%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL027+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 08:24:55 AM UTC 2026
% Result : Theorem 10.82s 1.83s
% Output : CNFRefutation 10.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 13
% Syntax : Number of formulae : 185 ( 151 unt; 0 def)
% Number of atoms : 223 ( 222 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 104 ( 66 ~; 32 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 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 : 219 ( 12 sgn 24 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('theBenchmark.p',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('theBenchmark.p',maddux2_join_associativity) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('theBenchmark.p',maddux4_definiton_of_meet) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0,
file('theBenchmark.p',composition_identity) ).
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('theBenchmark.p',composition_distributivity) ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0,
file('theBenchmark.p',converse_idempotence) ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('theBenchmark.p',converse_additivity) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('theBenchmark.p',converse_multiplicativity) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('theBenchmark.p',converse_cancellativity) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)),
file('theBenchmark.p',def_top) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('theBenchmark.p',def_zero) ).
fof(goals,conjecture,
! [X0] :
( join(X0,one) = one
=> ( join(meet(complement(X0),one),meet(complement(composition(X0,top)),one)) = meet(complement(composition(X0,top)),one)
& join(meet(complement(composition(X0,top)),one),meet(complement(X0),one)) = meet(complement(X0),one) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( join(X0,one) = one
=> ( join(meet(complement(X0),one),meet(complement(composition(X0,top)),one)) = meet(complement(composition(X0,top)),one)
& join(meet(complement(composition(X0,top)),one),meet(complement(X0),one)) = meet(complement(X0),one) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_15,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_16,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_17,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A,
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
cnf(c_18,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_15,c_17]) ).
cnf(c_19,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_21,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
cnf(c_22,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_23,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_24,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_25,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_26,plain,
complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)),
inference(clausify,[status(thm)],[converse_cancellativity]) ).
cnf(c_2709,plain,
complement(A) = join(complement(A),composition(converse(B),complement(composition(B,A)))),
inference(paramod,[status(thm)],[c_15,c_26]) ).
cnf(c_27,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(copy,[status(thm)],[c_2709]) ).
cnf(c_28,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_29,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_2710,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_19,c_29]) ).
cnf(c_30,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_28,c_2710]) ).
fof(nnf_14,plain,
? [X0] :
( ( meet(complement(composition(X0,top)),one) != join(meet(complement(X0),one),meet(complement(composition(X0,top)),one))
| meet(complement(X0),one) != join(meet(complement(composition(X0,top)),one),meet(complement(X0),one)) )
& join(X0,one) = one ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ( meet(complement(composition(sK0,top)),one) != join(meet(complement(sK0),one),meet(complement(composition(sK0,top)),one))
| meet(complement(sK0),one) != join(meet(complement(composition(sK0,top)),one),meet(complement(sK0),one)) )
& join(sK0,one) = one ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
join(sK0,one) = one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_32,negated_conjecture,
join(one,sK0) = one,
inference(paramod,[status(thm)],[c_15,c_31]) ).
cnf(c_33,negated_conjecture,
( meet(complement(composition(sK0,top)),one) != join(meet(complement(sK0),one),meet(complement(composition(sK0,top)),one))
| meet(complement(sK0),one) != join(meet(complement(composition(sK0,top)),one),meet(complement(sK0),one)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_2711,negated_conjecture,
( meet(complement(composition(sK0,top)),one) != join(meet(complement(sK0),one),meet(complement(composition(sK0,top)),one))
| complement(join(complement(complement(sK0)),complement(one))) != join(meet(complement(composition(sK0,top)),one),meet(complement(sK0),one)) ),
inference(paramod,[status(thm)],[c_19,c_33]) ).
cnf(c_2712,negated_conjecture,
( meet(complement(composition(sK0,top)),one) != join(meet(complement(sK0),one),meet(complement(composition(sK0,top)),one))
| complement(join(complement(one),complement(complement(sK0)))) != join(meet(complement(composition(sK0,top)),one),meet(complement(sK0),one)) ),
inference(paramod,[status(thm)],[c_15,c_2711]) ).
cnf(c_2713,negated_conjecture,
( meet(complement(composition(sK0,top)),one) != join(meet(complement(sK0),one),meet(complement(composition(sK0,top)),one))
| complement(join(complement(one),complement(complement(sK0)))) != join(complement(join(complement(complement(composition(sK0,top))),complement(one))),meet(complement(sK0),one)) ),
inference(paramod,[status(thm)],[c_19,c_2712]) ).
cnf(c_2714,negated_conjecture,
( meet(complement(composition(sK0,top)),one) != join(meet(complement(sK0),one),meet(complement(composition(sK0,top)),one))
| complement(join(complement(one),complement(complement(sK0)))) != join(complement(join(complement(one),complement(complement(composition(sK0,top))))),meet(complement(sK0),one)) ),
inference(paramod,[status(thm)],[c_15,c_2713]) ).
cnf(c_2715,negated_conjecture,
( meet(complement(composition(sK0,top)),one) != join(meet(complement(sK0),one),meet(complement(composition(sK0,top)),one))
| complement(join(complement(one),complement(complement(sK0)))) != join(complement(join(complement(one),complement(complement(composition(sK0,top))))),complement(join(complement(complement(sK0)),complement(one)))) ),
inference(paramod,[status(thm)],[c_19,c_2714]) ).
cnf(c_2716,negated_conjecture,
( meet(complement(composition(sK0,top)),one) != join(meet(complement(sK0),one),meet(complement(composition(sK0,top)),one))
| complement(join(complement(one),complement(complement(sK0)))) != join(complement(join(complement(one),complement(complement(composition(sK0,top))))),complement(join(complement(one),complement(complement(sK0))))) ),
inference(paramod,[status(thm)],[c_15,c_2715]) ).
cnf(c_2717,negated_conjecture,
( meet(complement(composition(sK0,top)),one) != join(meet(complement(sK0),one),meet(complement(composition(sK0,top)),one))
| complement(join(complement(one),complement(complement(sK0)))) != join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) ),
inference(paramod,[status(thm)],[c_15,c_2716]) ).
cnf(c_2718,negated_conjecture,
( complement(join(complement(complement(composition(sK0,top))),complement(one))) != join(meet(complement(sK0),one),meet(complement(composition(sK0,top)),one))
| complement(join(complement(one),complement(complement(sK0)))) != join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) ),
inference(paramod,[status(thm)],[c_19,c_2717]) ).
cnf(c_2719,negated_conjecture,
( complement(join(complement(one),complement(complement(composition(sK0,top))))) != join(meet(complement(sK0),one),meet(complement(composition(sK0,top)),one))
| complement(join(complement(one),complement(complement(sK0)))) != join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) ),
inference(paramod,[status(thm)],[c_15,c_2718]) ).
cnf(c_2720,negated_conjecture,
( complement(join(complement(one),complement(complement(composition(sK0,top))))) != join(complement(join(complement(complement(sK0)),complement(one))),meet(complement(composition(sK0,top)),one))
| complement(join(complement(one),complement(complement(sK0)))) != join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) ),
inference(paramod,[status(thm)],[c_19,c_2719]) ).
cnf(c_2721,negated_conjecture,
( complement(join(complement(one),complement(complement(composition(sK0,top))))) != join(complement(join(complement(one),complement(complement(sK0)))),meet(complement(composition(sK0,top)),one))
| complement(join(complement(one),complement(complement(sK0)))) != join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) ),
inference(paramod,[status(thm)],[c_15,c_2720]) ).
cnf(c_2722,negated_conjecture,
( complement(join(complement(one),complement(complement(composition(sK0,top))))) != join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(complement(composition(sK0,top))),complement(one))))
| complement(join(complement(one),complement(complement(sK0)))) != join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) ),
inference(paramod,[status(thm)],[c_19,c_2721]) ).
cnf(c_2723,negated_conjecture,
( complement(join(complement(one),complement(complement(composition(sK0,top))))) != join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top))))))
| complement(join(complement(one),complement(complement(sK0)))) != join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) ),
inference(paramod,[status(thm)],[c_15,c_2722]) ).
cnf(c_2724,negated_conjecture,
( complement(join(complement(one),complement(complement(composition(sK0,top))))) != join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top))))))
| join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) != complement(join(complement(one),complement(complement(sK0)))) ),
inference(copy,[status(thm)],[c_2723]) ).
cnf(c_34,negated_conjecture,
( join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) != complement(join(complement(one),complement(complement(composition(sK0,top)))))
| join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) != complement(join(complement(one),complement(complement(sK0)))) ),
inference(copy,[status(thm)],[c_2724]) ).
cnf(c_2725,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_15,c_16]) ).
cnf(c_36,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_16,c_2725]) ).
cnf(c_37,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_38,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_2726,plain,
join(A,B) = join(complement(join(complement(A),C)),join(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_18,c_16]) ).
cnf(c_39,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_2726]) ).
cnf(c_2727,plain,
join(complement(join(complement(join(complement(A),B)),join(complement(A),complement(B)))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_18,c_18]) ).
cnf(c_2728,plain,
join(complement(join(join(complement(A),complement(B)),complement(join(complement(A),B)))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_15,c_2727]) ).
cnf(c_2729,plain,
join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_16,c_2728]) ).
cnf(c_41,plain,
join(complement(A),complement(join(complement(A),join(complement(B),complement(join(complement(A),B)))))) = join(complement(A),B),
inference(paramod,[status(thm)],[c_15,c_2729]) ).
cnf(c_2730,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_45,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_2730]) ).
cnf(c_2731,plain,
join(complement(A),B) = join(complement(A),join(composition(converse(C),complement(composition(C,A))),B)),
inference(paramod,[status(thm)],[c_27,c_16]) ).
cnf(c_47,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(complement(A),C),
inference(copy,[status(thm)],[c_2731]) ).
cnf(c_2732,plain,
join(top,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_28,c_16]) ).
cnf(c_55,plain,
join(A,join(complement(A),B)) = join(top,B),
inference(copy,[status(thm)],[c_2732]) ).
cnf(c_2733,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_57,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_2733]) ).
cnf(c_2734,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_28,c_22]) ).
cnf(c_59,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_2734]) ).
cnf(c_2735,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_60,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_2735]) ).
cnf(c_2736,plain,
composition(one,A) = join(composition(one,A),composition(sK0,A)),
inference(paramod,[status(thm)],[c_32,c_22]) ).
cnf(c_67,plain,
join(composition(one,A),composition(sK0,A)) = composition(one,A),
inference(copy,[status(thm)],[c_2736]) ).
cnf(c_2737,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_38]) ).
cnf(c_2738,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_2737]) ).
cnf(c_2739,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_2738]) ).
cnf(c_93,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_2739]) ).
cnf(c_2740,plain,
join(complement(join(complement(join(complement(A),complement(B))),join(complement(B),A))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_38,c_38]) ).
cnf(c_2741,plain,
join(complement(join(join(complement(B),A),complement(join(complement(A),complement(B))))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_15,c_2740]) ).
cnf(c_2742,plain,
join(complement(join(complement(B),join(A,complement(join(complement(A),complement(B)))))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_16,c_2741]) ).
cnf(c_98,plain,
join(complement(A),complement(join(complement(A),join(B,complement(join(complement(B),complement(A))))))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_15,c_2742]) ).
cnf(c_99,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_93,c_57]) ).
cnf(c_100,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_99,c_93]) ).
cnf(c_2743,negated_conjecture,
( join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) != complement(join(complement(one),complement(complement(composition(sK0,top)))))
| join(complement(join(complement(one),sK0)),complement(join(complement(one),complement(complement(composition(sK0,top)))))) != complement(join(complement(one),complement(complement(sK0)))) ),
inference(paramod,[status(thm)],[c_99,c_34]) ).
cnf(c_2744,negated_conjecture,
( join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) != complement(join(complement(one),complement(complement(composition(sK0,top)))))
| join(complement(join(sK0,complement(one))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) != complement(join(complement(one),complement(complement(sK0)))) ),
inference(paramod,[status(thm)],[c_15,c_2743]) ).
cnf(c_2745,negated_conjecture,
( join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) != complement(join(complement(one),complement(complement(composition(sK0,top)))))
| join(complement(join(sK0,complement(one))),complement(join(complement(one),composition(sK0,top)))) != complement(join(complement(one),complement(complement(sK0)))) ),
inference(paramod,[status(thm)],[c_99,c_2744]) ).
cnf(c_2746,negated_conjecture,
( join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) != complement(join(complement(one),complement(complement(composition(sK0,top)))))
| join(complement(join(sK0,complement(one))),complement(join(complement(one),composition(sK0,top)))) != complement(join(complement(one),sK0)) ),
inference(paramod,[status(thm)],[c_99,c_2745]) ).
cnf(c_2747,negated_conjecture,
( join(complement(join(complement(one),complement(complement(sK0)))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) != complement(join(complement(one),complement(complement(composition(sK0,top)))))
| join(complement(join(sK0,complement(one))),complement(join(complement(one),composition(sK0,top)))) != complement(join(sK0,complement(one))) ),
inference(paramod,[status(thm)],[c_15,c_2746]) ).
cnf(c_2748,negated_conjecture,
( join(complement(join(complement(one),sK0)),complement(join(complement(one),complement(complement(composition(sK0,top)))))) != complement(join(complement(one),complement(complement(composition(sK0,top)))))
| join(complement(join(sK0,complement(one))),complement(join(complement(one),composition(sK0,top)))) != complement(join(sK0,complement(one))) ),
inference(paramod,[status(thm)],[c_99,c_2747]) ).
cnf(c_2749,negated_conjecture,
( join(complement(join(sK0,complement(one))),complement(join(complement(one),complement(complement(composition(sK0,top)))))) != complement(join(complement(one),complement(complement(composition(sK0,top)))))
| join(complement(join(sK0,complement(one))),complement(join(complement(one),composition(sK0,top)))) != complement(join(sK0,complement(one))) ),
inference(paramod,[status(thm)],[c_15,c_2748]) ).
cnf(c_2750,negated_conjecture,
( join(complement(join(sK0,complement(one))),complement(join(complement(one),composition(sK0,top)))) != complement(join(complement(one),complement(complement(composition(sK0,top)))))
| join(complement(join(sK0,complement(one))),complement(join(complement(one),composition(sK0,top)))) != complement(join(sK0,complement(one))) ),
inference(paramod,[status(thm)],[c_99,c_2749]) ).
cnf(c_102,negated_conjecture,
( join(complement(join(sK0,complement(one))),complement(join(complement(one),composition(sK0,top)))) != complement(join(complement(one),composition(sK0,top)))
| join(complement(join(sK0,complement(one))),complement(join(complement(one),composition(sK0,top)))) != complement(join(sK0,complement(one))) ),
inference(paramod,[status(thm)],[c_99,c_2750]) ).
cnf(c_2751,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_45]) ).
cnf(c_109,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_2751]) ).
cnf(c_2752,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_109,c_21]) ).
cnf(c_111,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_2752]) ).
cnf(c_115,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_109,c_27]) ).
cnf(c_116,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_111,c_109]) ).
cnf(c_2753,plain,
join(A,composition(sK0,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_116,c_67]) ).
cnf(c_118,plain,
join(A,composition(sK0,A)) = A,
inference(paramod,[status(thm)],[c_116,c_2753]) ).
cnf(c_119,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_116,c_115]) ).
cnf(c_2754,plain,
join(complement(join(complement(A),B)),B) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_37,c_39]) ).
cnf(c_2755,plain,
join(B,complement(join(complement(A),B))) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_15,c_2754]) ).
cnf(c_139,plain,
join(A,complement(join(complement(B),A))) = join(B,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_99,c_2755]) ).
cnf(c_2756,plain,
join(A,join(complement(B),C)) = join(complement(B),join(A,complement(join(complement(B),join(complement(C),complement(join(complement(B),C))))))),
inference(paramod,[status(thm)],[c_41,c_36]) ).
cnf(c_152,plain,
join(complement(A),join(B,complement(join(complement(A),join(complement(C),complement(join(complement(A),C))))))) = join(B,join(complement(A),C)),
inference(copy,[status(thm)],[c_2756]) ).
cnf(c_2757,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),complement(complement(A))))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_41,c_37]) ).
cnf(c_2758,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),A))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_99,c_2757]) ).
cnf(c_154,plain,
join(complement(join(complement(A),B)),complement(join(A,complement(join(complement(A),join(complement(B),complement(join(complement(A),B)))))))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_15,c_2758]) ).
cnf(c_2759,plain,
join(A,B) = join(B,join(A,composition(sK0,B))),
inference(paramod,[status(thm)],[c_118,c_36]) ).
cnf(c_179,plain,
join(A,join(B,composition(sK0,A))) = join(B,A),
inference(copy,[status(thm)],[c_2759]) ).
cnf(c_2760,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_119,c_18]) ).
cnf(c_2761,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_15,c_2760]) ).
cnf(c_2762,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_28,c_2761]) ).
cnf(c_2763,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_30,c_2762]) ).
cnf(c_190,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_99,c_2763]) ).
cnf(c_2764,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_119,c_39]) ).
cnf(c_2765,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_18,c_2764]) ).
cnf(c_193,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_2765]) ).
cnf(c_202,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_190,c_100]) ).
cnf(c_205,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_193,c_98]) ).
cnf(c_2766,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_202,c_18]) ).
cnf(c_2767,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_202,c_2766]) ).
cnf(c_2768,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_18,c_2767]) ).
cnf(c_268,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_2768]) ).
cnf(c_2769,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_268,c_39]) ).
cnf(c_2770,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_15,c_2769]) ).
cnf(c_2771,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_193,c_2770]) ).
cnf(c_272,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_15,c_2771]) ).
cnf(c_2772,plain,
join(complement(join(complement(A),B)),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_272,c_154]) ).
cnf(c_2773,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_15,c_2772]) ).
cnf(c_2774,plain,
join(complement(B),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_205,c_2773]) ).
cnf(c_274,plain,
join(complement(A),join(complement(B),complement(join(complement(A),B)))) = join(complement(B),complement(A)),
inference(copy,[status(thm)],[c_2774]) ).
cnf(c_277,plain,
join(complement(A),join(B,complement(join(complement(C),complement(A))))) = join(B,join(complement(A),C)),
inference(paramod,[status(thm)],[c_274,c_152]) ).
cnf(c_2775,plain,
join(A,complement(A)) = join(top,complement(A)),
inference(paramod,[status(thm)],[c_268,c_55]) ).
cnf(c_2776,plain,
top = join(top,complement(A)),
inference(paramod,[status(thm)],[c_28,c_2775]) ).
cnf(c_423,plain,
join(top,complement(A)) = top,
inference(copy,[status(thm)],[c_2776]) ).
cnf(c_2777,plain,
join(A,join(complement(A),top)) = top,
inference(paramod,[status(thm)],[c_268,c_55]) ).
cnf(c_2778,plain,
join(A,join(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_15,c_2777]) ).
cnf(c_424,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_423,c_2778]) ).
cnf(c_449,plain,
join(A,composition(complement(one),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_116,c_59]) ).
cnf(c_2779,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_424,c_15]) ).
cnf(c_454,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_2779]) ).
cnf(c_2780,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_424,c_24]) ).
cnf(c_456,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_2780]) ).
cnf(c_471,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_23,c_456]) ).
cnf(c_474,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_471,c_454]) ).
cnf(c_483,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_474,c_60]) ).
cnf(c_634,plain,
join(one,converse(complement(one))) = top,
inference(paramod,[status(thm)],[c_111,c_483]) ).
cnf(c_2781,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_449,c_24]) ).
cnf(c_2782,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_25,c_2781]) ).
cnf(c_2783,plain,
composition(converse(A),top) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_474,c_2782]) ).
cnf(c_2784,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(complement(one)))),
inference(paramod,[status(thm)],[c_25,c_2783]) ).
cnf(c_832,plain,
join(converse(A),composition(converse(A),converse(complement(one)))) = composition(converse(A),top),
inference(copy,[status(thm)],[c_2784]) ).
cnf(c_2785,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(complement(C),complement(A))))) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_139,c_47]) ).
cnf(c_2786,plain,
join(composition(converse(B),complement(composition(B,A))),join(complement(A),C)) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_277,c_2785]) ).
cnf(c_2787,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_36,c_2786]) ).
cnf(c_2788,plain,
join(complement(A),C) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_47,c_2787]) ).
cnf(c_2789,plain,
join(complement(A),C) = join(C,complement(join(A,C))),
inference(paramod,[status(thm)],[c_99,c_2788]) ).
cnf(c_1190,plain,
join(A,complement(join(B,A))) = join(complement(B),A),
inference(copy,[status(thm)],[c_2789]) ).
cnf(c_2790,plain,
join(converse(complement(one)),complement(top)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_634,c_1190]) ).
cnf(c_2791,plain,
join(converse(complement(one)),zero) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_30,c_2790]) ).
cnf(c_2792,plain,
join(zero,converse(complement(one))) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_15,c_2791]) ).
cnf(c_2793,plain,
converse(complement(one)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_190,c_2792]) ).
cnf(c_1269,plain,
join(complement(one),converse(complement(one))) = converse(complement(one)),
inference(copy,[status(thm)],[c_2793]) ).
cnf(c_2794,plain,
converse(converse(complement(one))) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_1269,c_24]) ).
cnf(c_2795,plain,
complement(one) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_23,c_2794]) ).
cnf(c_2796,plain,
complement(one) = join(converse(complement(one)),complement(one)),
inference(paramod,[status(thm)],[c_23,c_2795]) ).
cnf(c_2797,plain,
complement(one) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_15,c_2796]) ).
cnf(c_2798,plain,
complement(one) = converse(complement(one)),
inference(paramod,[status(thm)],[c_1269,c_2797]) ).
cnf(c_1481,plain,
converse(complement(one)) = complement(one),
inference(copy,[status(thm)],[c_2798]) ).
cnf(c_1489,plain,
join(converse(A),composition(converse(A),complement(one))) = composition(converse(A),top),
inference(paramod,[status(thm)],[c_1481,c_832]) ).
cnf(c_2799,plain,
join(A,composition(converse(converse(A)),complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_23,c_1489]) ).
cnf(c_2800,plain,
join(A,composition(A,complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_23,c_2799]) ).
cnf(c_2670,plain,
join(A,composition(A,complement(one))) = composition(A,top),
inference(paramod,[status(thm)],[c_23,c_2800]) ).
cnf(c_2701,plain,
join(complement(one),composition(sK0,top)) = join(sK0,complement(one)),
inference(paramod,[status(thm)],[c_2670,c_179]) ).
cnf(c_2801,negated_conjecture,
( join(complement(join(sK0,complement(one))),complement(join(complement(one),composition(sK0,top)))) != complement(join(complement(one),composition(sK0,top)))
| join(complement(join(sK0,complement(one))),complement(join(sK0,complement(one)))) != complement(join(sK0,complement(one))) ),
inference(paramod,[status(thm)],[c_2701,c_102]) ).
cnf(c_2802,negated_conjecture,
( join(complement(join(sK0,complement(one))),complement(join(complement(one),composition(sK0,top)))) != complement(join(complement(one),composition(sK0,top)))
| complement(join(sK0,complement(one))) != complement(join(sK0,complement(one))) ),
inference(paramod,[status(thm)],[c_268,c_2801]) ).
cnf(c_2803,negated_conjecture,
( join(complement(join(sK0,complement(one))),complement(join(sK0,complement(one)))) != complement(join(complement(one),composition(sK0,top)))
| complement(join(sK0,complement(one))) != complement(join(sK0,complement(one))) ),
inference(paramod,[status(thm)],[c_2701,c_2802]) ).
cnf(c_2804,negated_conjecture,
( complement(join(sK0,complement(one))) != complement(join(complement(one),composition(sK0,top)))
| complement(join(sK0,complement(one))) != complement(join(sK0,complement(one))) ),
inference(paramod,[status(thm)],[c_268,c_2803]) ).
cnf(c_2805,negated_conjecture,
( complement(join(sK0,complement(one))) != complement(join(sK0,complement(one)))
| complement(join(sK0,complement(one))) != complement(join(sK0,complement(one))) ),
inference(paramod,[status(thm)],[c_2701,c_2804]) ).
cnf(c_2806,negated_conjecture,
complement(join(sK0,complement(one))) != complement(join(sK0,complement(one))),
inference(copy,[status(thm)],[c_2805]) ).
cnf(c_2708,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_2806]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL027+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n005.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 05:32:48 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 1321493 was started by sandbox2 on n005,
% 0.17/0.43 % Sat Sep 26 05:32:48 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 10.82/1.83
% 10.82/1.83 % SZS status Theorem for theBenchmark
% 10.82/1.83
% 10.82/1.83 % Proof 1 at 1.06 (+ 0.29) seconds.
% 10.82/1.83 % Length of proof is 84.
% 10.82/1.83 % Level of proof is 22.
% 10.82/1.83 % Maximum clause weight is 117.000.
% 10.82/1.83 % Given clauses 219.
% 10.82/1.83
% 10.82/1.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------