%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL026+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 : n015.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 08:24:54 AM UTC 2026
% Result : Theorem 11.21s 2.31s
% Output : CNFRefutation 11.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 13
% Syntax : Number of formulae : 136 ( 119 unt; 0 def)
% Number of atoms : 157 ( 156 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 35 ~; 15 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 193 ( 4 sgn 26 !; 2 ?)
% 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,X1] :
( join(X0,one) = one
=> ( join(composition(X0,X1),meet(composition(X0,top),X1)) = meet(composition(X0,top),X1)
& join(meet(composition(X0,top),X1),composition(X0,X1)) = composition(X0,X1) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( join(X0,one) = one
=> ( join(composition(X0,X1),meet(composition(X0,top),X1)) = meet(composition(X0,top),X1)
& join(meet(composition(X0,top),X1),composition(X0,X1)) = composition(X0,X1) ) ),
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_2640,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_2640]) ).
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_2641,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_2641]) ).
fof(nnf_14,plain,
? [X0,X1] :
( ( meet(composition(X0,top),X1) != join(composition(X0,X1),meet(composition(X0,top),X1))
| composition(X0,X1) != join(meet(composition(X0,top),X1),composition(X0,X1)) )
& join(X0,one) = one ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ( meet(composition(sK0,top),sK1) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1))
| composition(sK0,sK1) != join(meet(composition(sK0,top),sK1),composition(sK0,sK1)) )
& join(sK0,one) = one ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[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(composition(sK0,top),sK1) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1))
| composition(sK0,sK1) != join(meet(composition(sK0,top),sK1),composition(sK0,sK1)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_2642,negated_conjecture,
( meet(composition(sK0,top),sK1) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1))
| composition(sK0,sK1) != join(complement(join(complement(composition(sK0,top)),complement(sK1))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_19,c_33]) ).
cnf(c_2643,negated_conjecture,
( meet(composition(sK0,top),sK1) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1))
| composition(sK0,sK1) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_15,c_2642]) ).
cnf(c_2644,negated_conjecture,
( complement(join(complement(composition(sK0,top)),complement(sK1))) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1))
| composition(sK0,sK1) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_19,c_2643]) ).
cnf(c_2645,negated_conjecture,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(composition(sK0,sK1),meet(composition(sK0,top),sK1))
| composition(sK0,sK1) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_15,c_2644]) ).
cnf(c_2646,negated_conjecture,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(composition(sK0,sK1),complement(join(complement(composition(sK0,top)),complement(sK1))))
| composition(sK0,sK1) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_19,c_2645]) ).
cnf(c_2647,negated_conjecture,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(composition(sK0,sK1),complement(join(complement(sK1),complement(composition(sK0,top)))))
| composition(sK0,sK1) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_15,c_2646]) ).
cnf(c_2648,negated_conjecture,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1))
| composition(sK0,sK1) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_15,c_2647]) ).
cnf(c_2649,negated_conjecture,
( complement(join(complement(sK1),complement(composition(sK0,top)))) != join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1))
| join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != composition(sK0,sK1) ),
inference(copy,[status(thm)],[c_2648]) ).
cnf(c_34,negated_conjecture,
( join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != complement(join(complement(sK1),complement(composition(sK0,top))))
| join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != composition(sK0,sK1) ),
inference(copy,[status(thm)],[c_2649]) ).
cnf(c_2650,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_2650]) ).
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_2651,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_41,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_2651]) ).
cnf(c_2652,plain,
converse(join(composition(A,B),composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_22,c_25]) ).
cnf(c_2653,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_24,c_2652]) ).
cnf(c_2654,plain,
join(composition(converse(B),converse(A)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_25,c_2653]) ).
cnf(c_2655,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_25,c_2654]) ).
cnf(c_2656,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),join(converse(A),converse(C))),
inference(paramod,[status(thm)],[c_24,c_2655]) ).
cnf(c_42,plain,
composition(converse(A),join(converse(B),converse(C))) = join(composition(converse(A),converse(B)),composition(converse(A),converse(C))),
inference(copy,[status(thm)],[c_2656]) ).
cnf(c_2657,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_48,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_2657]) ).
cnf(c_2658,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_2659,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_30,c_2658]) ).
cnf(c_49,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_2659]) ).
cnf(c_2660,plain,
composition(one,A) = join(composition(one,A),composition(sK0,A)),
inference(paramod,[status(thm)],[c_32,c_22]) ).
cnf(c_58,plain,
join(composition(one,A),composition(sK0,A)) = composition(one,A),
inference(copy,[status(thm)],[c_2660]) ).
cnf(c_2661,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_41]) ).
cnf(c_72,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_2661]) ).
cnf(c_2662,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_72,c_21]) ).
cnf(c_74,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_2662]) ).
cnf(c_78,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_72,c_27]) ).
cnf(c_79,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_74,c_72]) ).
cnf(c_2663,plain,
join(A,composition(sK0,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_79,c_58]) ).
cnf(c_81,plain,
join(A,composition(sK0,A)) = A,
inference(paramod,[status(thm)],[c_79,c_2663]) ).
cnf(c_82,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_79,c_78]) ).
cnf(c_83,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_82,c_49]) ).
cnf(c_2664,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_38]) ).
cnf(c_2665,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_2664]) ).
cnf(c_2666,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_2665]) ).
cnf(c_86,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_2666]) ).
cnf(c_87,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_86,c_48]) ).
cnf(c_88,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_87,c_86]) ).
cnf(c_89,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_87,c_83]) ).
cnf(c_90,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_89,c_88]) ).
cnf(c_2667,plain,
join(A,B) = join(B,join(A,composition(sK0,B))),
inference(paramod,[status(thm)],[c_81,c_36]) ).
cnf(c_112,plain,
join(A,join(B,composition(sK0,A))) = join(B,A),
inference(copy,[status(thm)],[c_2667]) ).
cnf(c_2668,plain,
composition(A,join(converse(B),converse(C))) = join(composition(converse(converse(A)),converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_23,c_42]) ).
cnf(c_2669,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_23,c_2668]) ).
cnf(c_114,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_23,c_2669]) ).
cnf(c_2670,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_87,c_18]) ).
cnf(c_128,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_87,c_2670]) ).
cnf(c_2671,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_87,c_37]) ).
cnf(c_130,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_87,c_2671]) ).
cnf(c_2672,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_90,c_87]) ).
cnf(c_2673,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_87,c_2672]) ).
cnf(c_137,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_2673]) ).
cnf(c_2674,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_137,c_16]) ).
cnf(c_143,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_2674]) ).
cnf(c_2675,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_23,c_114]) ).
cnf(c_404,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_23,c_2675]) ).
cnf(c_2676,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_128,c_143]) ).
cnf(c_2677,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_15,c_2676]) ).
cnf(c_516,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_128,c_2677]) ).
cnf(c_532,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_516]) ).
cnf(c_2678,plain,
join(A,complement(join(B,complement(A)))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_87,c_532]) ).
cnf(c_553,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_87,c_2678]) ).
cnf(c_2679,plain,
join(complement(complement(A)),complement(join(complement(join(A,complement(B))),complement(complement(join(A,B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_128,c_130]) ).
cnf(c_2680,plain,
join(A,complement(join(complement(join(A,complement(B))),complement(complement(join(A,B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_87,c_2679]) ).
cnf(c_2681,plain,
join(A,complement(join(complement(join(A,complement(B))),join(A,B)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_87,c_2680]) ).
cnf(c_2682,plain,
join(A,complement(join(join(A,B),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_15,c_2681]) ).
cnf(c_2683,plain,
join(A,complement(join(A,join(B,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_16,c_2682]) ).
cnf(c_2684,plain,
join(A,complement(join(A,B))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_553,c_2683]) ).
cnf(c_611,plain,
join(A,complement(join(A,B))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_87,c_2684]) ).
cnf(c_2685,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_23,c_404]) ).
cnf(c_2407,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_23,c_2685]) ).
cnf(c_2686,plain,
composition(A,top) = join(composition(A,B),composition(A,complement(B))),
inference(paramod,[status(thm)],[c_28,c_2407]) ).
cnf(c_2435,plain,
join(composition(A,B),composition(A,complement(B))) = composition(A,top),
inference(copy,[status(thm)],[c_2686]) ).
cnf(c_2687,plain,
join(complement(A),composition(sK0,top)) = join(composition(sK0,A),complement(A)),
inference(paramod,[status(thm)],[c_2435,c_112]) ).
cnf(c_2509,plain,
join(complement(A),composition(sK0,top)) = join(complement(A),composition(sK0,A)),
inference(paramod,[status(thm)],[c_15,c_2687]) ).
cnf(c_2688,plain,
join(complement(join(complement(A),composition(sK0,top))),complement(join(composition(sK0,A),complement(complement(A))))) = complement(composition(sK0,A)),
inference(paramod,[status(thm)],[c_2509,c_130]) ).
cnf(c_2689,plain,
join(complement(join(complement(A),composition(sK0,top))),complement(join(composition(sK0,A),A))) = complement(composition(sK0,A)),
inference(paramod,[status(thm)],[c_87,c_2688]) ).
cnf(c_2690,plain,
join(complement(join(complement(A),composition(sK0,top))),complement(join(A,composition(sK0,A)))) = complement(composition(sK0,A)),
inference(paramod,[status(thm)],[c_15,c_2689]) ).
cnf(c_2691,plain,
join(complement(join(complement(A),composition(sK0,top))),complement(A)) = complement(composition(sK0,A)),
inference(paramod,[status(thm)],[c_81,c_2690]) ).
cnf(c_2692,plain,
join(complement(A),complement(join(complement(A),composition(sK0,top)))) = complement(composition(sK0,A)),
inference(paramod,[status(thm)],[c_15,c_2691]) ).
cnf(c_2693,plain,
join(complement(A),complement(composition(sK0,top))) = complement(composition(sK0,A)),
inference(paramod,[status(thm)],[c_611,c_2692]) ).
cnf(c_2535,plain,
complement(composition(sK0,A)) = join(complement(A),complement(composition(sK0,top))),
inference(copy,[status(thm)],[c_2693]) ).
cnf(c_2694,plain,
meet(A,composition(sK0,top)) = complement(complement(composition(sK0,A))),
inference(paramod,[status(thm)],[c_2535,c_19]) ).
cnf(c_2695,plain,
complement(join(complement(A),complement(composition(sK0,top)))) = complement(complement(composition(sK0,A))),
inference(paramod,[status(thm)],[c_19,c_2694]) ).
cnf(c_2696,plain,
complement(join(complement(A),complement(composition(sK0,top)))) = composition(sK0,A),
inference(paramod,[status(thm)],[c_87,c_2695]) ).
cnf(c_2584,plain,
composition(sK0,A) = complement(join(complement(A),complement(composition(sK0,top)))),
inference(copy,[status(thm)],[c_2696]) ).
cnf(c_2697,plain,
( join(complement(complement(composition(sK0,sK1))),composition(sK0,sK1)) != complement(join(complement(sK1),complement(composition(sK0,top))))
| join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != composition(sK0,sK1) ),
inference(paramod,[status(thm)],[c_2535,c_34]) ).
cnf(c_2698,plain,
( join(composition(sK0,sK1),composition(sK0,sK1)) != complement(join(complement(sK1),complement(composition(sK0,top))))
| join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != composition(sK0,sK1) ),
inference(paramod,[status(thm)],[c_87,c_2697]) ).
cnf(c_2699,plain,
( composition(sK0,sK1) != complement(join(complement(sK1),complement(composition(sK0,top))))
| join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != composition(sK0,sK1) ),
inference(paramod,[status(thm)],[c_137,c_2698]) ).
cnf(c_2586,plain,
join(complement(join(complement(sK1),complement(composition(sK0,top)))),composition(sK0,sK1)) != composition(sK0,sK1),
inference(resolve,[status(thm)],[c_2584,c_2699]) ).
cnf(c_2700,plain,
join(complement(complement(composition(sK0,sK1))),composition(sK0,sK1)) != composition(sK0,sK1),
inference(paramod,[status(thm)],[c_2535,c_2586]) ).
cnf(c_2701,plain,
join(composition(sK0,sK1),composition(sK0,sK1)) != composition(sK0,sK1),
inference(paramod,[status(thm)],[c_87,c_2700]) ).
cnf(c_2702,plain,
composition(sK0,sK1) != composition(sK0,sK1),
inference(paramod,[status(thm)],[c_137,c_2701]) ).
cnf(c_2639,plain,
$false,
inference(copy,[status(thm)],[c_2702]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL026+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 05:35:43 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 3245220 was started by sandbox2 on n015,
% 0.12/0.38 % Sat Sep 26 05:35:43 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 11.21/2.31
% 11.21/2.31 % SZS status Theorem for theBenchmark
% 11.21/2.31
% 11.21/2.31 % Proof 1 at 1.29 (+ 0.50) seconds.
% 11.21/2.31 % Length of proof is 70.
% 11.21/2.31 % Level of proof is 19.
% 11.21/2.31 % Maximum clause weight is 49.000.
% 11.21/2.31 % Given clauses 389.
% 11.21/2.31
% 11.21/2.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------