fof(f969,plain,
! [X0] : X0 = join(complement(complement(X0)),zero),
inference(forward_demodulation,[status(thm)],[f27,f962]) ).
fof(f981,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(meet(X0,X1)),zero),
inference(paramodulation,[status(thm)],[f18,f969]) ).
fof(f982,plain,
! [X0] : complement(X0) = join(meet(complement(X0),zero),complement(X0)),
inference(paramodulation,[status(thm)],[f969,f34]) ).
fof(f1031,plain,
! [X0] : X0 = join(meet(X0,converse(complement(converse(complement(X0))))),complement(converse(top))),
inference(paramodulation,[status(thm)],[f555,f34]) ).
fof(f1063,plain,
! [X0] : complement(X0) = join(complement(X0),meet(complement(X0),zero)),
inference(paramodulation,[status(thm)],[f15,f982]) ).
fof(f1082,plain,
! [X0] : complement(complement(X0)) = join(meet(X0,X0),meet(complement(complement(X0)),zero)),
inference(paramodulation,[status(thm)],[f686,f1063]) ).
fof(f1084,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = join(meet(X0,X1),meet(complement(join(complement(X0),complement(X1))),zero)),
inference(paramodulation,[status(thm)],[f18,f1063]) ).
fof(f1085,plain,
! [X0] : complement(complement(X0)) = join(complement(complement(X0)),meet(meet(X0,X0),zero)),
inference(paramodulation,[status(thm)],[f686,f1063]) ).
fof(f1092,plain,
! [X0,X1] : meet(X0,X1) = join(meet(X0,X1),meet(complement(join(complement(X0),complement(X1))),zero)),
inference(forward_demodulation,[status(thm)],[f18,f1084]) ).
fof(f1093,plain,
! [X0,X1] : meet(X0,X1) = join(meet(X0,X1),meet(meet(X0,X1),zero)),
inference(forward_demodulation,[status(thm)],[f18,f1092]) ).
fof(f1156,plain,
! [X0,X1] : join(meet(X0,X0),join(complement(complement(X0)),X1)) = join(complement(complement(X0)),X1),
inference(paramodulation,[status(thm)],[f738,f16]) ).
fof(f1329,plain,
! [X0,X1] : join(complement(X0),complement(complement(X1))) = join(meet(join(complement(X0),complement(complement(X1))),meet(X0,X1)),complement(X0)),
inference(paramodulation,[status(thm)],[f690,f699]) ).
fof(f1479,plain,
! [X0] : join(complement(X0),X0) = join(top,zero),
inference(paramodulation,[status(thm)],[f969,f918]) ).
fof(f1480,plain,
! [X0] : join(complement(X0),complement(complement(X0))) = join(top,meet(X0,X0)),
inference(paramodulation,[status(thm)],[f737,f918]) ).
fof(f1483,plain,
! [X0] : join(X0,top) = join(top,meet(X0,X0)),
inference(paramodulation,[status(thm)],[f739,f918]) ).
fof(f1486,plain,
! [X0] : join(X0,converse(top)) = join(top,converse(complement(converse(complement(X0))))),
inference(paramodulation,[status(thm)],[f555,f918]) ).
fof(f1494,plain,
! [X0,X1] : X0 = join(meet(X0,join(complement(complement(X0)),X1)),complement(join(top,X1))),
inference(paramodulation,[status(thm)],[f918,f34]) ).
fof(f1510,plain,
! [X0] : join(complement(X0),X0) = top,
inference(forward_demodulation,[status(thm)],[f715,f1479]) ).
fof(f1512,plain,
! [X0] : top = join(top,meet(X0,X0)),
inference(forward_demodulation,[status(thm)],[f26,f1480]) ).
fof(f1517,plain,
! [X0] : join(X0,top) = top,
inference(forward_demodulation,[status(thm)],[f1512,f1483]) ).
fof(f1530,plain,
! [X0] : join(top,X0) = top,
inference(paramodulation,[status(thm)],[f15,f1517]) ).
fof(f1537,plain,
! [X0] : converse(top) = join(X0,converse(top)),
inference(paramodulation,[status(thm)],[f1517,f36]) ).
fof(f1543,plain,
! [X0] : join(X0,converse(top)) = top,
inference(backward_demodulation,[status(thm)],[f1530,f1486]) ).
fof(f1552,plain,
! [X0,X1] : X0 = join(meet(X0,join(complement(complement(X0)),X1)),complement(top)),
inference(backward_demodulation,[status(thm)],[f1530,f1494]) ).
fof(f1569,plain,
converse(top) = top,
inference(backward_demodulation,[status(thm)],[f1543,f1537]) ).
fof(f1572,plain,
! [X0,X1] : X0 = join(meet(X0,join(complement(complement(X0)),X1)),zero),
inference(forward_demodulation,[status(thm)],[f701,f1552]) ).
fof(f1578,plain,
! [X0] : X0 = join(meet(X0,converse(complement(converse(complement(X0))))),complement(top)),
inference(backward_demodulation,[status(thm)],[f1569,f1031]) ).
fof(f1585,plain,
! [X0] : X0 = join(meet(X0,converse(complement(converse(complement(X0))))),zero),
inference(forward_demodulation,[status(thm)],[f701,f1578]) ).
fof(f1617,plain,
! [X0] : meet(complement(X0),X0) = complement(top),
inference(paramodulation,[status(thm)],[f1510,f18]) ).
fof(f1637,plain,
! [X0] : meet(complement(X0),X0) = zero,
inference(forward_demodulation,[status(thm)],[f701,f1617]) ).
fof(f1653,plain,
complement(zero) = join(complement(zero),zero),
inference(paramodulation,[status(thm)],[f1637,f1063]) ).
fof(f1668,plain,
complement(zero) = top,
inference(forward_demodulation,[status(thm)],[f1510,f1653]) ).
fof(f1786,plain,
! [X0] : meet(X0,zero) = complement(join(complement(X0),top)),
inference(paramodulation,[status(thm)],[f1668,f18]) ).
fof(f1836,plain,
! [X0] : meet(X0,zero) = complement(top),
inference(forward_demodulation,[status(thm)],[f1517,f1786]) ).
fof(f1837,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(backward_demodulation,[status(thm)],[f1855,f1063]) ).
fof(f1840,plain,
! [X0] : complement(complement(X0)) = join(complement(complement(X0)),zero),
inference(backward_demodulation,[status(thm)],[f1855,f1085]) ).
fof(f1841,plain,
! [X0,X1] : meet(X0,X1) = join(meet(X0,X1),zero),
inference(backward_demodulation,[status(thm)],[f1855,f1093]) ).
fof(f1844,plain,
! [X0] : complement(complement(X0)) = join(meet(X0,X0),zero),
inference(backward_demodulation,[status(thm)],[f1855,f1082]) ).
fof(f1855,plain,
! [X0] : meet(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f701,f1836]) ).
fof(f1871,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = complement(meet(X0,X1)),
inference(backward_demodulation,[status(thm)],[f1837,f981]) ).
fof(f1900,plain,
! [X0,X1] : X0 = join(meet(X0,join(X0,X1)),zero),
inference(backward_demodulation,[status(thm)],[f1924,f1572]) ).
fof(f1904,plain,
! [X0,X1] : join(complement(X0),complement(complement(X1))) = join(meet(join(complement(X0),X1),meet(X0,X1)),complement(X0)),
inference(backward_demodulation,[status(thm)],[f1924,f1329]) ).
fof(f1913,plain,
! [X0,X1] : join(meet(X0,X0),join(complement(complement(X0)),X1)) = join(X0,X1),
inference(backward_demodulation,[status(thm)],[f1924,f1156]) ).
fof(f1924,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f969,f1840]) ).
fof(f1931,plain,
! [X0] : X0 = meet(X0,converse(complement(converse(complement(X0))))),
inference(backward_demodulation,[status(thm)],[f1841,f1585]) ).
fof(f1941,plain,
! [X0] : X0 = join(meet(X0,X0),zero),
inference(forward_demodulation,[status(thm)],[f1924,f1844]) ).
fof(f1966,plain,
! [X0] : X0 = meet(X0,X0),
inference(forward_demodulation,[status(thm)],[f1841,f1941]) ).
fof(f2005,plain,
! [X0,X1] : meet(X0,X1) = complement(complement(meet(X1,X0))),
inference(backward_demodulation,[status(thm)],[f1871,f834]) ).
fof(f2054,plain,
! [X0,X1] : X0 = meet(X0,join(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1841,f1900]) ).
fof(f2060,plain,
! [X0,X1] : complement(meet(X0,complement(X1))) = join(meet(join(complement(X0),X1),meet(X0,X1)),complement(X0)),
inference(forward_demodulation,[status(thm)],[f1871,f1904]) ).
fof(f2079,plain,
! [X0,X1] : join(X0,join(complement(complement(X0)),X1)) = join(X0,X1),
inference(forward_demodulation,[status(thm)],[f1966,f1913]) ).
fof(f2082,plain,
! [X0,X1] : join(X0,join(X0,X1)) = join(X0,X1),
inference(forward_demodulation,[status(thm)],[f1924,f2079]) ).
fof(f2129,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f1924,f2005]) ).
fof(f2499,plain,
! [X0,X1] : meet(X0,X1) = meet(meet(X0,X1),X0),
inference(paramodulation,[status(thm)],[f807,f2054]) ).
fof(f2593,plain,
! [X0,X1] : meet(X0,X1) = meet(meet(X1,X0),X0),
inference(paramodulation,[status(thm)],[f2129,f2499]) ).
fof(f2595,plain,
! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
inference(paramodulation,[status(thm)],[f2129,f807]) ).
fof(f2657,plain,
! [X0,X1] : join(complement(X0),X1) = join(meet(join(complement(X0),X1),meet(X0,X1)),complement(X0)),
inference(paramodulation,[status(thm)],[f34,f835]) ).
fof(f2700,plain,
! [X0,X1] : complement(meet(X0,complement(X1))) = join(complement(X0),X1),
inference(backward_demodulation,[status(thm)],[f2657,f2060]) ).
fof(f2975,plain,
! [X0] : meet(converse(complement(converse(complement(X0)))),X0) = meet(X0,converse(complement(converse(complement(X0))))),
inference(paramodulation,[status(thm)],[f1931,f2593]) ).
fof(f2994,plain,
! [X0] : meet(converse(complement(converse(complement(X0)))),X0) = X0,
inference(forward_demodulation,[status(thm)],[f1931,f2975]) ).
fof(f3809,plain,
! [X0,X1] : join(meet(X0,X1),X1) = join(meet(X0,X1),meet(X1,complement(X0))),
inference(paramodulation,[status(thm)],[f2595,f2082]) ).
fof(f3865,plain,
! [X0,X1] : join(meet(X0,X1),X1) = X1,
inference(forward_demodulation,[status(thm)],[f2595,f3809]) ).
fof(f3906,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f15,f3865]) ).
fof(f4044,plain,
! [X0,X1] : converse(converse(X0)) = join(X0,converse(meet(X1,converse(X0)))),
inference(paramodulation,[status(thm)],[f3906,f36]) ).
fof(f4071,plain,
! [X0,X1] : X0 = join(X0,converse(meet(X1,converse(X0)))),
inference(forward_demodulation,[status(thm)],[f22,f4044]) ).
fof(f4489,plain,
! [X0] : complement(converse(complement(X0))) = join(complement(converse(complement(X0))),converse(X0)),
inference(paramodulation,[status(thm)],[f1931,f4071]) ).
fof(f5969,plain,
! [X0] : complement(complement(X0)) = join(complement(converse(complement(converse(complement(complement(X0)))))),X0),
inference(paramodulation,[status(thm)],[f2994,f2700]) ).
fof(f6014,plain,
! [X0] : X0 = join(complement(converse(complement(converse(complement(complement(X0)))))),X0),
inference(forward_demodulation,[status(thm)],[f1924,f5969]) ).
fof(f6015,plain,
! [X0] : X0 = join(complement(converse(complement(converse(X0)))),X0),
inference(forward_demodulation,[status(thm)],[f1924,f6014]) ).
fof(f6331,plain,
! [X0] : converse(X0) = join(complement(converse(complement(X0))),converse(X0)),
inference(paramodulation,[status(thm)],[f22,f6015]) ).
fof(f6365,plain,
! [X0] : complement(converse(complement(X0))) = converse(X0),
inference(backward_demodulation,[status(thm)],[f6331,f4489]) ).
fof(f6597,plain,
! [X0] : complement(converse(X0)) = converse(complement(X0)),
inference(paramodulation,[status(thm)],[f1924,f6365]) ).
fof(f6634,plain,
converse(complement(sk1)) != converse(complement(sk1)),
inference(backward_demodulation,[status(thm)],[f6597,f28]) ).
fof(f6723,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f6634]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL004-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n004.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Mon Sep 21 03:57:05 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.15/0.58 % Drodi V4.1.1
% 7.17/1.60 % Refutation found
% 7.17/1.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.17/1.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.51/2.81 % Elapsed time: 2.017944 seconds
% 10.51/2.81 % CPU time: 6.762111 seconds
% 10.51/2.81 % Total memory used: 124.332 MB
% 10.51/2.81 % Net memory used: 118.644 MB
%------------------------------------------------------------------------------