%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT241-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 07:49:52 AM UTC 2026
% Result : Unsatisfiable 208.62s 42.67s
% Output : CNFRefutation 208.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 78 unt; 0 def)
% Number of atoms : 78 ( 77 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 121 ( 26 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ifeq_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c_1,plain,
ifeq(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom]) ).
fof(idempotence_of_meet,axiom,
! [VAR_0] : meet(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_meet) ).
cnf(c_2,plain,
meet(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_meet]) ).
fof(absorption1,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,join(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption1) ).
cnf(c_4,plain,
meet(A,join(A,B)) = A,
inference(clausify,[status(thm)],[absorption1]) ).
fof(absorption2,axiom,
! [VAR_0,VAR_1] : join(VAR_0,meet(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption2) ).
cnf(c_5,plain,
join(A,meet(A,B)) = A,
inference(clausify,[status(thm)],[absorption2]) ).
fof(commutativity_of_meet,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = meet(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_meet) ).
cnf(c_6,plain,
meet(A,B) = meet(B,A),
inference(clausify,[status(thm)],[commutativity_of_meet]) ).
fof(commutativity_of_join,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_join) ).
cnf(c_7,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[commutativity_of_join]) ).
fof(associativity_of_meet,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(meet(VAR_0,VAR_1),VAR_2) = meet(VAR_0,meet(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_meet) ).
cnf(c_8,plain,
meet(meet(A,B),C) = meet(A,meet(B,C)),
inference(clausify,[status(thm)],[associativity_of_meet]) ).
fof(associativity_of_join,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(VAR_0,VAR_1),VAR_2) = join(VAR_0,join(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_join) ).
cnf(c_9,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[associativity_of_join]) ).
fof(complement_join,axiom,
! [VAR_0] : join(VAR_0,complement(VAR_0)) = one,
file('theBenchmark.p',complement_join) ).
cnf(c_10,plain,
join(A,complement(A)) = one,
inference(clausify,[status(thm)],[complement_join]) ).
fof(complement_meet,axiom,
! [VAR_0] : meet(VAR_0,complement(VAR_0)) = zero,
file('theBenchmark.p',complement_meet) ).
cnf(c_11,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[complement_meet]) ).
fof(meet_join_complement,axiom,
! [VAR_0,VAR_1] : ifeq(join(VAR_0,VAR_1),one,ifeq(meet(VAR_0,VAR_1),zero,complement(VAR_0),VAR_1),VAR_1) = VAR_1,
file('theBenchmark.p',meet_join_complement) ).
cnf(c_12,plain,
ifeq(join(A,B),one,ifeq(meet(A,B),zero,complement(A),B),B) = B,
inference(clausify,[status(thm)],[meet_join_complement]) ).
fof(equation_H51,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : meet(VAR_0,join(VAR_1,meet(VAR_2,join(VAR_0,VAR_3)))) = meet(VAR_0,join(VAR_1,join(meet(VAR_0,VAR_2),meet(VAR_2,VAR_3)))),
file('theBenchmark.p',equation_H51) ).
cnf(c_13,plain,
meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,join(meet(A,C),meet(C,D)))),
inference(clausify,[status(thm)],[equation_H51]) ).
cnf(c_14,plain,
meet(A,join(B,join(meet(A,C),meet(C,D)))) = meet(A,join(B,meet(C,join(A,D)))),
inference(copy,[status(thm)],[c_13]) ).
fof(prove_distributivity_hypothesis,axiom,
meet(b,a) = a,
file('theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(c_15,plain,
meet(b,a) = a,
inference(clausify,[status(thm)],[prove_distributivity_hypothesis]) ).
cnf(c_16,plain,
meet(a,b) = a,
inference(paramod,[status(thm)],[c_6,c_15]) ).
fof(prove_distributivity,axiom,
join(complement(b),complement(a)) != complement(a),
file('theBenchmark.p',prove_distributivity) ).
cnf(c_17,plain,
join(complement(b),complement(a)) != complement(a),
inference(clausify,[status(thm)],[prove_distributivity]) ).
cnf(c_18,plain,
join(complement(a),complement(b)) != complement(a),
inference(paramod,[status(thm)],[c_7,c_17]) ).
cnf(c_19,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_37160,plain,
meet(A,B) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_25,plain,
meet(A,meet(join(A,B),C)) = meet(A,C),
inference(copy,[status(thm)],[c_37160]) ).
cnf(c_37161,plain,
join(A,B) = join(A,join(meet(A,C),B)),
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_34,plain,
join(A,join(meet(A,B),C)) = join(A,C),
inference(copy,[status(thm)],[c_37161]) ).
cnf(c_37,plain,
meet(A,one) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_37162,plain,
join(one,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_10,c_9]) ).
cnf(c_38,plain,
join(A,join(complement(A),B)) = join(one,B),
inference(copy,[status(thm)],[c_37162]) ).
cnf(c_40,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_11,c_5]) ).
cnf(c_46,plain,
ifeq(join(A,B),one,ifeq(meet(B,A),zero,complement(A),B),B) = B,
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_37163,plain,
join(b,a) = b,
inference(paramod,[status(thm)],[c_16,c_19]) ).
cnf(c_76,plain,
join(a,b) = b,
inference(paramod,[status(thm)],[c_7,c_37163]) ).
cnf(c_37164,plain,
A = meet(one,A),
inference(paramod,[status(thm)],[c_37,c_6]) ).
cnf(c_78,plain,
meet(one,A) = A,
inference(copy,[status(thm)],[c_37164]) ).
cnf(c_81,plain,
join(one,A) = one,
inference(paramod,[status(thm)],[c_37,c_19]) ).
cnf(c_82,plain,
join(A,join(complement(A),B)) = one,
inference(paramod,[status(thm)],[c_81,c_38]) ).
cnf(c_37165,plain,
A = join(zero,A),
inference(paramod,[status(thm)],[c_40,c_7]) ).
cnf(c_83,plain,
join(zero,A) = A,
inference(copy,[status(thm)],[c_37165]) ).
cnf(c_102,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_83,c_19]) ).
cnf(c_37166,plain,
meet(A,zero) = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_11,c_25]) ).
cnf(c_37167,plain,
zero = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_102,c_37166]) ).
cnf(c_141,plain,
meet(A,complement(join(A,B))) = zero,
inference(copy,[status(thm)],[c_37167]) ).
cnf(c_156,plain,
meet(A,complement(join(B,A))) = zero,
inference(paramod,[status(thm)],[c_7,c_141]) ).
cnf(c_162,plain,
meet(a,complement(b)) = zero,
inference(paramod,[status(thm)],[c_76,c_141]) ).
cnf(c_37168,plain,
meet(a,join(A,join(zero,meet(complement(b),B)))) = meet(a,join(A,meet(complement(b),join(a,B)))),
inference(paramod,[status(thm)],[c_162,c_14]) ).
cnf(c_37169,plain,
meet(a,join(A,meet(complement(b),B))) = meet(a,join(A,meet(complement(b),join(a,B)))),
inference(paramod,[status(thm)],[c_83,c_37168]) ).
cnf(c_165,plain,
meet(a,join(A,meet(complement(b),join(a,B)))) = meet(a,join(A,meet(complement(b),B))),
inference(copy,[status(thm)],[c_37169]) ).
cnf(c_306,plain,
meet(join(meet(A,B),C),complement(join(A,C))) = zero,
inference(paramod,[status(thm)],[c_34,c_156]) ).
cnf(c_37170,plain,
ifeq(join(complement(A),A),one,ifeq(zero,zero,complement(complement(A)),A),A) = A,
inference(paramod,[status(thm)],[c_11,c_46]) ).
cnf(c_37171,plain,
ifeq(join(A,complement(A)),one,ifeq(zero,zero,complement(complement(A)),A),A) = A,
inference(paramod,[status(thm)],[c_7,c_37170]) ).
cnf(c_37172,plain,
ifeq(one,one,ifeq(zero,zero,complement(complement(A)),A),A) = A,
inference(paramod,[status(thm)],[c_10,c_37171]) ).
cnf(c_37173,plain,
ifeq(one,one,complement(complement(A)),A) = A,
inference(paramod,[status(thm)],[c_1,c_37172]) ).
cnf(c_523,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_1,c_37173]) ).
cnf(c_5206,plain,
meet(join(meet(A,B),meet(C,A)),complement(A)) = zero,
inference(paramod,[status(thm)],[c_19,c_306]) ).
cnf(c_37174,plain,
meet(join(meet(complement(A),B),meet(C,complement(A))),A) = zero,
inference(paramod,[status(thm)],[c_523,c_5206]) ).
cnf(c_18852,plain,
meet(A,join(meet(complement(A),B),meet(C,complement(A)))) = zero,
inference(paramod,[status(thm)],[c_6,c_37174]) ).
cnf(c_37175,plain,
meet(a,join(meet(complement(a),A),meet(complement(b),join(a,complement(a))))) = zero,
inference(paramod,[status(thm)],[c_18852,c_165]) ).
cnf(c_37176,plain,
meet(a,join(meet(complement(a),A),meet(complement(b),one))) = zero,
inference(paramod,[status(thm)],[c_10,c_37175]) ).
cnf(c_37177,plain,
meet(a,join(meet(complement(a),A),meet(one,complement(b)))) = zero,
inference(paramod,[status(thm)],[c_6,c_37176]) ).
cnf(c_37136,plain,
meet(a,join(meet(complement(a),A),complement(b))) = zero,
inference(paramod,[status(thm)],[c_78,c_37177]) ).
cnf(c_37147,plain,
meet(a,join(complement(a),complement(b))) = zero,
inference(paramod,[status(thm)],[c_2,c_37136]) ).
cnf(c_37178,plain,
ifeq(join(a,join(complement(a),complement(b))),one,ifeq(zero,zero,complement(a),join(complement(a),complement(b))),join(complement(a),complement(b))) = join(complement(a),complement(b)),
inference(paramod,[status(thm)],[c_37147,c_12]) ).
cnf(c_37179,plain,
ifeq(one,one,ifeq(zero,zero,complement(a),join(complement(a),complement(b))),join(complement(a),complement(b))) = join(complement(a),complement(b)),
inference(paramod,[status(thm)],[c_82,c_37178]) ).
cnf(c_37180,plain,
ifeq(one,one,complement(a),join(complement(a),complement(b))) = join(complement(a),complement(b)),
inference(paramod,[status(thm)],[c_1,c_37179]) ).
cnf(c_37181,plain,
complement(a) = join(complement(a),complement(b)),
inference(paramod,[status(thm)],[c_1,c_37180]) ).
cnf(c_37158,plain,
join(complement(a),complement(b)) = complement(a),
inference(copy,[status(thm)],[c_37181]) ).
cnf(c_37159,plain,
$false,
inference(resolve,[status(thm)],[c_37158,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT241-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 20:18:37 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.37 % Process 1108248 was started by sandbox on n013,
% 0.02/0.37 % Fri Sep 25 20:18:37 2026
% 0.02/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.37
% 0.02/0.37 % From the command line: assign(max_seconds, 300).
% 208.62/42.67
% 208.62/42.67 % given #500 (T,wt=12): 3014 meet(A,meet(a,complement(meet(b,join(B,A))))) = zero. [para(1354(a,1),91(a,1,2)),rewrite([102(2)]),flip(a)].
% 208.62/42.67
% 208.62/42.67 % given #1000 (T,wt=13): 4794 join(meet(A,meet(a,B)),join(C,b)) = join(C,b). [para(28(a,1),3723(a,1,1))].
% 208.62/42.67
% 208.62/42.67 % SZS status Unsatisfiable for theBenchmark
% 208.62/42.67
% 208.62/42.67 % Proof 1 at 21.72 (+ 5.21) seconds.
% 208.62/42.67 % Length of proof is 42.
% 208.62/42.67 % Level of proof is 12.
% 208.62/42.67 % Maximum clause weight is 21.000.
% 208.62/42.67 % Given clauses 1060.
% 208.62/42.67
% 208.62/42.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------