%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL008+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 08:24:46 AM UTC 2026
% Result : Theorem 12.04s 1.98s
% Output : CNFRefutation 12.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 11
% Syntax : Number of formulae : 113 ( 90 unt; 0 def)
% Number of atoms : 136 ( 135 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 67 ( 44 ~; 21 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 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 : 132 ( 0 sgn 25 !; 3 ?)
% 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_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(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,X2] :
( join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2))) = composition(X0,join(X1,X2))
& join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) = join(composition(X0,X1),composition(X0,X2)) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2))) = composition(X0,join(X1,X2))
& join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) = join(composition(X0,X1),composition(X0,X2)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_18,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_19,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_20,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_21,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_18,c_20]) ).
cnf(c_22,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_25,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_26,plain,
join(composition(A,B),composition(C,B)) = composition(join(A,C),B),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_27,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_28,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_29,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_30,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_31,plain,
composition(converse(A),converse(B)) = converse(composition(B,A)),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_34,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_35,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_3618,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_22,c_35]) ).
cnf(c_36,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_34,c_3618]) ).
fof(nnf_17,plain,
? [X0,X1,X2] :
( composition(X0,join(X1,X2)) != join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2)))
| join(composition(X0,X1),composition(X0,X2)) != join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( composition(sK0,join(sK1,sK2)) != join(join(composition(sK0,sK1),composition(sK0,sK2)),composition(sK0,join(sK1,sK2)))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(join(composition(sK0,join(sK1,sK2)),composition(sK0,sK1)),composition(sK0,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_17]) ).
cnf(c_43,negated_conjecture,
( composition(sK0,join(sK1,sK2)) != join(join(composition(sK0,sK1),composition(sK0,sK2)),composition(sK0,join(sK1,sK2)))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(join(composition(sK0,join(sK1,sK2)),composition(sK0,sK1)),composition(sK0,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_3619,negated_conjecture,
( composition(sK0,join(sK1,sK2)) != join(join(composition(sK0,sK1),composition(sK0,sK2)),composition(sK0,join(sK1,sK2)))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(join(composition(sK0,sK1),composition(sK0,join(sK1,sK2))),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_18,c_43]) ).
cnf(c_3620,negated_conjecture,
( composition(sK0,join(sK1,sK2)) != join(join(composition(sK0,sK1),composition(sK0,sK2)),composition(sK0,join(sK1,sK2)))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(composition(sK0,sK2),join(composition(sK0,sK1),composition(sK0,join(sK1,sK2)))) ),
inference(paramod,[status(thm)],[c_18,c_3619]) ).
cnf(c_3621,negated_conjecture,
( composition(sK0,join(sK1,sK2)) != join(composition(sK0,join(sK1,sK2)),join(composition(sK0,sK1),composition(sK0,sK2)))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(composition(sK0,sK2),join(composition(sK0,sK1),composition(sK0,join(sK1,sK2)))) ),
inference(paramod,[status(thm)],[c_18,c_3620]) ).
cnf(c_3622,negated_conjecture,
( composition(sK0,join(sK1,sK2)) != join(composition(sK0,join(sK1,sK2)),join(composition(sK0,sK1),composition(sK0,sK2)))
| join(composition(sK0,sK2),join(composition(sK0,sK1),composition(sK0,join(sK1,sK2)))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(copy,[status(thm)],[c_3621]) ).
cnf(c_44,negated_conjecture,
( join(composition(sK0,join(sK1,sK2)),join(composition(sK0,sK1),composition(sK0,sK2))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK2),join(composition(sK0,sK1),composition(sK0,join(sK1,sK2)))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(copy,[status(thm)],[c_3622]) ).
cnf(c_45,plain,
join(A,join(B,C)) = join(C,join(A,B)),
inference(paramod,[status(thm)],[c_19,c_18]) ).
cnf(c_3623,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_46,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_19,c_3623]) ).
cnf(c_3624,negated_conjecture,
( join(composition(sK0,join(sK1,sK2)),join(composition(sK0,sK1),composition(sK0,sK2))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_46,c_44]) ).
cnf(c_3625,negated_conjecture,
( join(composition(sK0,sK2),join(composition(sK0,join(sK1,sK2)),composition(sK0,sK1))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_45,c_3624]) ).
cnf(c_3626,negated_conjecture,
( join(composition(sK0,sK2),join(composition(sK0,sK1),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_18,c_3625]) ).
cnf(c_47,negated_conjecture,
( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_46,c_3626]) ).
cnf(c_48,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_49,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_3627,plain,
join(A,converse(B)) = converse(join(converse(A),B)),
inference(paramod,[status(thm)],[c_27,c_29]) ).
cnf(c_59,plain,
converse(join(converse(A),B)) = join(A,converse(B)),
inference(copy,[status(thm)],[c_3627]) ).
cnf(c_62,plain,
join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(converse(B),C),converse(A)),
inference(paramod,[status(thm)],[c_31,c_26]) ).
cnf(c_3628,plain,
composition(A,converse(B)) = converse(composition(B,converse(A))),
inference(paramod,[status(thm)],[c_27,c_31]) ).
cnf(c_64,plain,
converse(composition(A,converse(B))) = composition(B,converse(A)),
inference(copy,[status(thm)],[c_3628]) ).
cnf(c_3629,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_34,c_21]) ).
cnf(c_76,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_36,c_3629]) ).
cnf(c_81,plain,
join(top,zero) = top,
inference(paramod,[status(thm)],[c_36,c_34]) ).
cnf(c_3630,plain,
join(top,A) = join(top,join(zero,A)),
inference(paramod,[status(thm)],[c_81,c_19]) ).
cnf(c_118,plain,
join(top,join(zero,A)) = join(top,A),
inference(copy,[status(thm)],[c_3630]) ).
cnf(c_3631,plain,
join(top,top) = join(top,complement(zero)),
inference(paramod,[status(thm)],[c_34,c_118]) ).
cnf(c_123,plain,
join(top,complement(zero)) = join(top,top),
inference(copy,[status(thm)],[c_3631]) ).
cnf(c_3632,plain,
join(complement(join(top,top)),complement(join(complement(zero),complement(top)))) = zero,
inference(paramod,[status(thm)],[c_123,c_48]) ).
cnf(c_3633,plain,
join(complement(join(top,top)),complement(join(complement(zero),zero))) = zero,
inference(paramod,[status(thm)],[c_36,c_3632]) ).
cnf(c_3634,plain,
join(complement(join(top,top)),complement(join(zero,complement(zero)))) = zero,
inference(paramod,[status(thm)],[c_18,c_3633]) ).
cnf(c_3635,plain,
join(complement(join(top,top)),complement(top)) = zero,
inference(paramod,[status(thm)],[c_34,c_3634]) ).
cnf(c_3636,plain,
join(complement(join(top,top)),zero) = zero,
inference(paramod,[status(thm)],[c_36,c_3635]) ).
cnf(c_139,plain,
join(zero,complement(join(top,top))) = zero,
inference(paramod,[status(thm)],[c_18,c_3636]) ).
cnf(c_3637,plain,
join(zero,A) = join(zero,join(complement(join(top,top)),A)),
inference(paramod,[status(thm)],[c_139,c_19]) ).
cnf(c_141,plain,
join(zero,join(complement(join(top,top)),A)) = join(zero,A),
inference(copy,[status(thm)],[c_3637]) ).
cnf(c_3638,plain,
join(top,zero) = join(top,complement(join(top,top))),
inference(paramod,[status(thm)],[c_139,c_118]) ).
cnf(c_3639,plain,
top = join(top,complement(join(top,top))),
inference(paramod,[status(thm)],[c_81,c_3638]) ).
cnf(c_143,plain,
join(top,complement(join(top,top))) = top,
inference(copy,[status(thm)],[c_3639]) ).
cnf(c_3640,plain,
join(complement(top),complement(join(complement(join(top,top)),complement(top)))) = join(top,top),
inference(paramod,[status(thm)],[c_143,c_48]) ).
cnf(c_3641,plain,
join(zero,complement(join(complement(join(top,top)),complement(top)))) = join(top,top),
inference(paramod,[status(thm)],[c_36,c_3640]) ).
cnf(c_3642,plain,
join(zero,complement(join(complement(join(top,top)),zero))) = join(top,top),
inference(paramod,[status(thm)],[c_36,c_3641]) ).
cnf(c_3643,plain,
join(zero,complement(join(zero,complement(join(top,top))))) = join(top,top),
inference(paramod,[status(thm)],[c_18,c_3642]) ).
cnf(c_3644,plain,
join(zero,complement(zero)) = join(top,top),
inference(paramod,[status(thm)],[c_139,c_3643]) ).
cnf(c_3645,plain,
top = join(top,top),
inference(paramod,[status(thm)],[c_34,c_3644]) ).
cnf(c_147,plain,
join(top,top) = top,
inference(copy,[status(thm)],[c_3645]) ).
cnf(c_3646,plain,
join(zero,join(complement(top),A)) = join(zero,A),
inference(paramod,[status(thm)],[c_147,c_141]) ).
cnf(c_149,plain,
join(zero,join(zero,A)) = join(zero,A),
inference(paramod,[status(thm)],[c_36,c_3646]) ).
cnf(c_3647,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_34,c_49]) ).
cnf(c_3648,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_3647]) ).
cnf(c_3649,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_36,c_3648]) ).
cnf(c_164,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_3649]) ).
cnf(c_170,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_164,c_76]) ).
cnf(c_171,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_170,c_164]) ).
cnf(c_3650,plain,
join(zero,complement(A)) = join(zero,complement(join(A,A))),
inference(paramod,[status(thm)],[c_171,c_149]) ).
cnf(c_202,plain,
join(zero,complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_171,c_3650]) ).
cnf(c_3651,plain,
join(zero,join(zero,complement(join(A,A)))) = complement(A),
inference(paramod,[status(thm)],[c_171,c_149]) ).
cnf(c_3652,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_202,c_3651]) ).
cnf(c_203,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_202,c_3652]) ).
cnf(c_3653,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_203,c_170]) ).
cnf(c_3654,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_170,c_3653]) ).
cnf(c_252,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_3654]) ).
cnf(c_3655,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_252,c_19]) ).
cnf(c_262,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_3655]) ).
cnf(c_3656,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_252,c_19]) ).
cnf(c_264,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_18,c_3656]) ).
cnf(c_3657,plain,
join(converse(converse(composition(A,B))),converse(composition(C,converse(A)))) = converse(composition(join(converse(B),C),converse(A))),
inference(paramod,[status(thm)],[c_62,c_29]) ).
cnf(c_3658,plain,
join(composition(A,B),converse(composition(C,converse(A)))) = converse(composition(join(converse(B),C),converse(A))),
inference(paramod,[status(thm)],[c_27,c_3657]) ).
cnf(c_3659,plain,
join(composition(A,B),composition(A,converse(C))) = converse(composition(join(converse(B),C),converse(A))),
inference(paramod,[status(thm)],[c_64,c_3658]) ).
cnf(c_3660,plain,
join(composition(A,B),composition(A,converse(C))) = composition(A,converse(join(converse(B),C))),
inference(paramod,[status(thm)],[c_64,c_3659]) ).
cnf(c_602,plain,
join(composition(A,B),composition(A,converse(C))) = composition(A,join(B,converse(C))),
inference(paramod,[status(thm)],[c_59,c_3660]) ).
cnf(c_3661,plain,
join(composition(A,B),composition(A,C)) = composition(A,join(B,converse(converse(C)))),
inference(paramod,[status(thm)],[c_27,c_602]) ).
cnf(c_3551,plain,
join(composition(A,B),composition(A,C)) = composition(A,join(B,C)),
inference(paramod,[status(thm)],[c_27,c_3661]) ).
cnf(c_3662,negated_conjecture,
( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK1),composition(sK0,join(sK2,join(sK1,sK2)))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_3551,c_47]) ).
cnf(c_3663,negated_conjecture,
( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK1),composition(sK0,join(sK1,sK2))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_264,c_3662]) ).
cnf(c_3664,negated_conjecture,
( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2))
| composition(sK0,join(sK1,join(sK1,sK2))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_3551,c_3663]) ).
cnf(c_3665,negated_conjecture,
( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2))
| composition(sK0,join(sK1,sK2)) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_262,c_3664]) ).
cnf(c_3666,negated_conjecture,
( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2))
| composition(sK0,join(sK1,sK2)) != composition(sK0,join(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_3551,c_3665]) ).
cnf(c_3667,negated_conjecture,
( join(composition(sK0,sK1),composition(sK0,join(sK2,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2))
| composition(sK0,join(sK1,sK2)) != composition(sK0,join(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_3551,c_3666]) ).
cnf(c_3668,negated_conjecture,
( join(composition(sK0,sK1),composition(sK0,join(sK1,sK2))) != composition(sK0,join(sK1,sK2))
| composition(sK0,join(sK1,sK2)) != composition(sK0,join(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_264,c_3667]) ).
cnf(c_3669,negated_conjecture,
( composition(sK0,join(sK1,join(sK1,sK2))) != composition(sK0,join(sK1,sK2))
| composition(sK0,join(sK1,sK2)) != composition(sK0,join(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_3551,c_3668]) ).
cnf(c_3670,negated_conjecture,
( composition(sK0,join(sK1,sK2)) != composition(sK0,join(sK1,sK2))
| composition(sK0,join(sK1,sK2)) != composition(sK0,join(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_262,c_3669]) ).
cnf(c_3671,negated_conjecture,
composition(sK0,join(sK1,sK2)) != composition(sK0,join(sK1,sK2)),
inference(copy,[status(thm)],[c_3670]) ).
cnf(c_3617,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_3671]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL008+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 05:23:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 2875832 was started by sandbox on n007,
% 0.08/0.37 % Sat Sep 26 05:23:39 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 12.04/1.98
% 12.04/1.98 % SZS status Theorem for theBenchmark
% 12.04/1.98
% 12.04/1.98 % Proof 1 at 1.24 (+ 0.34) seconds.
% 12.04/1.98 % Length of proof is 56.
% 12.04/1.98 % Level of proof is 14.
% 12.04/1.98 % Maximum clause weight is 75.000.
% 12.04/1.98 % Given clauses 244.
% 12.04/1.98
% 12.04/1.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------