%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : REL048+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 : Sun Sep 27 08:24:26 AM UTC 2026
% Result : Theorem 61.55s 9.32s
% Output : CNFRefutation 61.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 12
% Syntax : Number of formulae : 133 ( 128 unt; 0 def)
% Number of atoms : 140 ( 139 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 8 ~; 3 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Maximal term depth : 7 ( 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 : 165 ( 3 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0 ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0 ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( join(join(X0,X1),X2) = X2
=> ( join(X1,X2) = X2
& join(X0,X2) = X2 ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( join(join(X0,X1),X2) = X2
=> ( join(X1,X2) = X2
& join(X0,X2) = X2 ) ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
join(X0,X1) = join(X1,X0),
inference(clausification,[status(esa)],[maddux1_join_commutativity]) ).
cnf(c1,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(clausification,[status(esa)],[maddux2_join_associativity]) ).
cnf(c2,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(clausification,[status(esa)],[maddux3_a_kind_of_de_Morgan]) ).
cnf(c3,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(clausification,[status(esa)],[maddux4_definiton_of_meet]) ).
cnf(c5,plain,
composition(X0,one) = X0,
inference(clausification,[status(esa)],[composition_identity]) ).
cnf(c7,plain,
converse(converse(X0)) = X0,
inference(clausification,[status(esa)],[converse_idempotence]) ).
cnf(c8,plain,
converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(clausification,[status(esa)],[converse_additivity]) ).
cnf(c9,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(clausification,[status(esa)],[converse_multiplicativity]) ).
cnf(c10,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(clausification,[status(esa)],[converse_cancellativity]) ).
cnf(c11,plain,
top = join(X0,complement(X0)),
inference(clausification,[status(esa)],[def_top]) ).
cnf(c12,plain,
zero = meet(X0,complement(X0)),
inference(clausification,[status(esa)],[def_zero]) ).
cnf(c13,plain,
join(join(sK25,sK26),sK27) = sK27,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c14,plain,
( join(sK26,sK27) != sK27
| join(sK25,sK27) != sK27 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
join(sK27,join(sK25,sK26)) = sK27,
inference(demodulation,[status(thm)],[c13,c0]) ).
cnf(d1,plain,
join(sK27,join(join(sK25,sK26),X0)) = join(sK27,X0),
inference(superposition,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
join(sK27,join(sK25,join(sK26,X0))) = join(sK27,X0),
inference(demodulation,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
join(sK27,join(join(sK25,join(sK26,X0)),X1)) = join(join(sK27,X0),X1),
inference(superposition,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
join(sK27,join(sK25,join(join(sK26,X0),X1))) = join(join(sK27,X0),X1),
inference(demodulation,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
join(sK27,join(sK25,join(sK26,join(X0,X1)))) = join(join(sK27,X0),X1),
inference(demodulation,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
join(sK27,join(X0,X1)) = join(join(sK27,X0),X1),
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
join(sK27,join(X0,X1)) = join(sK27,join(X0,X1)),
inference(demodulation,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
join(sK27,join(sK25,join(X0,sK26))) = join(sK27,X0),
inference(superposition,[status(thm)],[c0,d2]) ).
cnf(d9,plain,
join(sK27,X0) = join(sK27,join(sK25,join(X0,sK26))),
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
join(sK27,join(X1,X0)) = join(sK27,join(X0,X1)),
inference(superposition,[status(thm)],[c0,d7]) ).
cnf(d11,plain,
join(sK27,join(join(X0,X1),X2)) = join(join(sK27,join(X1,X0)),X2),
inference(superposition,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
join(sK27,join(X0,join(X1,X2))) = join(join(sK27,join(X1,X0)),X2),
inference(demodulation,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
join(sK27,join(X1,join(X0,X2))) = join(sK27,join(join(X0,X1),X2)),
inference(demodulation,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
join(sK27,join(X1,join(X0,X2))) = join(sK27,join(X0,join(X1,X2))),
inference(demodulation,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
join(sK27,X0) = join(sK27,join(X0,join(sK25,sK26))),
inference(superposition,[status(thm)],[d14,d9]) ).
cnf(d16,plain,
join(X0,join(X1,X2)) = join(join(X1,X0),X2),
inference(superposition,[status(thm)],[c0,c1]) ).
cnf(d17,plain,
X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(demodulation,[status(thm)],[c2,c0]) ).
cnf(d18,plain,
X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(demodulation,[status(thm)],[d17,c3]) ).
cnf(d19,plain,
X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(demodulation,[status(thm)],[d18,c0]) ).
cnf(d20,plain,
X0 = join(zero,complement(join(complement(X0),complement(X0)))),
inference(superposition,[status(thm)],[c12,d19]) ).
cnf(d21,plain,
X0 = join(zero,meet(X0,X0)),
inference(demodulation,[status(thm)],[d20,c3]) ).
cnf(d22,plain,
meet(X0,complement(X0)) = complement(top),
inference(superposition,[status(thm)],[c11,c3]) ).
cnf(d23,plain,
zero = complement(top),
inference(demodulation,[status(thm)],[d22,c12]) ).
cnf(d24,plain,
join(X0,join(X1,complement(join(X0,X1)))) = top,
inference(superposition,[status(thm)],[c11,c1]) ).
cnf(d25,plain,
top = join(top,zero),
inference(superposition,[status(thm)],[d23,c11]) ).
cnf(d26,plain,
join(X2,join(X0,X1)) = join(X0,join(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d27,plain,
join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c11,c1]) ).
cnf(d28,plain,
join(sK27,X0) = join(sK27,join(meet(X0,X1),complement(join(complement(X0),X1)))),
inference(superposition,[status(thm)],[d19,d7]) ).
cnf(d29,plain,
join(sK27,X0) = join(sK27,X0),
inference(demodulation,[status(thm)],[d28,d19]) ).
cnf(d30,plain,
join(sK27,join(complement(sK27),X0)) = join(top,X0),
inference(superposition,[status(thm)],[d27,d29]) ).
cnf(d31,plain,
join(top,X0) = join(top,X0),
inference(demodulation,[status(thm)],[d30,d27]) ).
cnf(d32,plain,
join(top,zero) = top,
inference(superposition,[status(thm)],[d25,d31]) ).
cnf(d33,plain,
join(X0,top) = join(top,join(zero,X0)),
inference(superposition,[status(thm)],[d32,d26]) ).
cnf(d34,plain,
zero = meet(top,zero),
inference(superposition,[status(thm)],[d23,c12]) ).
cnf(d35,plain,
meet(top,X0) = complement(join(zero,complement(X0))),
inference(superposition,[status(thm)],[d23,c3]) ).
cnf(d36,plain,
meet(X0,top) = complement(join(complement(X0),zero)),
inference(superposition,[status(thm)],[d23,c3]) ).
cnf(d37,plain,
meet(X0,top) = complement(join(zero,complement(X0))),
inference(demodulation,[status(thm)],[d36,c0]) ).
cnf(d38,plain,
meet(top,X0) = meet(X0,top),
inference(superposition,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
X0 = join(meet(top,X0),complement(join(complement(X0),top))),
inference(superposition,[status(thm)],[d38,d19]) ).
cnf(d40,plain,
X0 = join(meet(top,X0),complement(join(top,complement(X0)))),
inference(demodulation,[status(thm)],[d39,c0]) ).
cnf(d41,plain,
join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[d25,c1]) ).
cnf(d42,plain,
join(top,X0) = join(top,join(zero,X0)),
inference(superposition,[status(thm)],[d41,d31]) ).
cnf(d43,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[status(thm)],[c11,d42]) ).
cnf(d44,plain,
zero = join(meet(top,zero),complement(join(top,top))),
inference(superposition,[status(thm)],[d43,d40]) ).
cnf(d45,plain,
zero = join(zero,complement(join(top,top))),
inference(demodulation,[status(thm)],[d44,d34]) ).
cnf(d46,plain,
join(complement(join(top,top)),top) = join(top,zero),
inference(superposition,[status(thm)],[d45,d33]) ).
cnf(d47,plain,
join(top,complement(join(top,top))) = join(top,zero),
inference(demodulation,[status(thm)],[d46,c0]) ).
cnf(d48,plain,
join(top,complement(join(top,top))) = top,
inference(demodulation,[status(thm)],[d47,d25]) ).
cnf(d49,plain,
join(top,top) = top,
inference(superposition,[status(thm)],[d48,d24]) ).
cnf(d50,plain,
zero = join(zero,complement(top)),
inference(demodulation,[status(thm)],[d45,d49]) ).
cnf(d51,plain,
zero = join(zero,zero),
inference(demodulation,[status(thm)],[d50,d23]) ).
cnf(d52,plain,
join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[d51,d16]) ).
cnf(d53,plain,
join(zero,X0) = join(zero,meet(X0,X0)),
inference(superposition,[status(thm)],[d21,d52]) ).
cnf(d54,plain,
join(zero,X0) = X0,
inference(demodulation,[status(thm)],[d53,d21]) ).
cnf(d55,plain,
join(X0,zero) = join(zero,join(zero,X0)),
inference(superposition,[status(thm)],[d51,d26]) ).
cnf(d56,plain,
join(X0,zero) = join(zero,X0),
inference(demodulation,[status(thm)],[d55,d54]) ).
cnf(d57,plain,
join(X0,zero) = X0,
inference(demodulation,[status(thm)],[d56,d54]) ).
cnf(d58,plain,
top = join(join(complement(X0),complement(X1)),meet(X0,X1)),
inference(superposition,[status(thm)],[c3,c11]) ).
cnf(d59,plain,
top = join(complement(X0),join(complement(X1),meet(X0,X1))),
inference(demodulation,[status(thm)],[d58,c1]) ).
cnf(d60,plain,
X0 = meet(X0,X0),
inference(demodulation,[status(thm)],[d21,d54]) ).
cnf(d61,plain,
top = join(complement(X0),join(complement(X0),X0)),
inference(superposition,[status(thm)],[d60,d59]) ).
cnf(d62,plain,
top = join(X0,join(complement(X0),complement(X0))),
inference(demodulation,[status(thm)],[d61,d26]) ).
cnf(d63,plain,
top = join(top,complement(X0)),
inference(demodulation,[status(thm)],[d62,d27]) ).
cnf(d64,plain,
top = complement(zero),
inference(superposition,[status(thm)],[d54,c11]) ).
cnf(d65,plain,
meet(X0,zero) = complement(join(complement(X0),top)),
inference(superposition,[status(thm)],[d64,c3]) ).
cnf(d66,plain,
meet(X0,zero) = complement(join(top,complement(X0))),
inference(demodulation,[status(thm)],[d65,c0]) ).
cnf(d67,plain,
meet(X0,zero) = complement(top),
inference(demodulation,[status(thm)],[d66,d63]) ).
cnf(d68,plain,
meet(X0,zero) = zero,
inference(demodulation,[status(thm)],[d67,d23]) ).
cnf(d69,plain,
X0 = join(meet(X0,X1),complement(join(X1,complement(X0)))),
inference(superposition,[status(thm)],[c0,d19]) ).
cnf(d70,plain,
X0 = join(meet(X0,zero),complement(complement(X0))),
inference(superposition,[status(thm)],[d54,d69]) ).
cnf(d71,plain,
X0 = join(complement(complement(X0)),meet(X0,zero)),
inference(demodulation,[status(thm)],[d70,c0]) ).
cnf(d72,plain,
X0 = join(complement(complement(X0)),zero),
inference(demodulation,[status(thm)],[d71,d68]) ).
cnf(d73,plain,
X0 = complement(complement(X0)),
inference(demodulation,[status(thm)],[d72,d57]) ).
cnf(d74,plain,
converse(join(X1,converse(X0))) = join(converse(X1),X0),
inference(superposition,[status(thm)],[c7,c8]) ).
cnf(d75,plain,
converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c7,c8]) ).
cnf(d76,plain,
converse(converse(X0)) = join(X0,converse(zero)),
inference(superposition,[status(thm)],[d57,d75]) ).
cnf(d77,plain,
X0 = join(X0,converse(zero)),
inference(demodulation,[status(thm)],[d76,c7]) ).
cnf(d78,plain,
converse(X0) = join(converse(X0),zero),
inference(superposition,[status(thm)],[d77,d74]) ).
cnf(d79,plain,
converse(X0) = converse(X0),
inference(demodulation,[status(thm)],[d78,d57]) ).
cnf(d80,plain,
X0 = converse(converse(X0)),
inference(superposition,[status(thm)],[c7,d79]) ).
cnf(d81,plain,
converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c7,c9]) ).
cnf(d82,plain,
composition(converse(X0),X1) = converse(composition(converse(X1),X0)),
inference(superposition,[status(thm)],[d81,d80]) ).
cnf(d83,plain,
composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c5,d82]) ).
cnf(d84,plain,
composition(converse(one),X0) = X0,
inference(demodulation,[status(thm)],[d83,c7]) ).
cnf(d85,plain,
one = converse(one),
inference(superposition,[status(thm)],[d84,c5]) ).
cnf(d86,plain,
composition(one,X0) = X0,
inference(demodulation,[status(thm)],[d84,d85]) ).
cnf(d87,plain,
meet(X0,top) = complement(complement(X0)),
inference(demodulation,[status(thm)],[d37,d54]) ).
cnf(d88,plain,
meet(X0,top) = X0,
inference(demodulation,[status(thm)],[d87,d73]) ).
cnf(d89,plain,
join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1),
inference(demodulation,[status(thm)],[c10,c0]) ).
cnf(d90,plain,
join(meet(X0,top),composition(converse(X1),complement(composition(X1,join(zero,complement(X0)))))) = complement(join(zero,complement(X0))),
inference(superposition,[status(thm)],[d37,d89]) ).
cnf(d91,plain,
join(X0,composition(converse(X1),complement(composition(X1,join(zero,complement(X0)))))) = complement(join(zero,complement(X0))),
inference(demodulation,[status(thm)],[d90,d88]) ).
cnf(d92,plain,
join(X0,composition(converse(X1),complement(composition(X1,complement(X0))))) = complement(join(zero,complement(X0))),
inference(demodulation,[status(thm)],[d91,d54]) ).
cnf(d93,plain,
join(X0,composition(converse(X1),complement(composition(X1,complement(X0))))) = complement(complement(X0)),
inference(demodulation,[status(thm)],[d92,d54]) ).
cnf(d94,plain,
join(X0,composition(converse(X1),complement(composition(X1,complement(X0))))) = X0,
inference(demodulation,[status(thm)],[d93,d73]) ).
cnf(d95,plain,
join(X0,complement(composition(one,complement(X0)))) = X0,
inference(superposition,[status(thm)],[d84,d94]) ).
cnf(d96,plain,
join(X0,complement(complement(X0))) = X0,
inference(demodulation,[status(thm)],[d95,d86]) ).
cnf(d97,plain,
join(X0,X0) = X0,
inference(demodulation,[status(thm)],[d96,d73]) ).
cnf(d98,plain,
join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[d97,d16]) ).
cnf(d99,plain,
join(sK27,sK25) = join(sK27,join(sK25,sK26)),
inference(superposition,[status(thm)],[d98,d15]) ).
cnf(d100,plain,
join(sK27,sK25) = sK27,
inference(demodulation,[status(thm)],[d99,d0]) ).
cnf(d101,plain,
( join(sK26,sK27) != sK27
| join(sK27,sK25) != sK27 ),
inference(demodulation,[status(thm)],[c14,c0]) ).
cnf(d102,plain,
( join(sK27,sK26) != sK27
| join(sK27,sK25) != sK27 ),
inference(demodulation,[status(thm)],[d101,c0]) ).
cnf(d103,plain,
join(sK27,sK26) = join(sK27,join(sK25,sK26)),
inference(superposition,[status(thm)],[d97,d9]) ).
cnf(d104,plain,
join(sK27,sK26) = sK27,
inference(demodulation,[status(thm)],[d103,d0]) ).
cnf(d105,plain,
join(sK27,sK25) != sK27,
inference(resolution,[status(thm)],[d104,d102]) ).
cnf(d106,plain,
$false,
inference(resolution,[status(thm)],[d105,d100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 05:41:59 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.55/9.32 % SZS status Theorem for theBenchmark.p
% 61.55/9.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------