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FindProof---0.1.UNS-Prf.s

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%------------------------------------------------------------------------------
% File     : FindProof---0.1
% Problem  : LAT218-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300

% 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 : Fri Sep 25 01:56:20 PM UTC 2026

% Result   : Unsatisfiable 198.09s 29.05s
% Output   : Proof 198.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   55
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  295 ( 291 unt;   0 def)
%            Number of atoms       :  303 ( 302 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   25 (  17   ~;   8   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-4 aty)
%            Number of variables   :  452 (  88 sgn  48   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
cnf(t14,axiom,
    sFlat0 = complement(b),
    introduced(definition) ).

cnf(t83,plain,
    complement(b) = sFlat0,
    inference(orient,[status(thm)],[t14]) ).

cnf(t15,axiom,
    sFlat1 = complement(a),
    introduced(definition) ).

cnf(t78,plain,
    complement(a) = sFlat1,
    inference(orient,[status(thm)],[t15]) ).

cnf(t16,axiom,
    sFlat2 = join(complement(b),complement(a)),
    introduced(definition) ).

cnf(t74,plain,
    join(complement(b),complement(a)) = sFlat2,
    inference(orient,[status(thm)],[t16]) ).

cnf(t62114,plain,
    join(complement(b),sFlat1) = sFlat2,
    inference(step,[status(thm)],[t74,t78]) ).

cnf(t82,plain,
    join(complement(b),sFlat1) = sFlat2,
    inference(rw,[status(thm)],[t62114]) ).

cnf(f5,axiom,
    join(X,Y) = join(Y,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).

fof(f5_nnf,plain,
    ! [X,Y] : join(X,Y) = join(Y,X),
    inference(nnf_transformation,[status(thm)],[f5]) ).

fof(f5_sk,plain,
    ! [X,Y] : join(X,Y) = join(Y,X),
    inference(skolemisation,[status(esa)],[f5_nnf]) ).

cnf(c5,plain,
    join(X0,X1) = join(X1,X0),
    inference(cnf_transformation,[status(esa)],[f5_sk]) ).

cnf(t6,plain,
    join(X1,X2) = join(X2,X1),
    inference(equality_encoding,[status(esa)],[c5]) ).

cnf(t58,plain,
    join(X1,X2) = join(X2,X1),
    inference(orient,[status(thm)],[t6]) ).

cnf(t62125,plain,
    join(sFlat1,complement(b)) = sFlat2,
    inference(step,[status(thm)],[t82,t58]) ).

cnf(t62126,plain,
    join(sFlat1,sFlat0) = sFlat2,
    inference(step,[status(thm)],[t62125,t83]) ).

cnf(t62127,plain,
    join(sFlat0,sFlat1) = sFlat2,
    inference(step,[status(thm)],[t62126,t58]) ).

cnf(t113,plain,
    join(sFlat0,sFlat1) = sFlat2,
    inference(orient,[status(thm)],[t62127]) ).

cnf(f3,axiom,
    join(X,meet(X,Y)) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).

fof(f3_nnf,plain,
    ! [X,Y] : join(X,meet(X,Y)) = X,
    inference(nnf_transformation,[status(thm)],[f3]) ).

fof(f3_sk,plain,
    ! [X,Y] : join(X,meet(X,Y)) = X,
    inference(skolemisation,[status(esa)],[f3_nnf]) ).

cnf(c3,plain,
    join(X0,meet(X0,X1)) = X0,
    inference(cnf_transformation,[status(esa)],[f3_sk]) ).

cnf(t7,plain,
    join(X1,meet(X1,X2)) = X1,
    inference(equality_encoding,[status(esa)],[c3]) ).

cnf(t20,plain,
    join(X1,meet(X1,X2)) = X1,
    inference(orient,[status(thm)],[t7]) ).

cnf(f6,axiom,
    meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).

fof(f6_nnf,plain,
    ! [X,Y,Z] : meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
    inference(nnf_transformation,[status(thm)],[f6]) ).

fof(f6_sk,plain,
    ! [X,Y,Z] : meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
    inference(skolemisation,[status(esa)],[f6_nnf]) ).

cnf(c6,plain,
    meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f6_sk]) ).

cnf(t11,plain,
    meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
    inference(equality_encoding,[status(esa)],[c6]) ).

cnf(t28,plain,
    meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
    inference(orient,[status(thm)],[t11]) ).

cnf(f4,axiom,
    meet(X,Y) = meet(Y,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).

fof(f4_nnf,plain,
    ! [X,Y] : meet(X,Y) = meet(Y,X),
    inference(nnf_transformation,[status(thm)],[f4]) ).

fof(f4_sk,plain,
    ! [X,Y] : meet(X,Y) = meet(Y,X),
    inference(skolemisation,[status(esa)],[f4_nnf]) ).

cnf(c4,plain,
    meet(X0,X1) = meet(X1,X0),
    inference(cnf_transformation,[status(esa)],[f4_sk]) ).

cnf(t8,plain,
    meet(X1,X2) = meet(X2,X1),
    inference(equality_encoding,[status(esa)],[c4]) ).

cnf(t27,plain,
    meet(X1,X2) = meet(X2,X1),
    inference(orient,[status(thm)],[t8]) ).

cnf(t31,plain,
    meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
    inference(cp,[status(thm)],[t28,t27]) ).

cnf(t152,plain,
    meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
    inference(orient,[status(thm)],[t31]) ).

cnf(t155,plain,
    X1 = join(X1,meet(X2,meet(X3,X1))),
    inference(cp,[status(thm)],[t20,t152]) ).

cnf(t727,plain,
    join(X1,meet(X2,meet(X3,X1))) = X1,
    inference(orient,[status(thm)],[t155]) ).

cnf(f2,axiom,
    meet(X,join(X,Y)) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).

fof(f2_nnf,plain,
    ! [X,Y] : meet(X,join(X,Y)) = X,
    inference(nnf_transformation,[status(thm)],[f2]) ).

fof(f2_sk,plain,
    ! [X,Y] : meet(X,join(X,Y)) = X,
    inference(skolemisation,[status(esa)],[f2_nnf]) ).

cnf(c2,plain,
    meet(X0,join(X0,X1)) = X0,
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(t9,plain,
    meet(X1,join(X1,X2)) = X1,
    inference(equality_encoding,[status(esa)],[c2]) ).

cnf(t18,plain,
    meet(X1,join(X1,X2)) = X1,
    inference(orient,[status(thm)],[t9]) ).

cnf(t735,plain,
    join(X1,X2) = join(join(X1,X2),meet(X3,X1)),
    inference(cp,[status(thm)],[t727,t18]) ).

cnf(f7,axiom,
    join(join(X,Y),Z) = join(X,join(Y,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).

fof(f7_nnf,plain,
    ! [X,Y,Z] : join(join(X,Y),Z) = join(X,join(Y,Z)),
    inference(nnf_transformation,[status(thm)],[f7]) ).

fof(f7_sk,plain,
    ! [X,Y,Z] : join(join(X,Y),Z) = join(X,join(Y,Z)),
    inference(skolemisation,[status(esa)],[f7_nnf]) ).

cnf(c7,plain,
    join(join(X0,X1),X2) = join(X0,join(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f7_sk]) ).

cnf(t10,plain,
    join(join(X1,X2),X3) = join(X1,join(X2,X3)),
    inference(equality_encoding,[status(esa)],[c7]) ).

cnf(t59,plain,
    join(join(X1,X2),X3) = join(X1,join(X2,X3)),
    inference(orient,[status(thm)],[t10]) ).

cnf(t62203,plain,
    join(X1,X2) = join(X1,join(X2,meet(X3,X1))),
    inference(step,[status(thm)],[t735,t59]) ).

cnf(t970,plain,
    join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
    inference(orient,[status(thm)],[t62203]) ).

cnf(t114,plain,
    sFlat0 = meet(sFlat0,sFlat2),
    inference(cp,[status(thm)],[t18,t113]) ).

cnf(t117,plain,
    meet(sFlat0,sFlat2) = sFlat0,
    inference(orient,[status(thm)],[t114]) ).

cnf(t118,plain,
    meet(sFlat0,meet(sFlat2,X1)) = meet(sFlat0,X1),
    inference(cp,[status(thm)],[t28,t117]) ).

cnf(t359,plain,
    meet(sFlat0,meet(sFlat2,X1)) = meet(sFlat0,X1),
    inference(orient,[status(thm)],[t118]) ).

cnf(t983,plain,
    join(meet(sFlat2,X1),X2) = join(meet(sFlat2,X1),join(X2,meet(sFlat0,X1))),
    inference(cp,[status(thm)],[t970,t359]) ).

cnf(t62,plain,
    join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
    inference(cp,[status(thm)],[t59,t58]) ).

cnf(t160,plain,
    join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
    inference(orient,[status(thm)],[t62]) ).

cnf(t62593,plain,
    join(meet(sFlat2,X1),X2) = join(meet(sFlat0,X1),join(meet(sFlat2,X1),X2)),
    inference(step,[status(thm)],[t983,t160]) ).

cnf(t19863,plain,
    join(meet(sFlat0,X1),join(meet(sFlat2,X1),X2)) = join(meet(sFlat2,X1),X2),
    inference(orient,[status(thm)],[t62593]) ).

cnf(f0,axiom,
    meet(X,X) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).

fof(f0_nnf,plain,
    ! [X] : meet(X,X) = X,
    inference(nnf_transformation,[status(thm)],[f0]) ).

fof(f0_sk,plain,
    ! [X] : meet(X,X) = X,
    inference(skolemisation,[status(esa)],[f0_nnf]) ).

cnf(c0,plain,
    meet(X0,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f0_sk]) ).

cnf(t1,plain,
    meet(X1,X1) = X1,
    inference(equality_encoding,[status(esa)],[c0]) ).

cnf(t17,plain,
    meet(X1,X1) = X1,
    inference(orient,[status(thm)],[t1]) ).

cnf(t32,plain,
    meet(X1,meet(X1,X2)) = meet(X1,X2),
    inference(cp,[status(thm)],[t28,t17]) ).

cnf(t121,plain,
    meet(X1,meet(X1,X2)) = meet(X1,X2),
    inference(orient,[status(thm)],[t32]) ).

cnf(t729,plain,
    X1 = join(X1,meet(X2,X1)),
    inference(cp,[status(thm)],[t727,t121]) ).

cnf(t752,plain,
    join(X1,meet(X2,X1)) = X1,
    inference(orient,[status(thm)],[t729]) ).

cnf(t161,plain,
    X1 = meet(X1,join(X2,join(X3,X1))),
    inference(cp,[status(thm)],[t18,t160]) ).

cnf(t770,plain,
    meet(X1,join(X2,join(X3,X1))) = X1,
    inference(orient,[status(thm)],[t161]) ).

cnf(t778,plain,
    meet(X1,X2) = meet(meet(X1,X2),join(X3,X1)),
    inference(cp,[status(thm)],[t770,t20]) ).

cnf(t62204,plain,
    meet(X1,X2) = meet(X1,meet(X2,join(X3,X1))),
    inference(step,[status(thm)],[t778,t28]) ).

cnf(t990,plain,
    meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
    inference(orient,[status(thm)],[t62204]) ).

cnf(t1007,plain,
    meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X3,X1)),
    inference(cp,[status(thm)],[t752,t990]) ).

cnf(t62529,plain,
    meet(X1,join(X2,X3)) = join(meet(X3,X1),meet(X1,join(X2,X3))),
    inference(step,[status(thm)],[t1007,t58]) ).

cnf(t14524,plain,
    join(meet(X1,X2),meet(X2,join(X3,X1))) = meet(X2,join(X3,X1)),
    inference(orient,[status(thm)],[t62529]) ).

cnf(t19915,plain,
    join(meet(sFlat2,X1),meet(X1,join(X2,sFlat2))) = join(meet(sFlat0,X1),meet(X1,join(X2,sFlat2))),
    inference(cp,[status(thm)],[t19863,t14524]) ).

cnf(t62953,plain,
    meet(X1,join(X2,sFlat2)) = join(meet(sFlat0,X1),meet(X1,join(X2,sFlat2))),
    inference(step,[status(thm)],[t19915,t14524]) ).

cnf(t45671,plain,
    join(meet(sFlat0,X1),meet(X1,join(X2,sFlat2))) = meet(X1,join(X2,sFlat2)),
    inference(orient,[status(thm)],[t62953]) ).

cnf(f10,axiom,
    ( complement(X) = Y
    | join(X,Y) != one
    | meet(X,Y) != zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_join_complement) ).

fof(f10_nnf,plain,
    ! [X,Y] :
      ( complement(X) = Y
      | join(X,Y) != one
      | meet(X,Y) != zero ),
    inference(nnf_transformation,[status(thm)],[f10]) ).

fof(f10_sk,plain,
    ! [X,Y] :
      ( complement(X) = Y
      | join(X,Y) != one
      | meet(X,Y) != zero ),
    inference(skolemisation,[status(esa)],[f10_nnf]) ).

cnf(c10,plain,
    ( complement(X0) = X1
    | join(X0,X1) != one
    | meet(X0,X1) != zero ),
    inference(cnf_transformation,[status(esa)],[f10_sk]) ).

cnf(t12,plain,
    ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X1),X2),X2) = X2,
    inference(equality_encoding,[status(esa)],[c10]) ).

cnf(t22,plain,
    ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X1),X2),X2) = X2,
    inference(orient,[status(thm)],[t12]) ).

cnf(t156,plain,
    meet(X1,X2) = ifeq(meet(X1,meet(X2,X3)),zero,ifeq(join(X3,meet(X1,X2)),one,complement(X3),meet(X1,X2)),meet(X1,X2)),
    inference(cp,[status(thm)],[t22,t152]) ).

cnf(t56920,plain,
    ifeq(meet(X1,meet(X2,X3)),zero,ifeq(join(X3,meet(X1,X2)),one,complement(X3),meet(X1,X2)),meet(X1,X2)) = meet(X1,X2),
    inference(orient,[status(thm)],[t156]) ).

cnf(t64,plain,
    join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
    inference(cp,[status(thm)],[t59,t20]) ).

cnf(t661,plain,
    join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
    inference(orient,[status(thm)],[t64]) ).

cnf(t61,plain,
    join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
    inference(cp,[status(thm)],[t59,t20]) ).

cnf(t1663,plain,
    join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
    inference(orient,[status(thm)],[t61]) ).

cnf(t1693,plain,
    join(X1,join(X2,meet(join(meet(X1,X3),X2),X4))) = join(X1,join(meet(X1,X3),X2)),
    inference(cp,[status(thm)],[t661,t1663]) ).

cnf(t62665,plain,
    join(X1,join(X2,meet(join(meet(X1,X3),X2),X4))) = join(X1,X2),
    inference(step,[status(thm)],[t1693,t661]) ).

cnf(t28394,plain,
    join(X1,join(X2,meet(join(meet(X1,X3),X2),X4))) = join(X1,X2),
    inference(orient,[status(thm)],[t62665]) ).

cnf(t28406,plain,
    join(X1,X2) = join(X1,join(X2,meet(X3,join(meet(X1,X4),X2)))),
    inference(cp,[status(thm)],[t28394,t27]) ).

cnf(t60641,plain,
    join(X1,join(X2,meet(X3,join(meet(X1,X4),X2)))) = join(X1,X2),
    inference(orient,[status(thm)],[t28406]) ).

cnf(f11,axiom,
    meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(X,meet(Z,U))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H1) ).

fof(f11_nnf,plain,
    ! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(X,meet(Z,U))))),
    inference(nnf_transformation,[status(thm)],[f11]) ).

fof(f11_sk,plain,
    ! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(X,meet(Z,U))))),
    inference(skolemisation,[status(esa)],[f11_nnf]) ).

cnf(c11,plain,
    meet(X0,join(X1,meet(X2,join(X0,X3)))) = meet(X0,join(X1,meet(X2,join(X0,meet(X2,X3))))),
    inference(cnf_transformation,[status(esa)],[f11_sk]) ).

cnf(t13,plain,
    meet(X1,join(X2,meet(X3,join(X1,meet(X3,X4))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
    inference(equality_encoding,[status(esa)],[c11]) ).

cnf(t37,plain,
    meet(X1,join(X2,meet(X3,join(X1,meet(X3,X4))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
    inference(orient,[status(thm)],[t13]) ).

cnf(f9,axiom,
    meet(X,complement(X)) = zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_meet) ).

fof(f9_nnf,plain,
    ! [X] : meet(X,complement(X)) = zero,
    inference(nnf_transformation,[status(thm)],[f9]) ).

fof(f9_sk,plain,
    ! [X] : meet(X,complement(X)) = zero,
    inference(skolemisation,[status(esa)],[f9_nnf]) ).

cnf(c9,plain,
    meet(X0,complement(X0)) = zero,
    inference(cnf_transformation,[status(esa)],[f9_sk]) ).

cnf(t4,plain,
    meet(X1,complement(X1)) = zero,
    inference(equality_encoding,[status(esa)],[c9]) ).

cnf(t48,plain,
    meet(X1,complement(X1)) = zero,
    inference(orient,[status(thm)],[t4]) ).

cnf(t85,plain,
    zero = meet(b,sFlat0),
    inference(cp,[status(thm)],[t48,t83]) ).

cnf(t62121,plain,
    zero = meet(sFlat0,b),
    inference(step,[status(thm)],[t85,t27]) ).

cnf(t107,plain,
    meet(sFlat0,b) = zero,
    inference(orient,[status(thm)],[t62121]) ).

cnf(t110,plain,
    meet(X1,join(X2,meet(sFlat0,join(X1,b)))) = meet(X1,join(X2,meet(sFlat0,join(X1,zero)))),
    inference(cp,[status(thm)],[t37,t107]) ).

cnf(t51,plain,
    X1 = join(X1,zero),
    inference(cp,[status(thm)],[t20,t48]) ).

cnf(t87,plain,
    join(X1,zero) = X1,
    inference(orient,[status(thm)],[t51]) ).

cnf(t62472,plain,
    meet(X1,join(X2,meet(sFlat0,join(X1,b)))) = meet(X1,join(X2,meet(sFlat0,X1))),
    inference(step,[status(thm)],[t110,t87]) ).

cnf(t10040,plain,
    meet(X1,join(X2,meet(sFlat0,join(X1,b)))) = meet(X1,join(X2,meet(sFlat0,X1))),
    inference(orient,[status(thm)],[t62472]) ).

cnf(f12,hypothesis,
    meet(b,a) = a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).

fof(f12_nnf,plain,
    meet(b,a) = a,
    inference(nnf_transformation,[status(thm)],[f12]) ).

cnf(c12,plain,
    meet(b,a) = a,
    inference(cnf_transformation,[status(esa)],[f12_nnf]) ).

cnf(t2,plain,
    meet(b,a) = a,
    inference(equality_encoding,[status(esa)],[c12]) ).

cnf(t54,plain,
    meet(b,a) = a,
    inference(orient,[status(thm)],[t2]) ).

cnf(t56,plain,
    b = join(b,a),
    inference(cp,[status(thm)],[t20,t54]) ).

cnf(t92,plain,
    join(b,a) = b,
    inference(orient,[status(thm)],[t56]) ).

cnf(t93,plain,
    join(b,join(a,X1)) = join(b,X1),
    inference(cp,[status(thm)],[t59,t92]) ).

cnf(t164,plain,
    join(b,join(a,X1)) = join(b,X1),
    inference(orient,[status(thm)],[t93]) ).

cnf(f8,axiom,
    join(X,complement(X)) = one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_join) ).

fof(f8_nnf,plain,
    ! [X] : join(X,complement(X)) = one,
    inference(nnf_transformation,[status(thm)],[f8]) ).

fof(f8_sk,plain,
    ! [X] : join(X,complement(X)) = one,
    inference(skolemisation,[status(esa)],[f8_nnf]) ).

cnf(c8,plain,
    join(X0,complement(X0)) = one,
    inference(cnf_transformation,[status(esa)],[f8_sk]) ).

cnf(t3,plain,
    join(X1,complement(X1)) = one,
    inference(equality_encoding,[status(esa)],[c8]) ).

cnf(t70,plain,
    join(X1,complement(X1)) = one,
    inference(orient,[status(thm)],[t3]) ).

cnf(t165,plain,
    join(b,complement(a)) = join(b,one),
    inference(cp,[status(thm)],[t164,t70]) ).

cnf(t62133,plain,
    join(b,sFlat1) = join(b,one),
    inference(step,[status(thm)],[t165,t78]) ).

cnf(t62134,plain,
    join(sFlat1,b) = join(b,one),
    inference(step,[status(thm)],[t62133,t58]) ).

cnf(f1,axiom,
    join(X,X) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).

fof(f1_nnf,plain,
    ! [X] : join(X,X) = X,
    inference(nnf_transformation,[status(thm)],[f1]) ).

fof(f1_sk,plain,
    ! [X] : join(X,X) = X,
    inference(skolemisation,[status(esa)],[f1_nnf]) ).

cnf(c1,plain,
    join(X0,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f1_sk]) ).

cnf(t0,plain,
    join(X1,X1) = X1,
    inference(equality_encoding,[status(esa)],[c1]) ).

cnf(t19,plain,
    join(X1,X1) = X1,
    inference(orient,[status(thm)],[t0]) ).

cnf(t63,plain,
    join(X1,join(X1,X2)) = join(X1,X2),
    inference(cp,[status(thm)],[t59,t19]) ).

cnf(t130,plain,
    join(X1,join(X1,X2)) = join(X1,X2),
    inference(orient,[status(thm)],[t63]) ).

cnf(t132,plain,
    join(X1,complement(X1)) = join(X1,one),
    inference(cp,[status(thm)],[t130,t70]) ).

cnf(t62129,plain,
    one = join(X1,one),
    inference(step,[status(thm)],[t132,t70]) ).

cnf(t138,plain,
    join(X1,one) = one,
    inference(orient,[status(thm)],[t62129]) ).

cnf(t62135,plain,
    join(sFlat1,b) = one,
    inference(step,[status(thm)],[t62134,t138]) ).

cnf(t167,plain,
    join(sFlat1,b) = one,
    inference(orient,[status(thm)],[t62135]) ).

cnf(t10044,plain,
    meet(sFlat1,join(X1,meet(sFlat0,sFlat1))) = meet(sFlat1,join(X1,meet(sFlat0,one))),
    inference(cp,[status(thm)],[t10040,t167]) ).

cnf(t72,plain,
    X1 = meet(X1,one),
    inference(cp,[status(thm)],[t18,t70]) ).

cnf(t89,plain,
    meet(X1,one) = X1,
    inference(orient,[status(thm)],[t72]) ).

cnf(t62473,plain,
    meet(sFlat1,join(X1,meet(sFlat0,sFlat1))) = meet(sFlat1,join(X1,sFlat0)),
    inference(step,[status(thm)],[t10044,t89]) ).

cnf(t10097,plain,
    meet(sFlat1,join(X1,meet(sFlat0,sFlat1))) = meet(sFlat1,join(X1,sFlat0)),
    inference(orient,[status(thm)],[t62473]) ).

cnf(t60664,plain,
    join(X1,meet(sFlat0,sFlat1)) = join(X1,join(meet(sFlat0,sFlat1),meet(sFlat1,join(meet(X1,X2),sFlat0)))),
    inference(cp,[status(thm)],[t60641,t10097]) ).

cnf(t63157,plain,
    join(X1,meet(sFlat0,sFlat1)) = join(X1,meet(sFlat1,join(meet(X1,X2),sFlat0))),
    inference(step,[status(thm)],[t60664,t14524]) ).

cnf(t63158,plain,
    join(X1,meet(sFlat0,sFlat1)) = join(X1,meet(sFlat1,join(sFlat0,meet(X1,X2)))),
    inference(step,[status(thm)],[t63157,t58]) ).

cnf(t61208,plain,
    join(X1,meet(sFlat1,join(sFlat0,meet(X1,X2)))) = join(X1,meet(sFlat0,sFlat1)),
    inference(orient,[status(thm)],[t63158]) ).

cnf(t61212,plain,
    join(X1,meet(sFlat0,sFlat1)) = join(X1,meet(sFlat1,join(sFlat0,X1))),
    inference(cp,[status(thm)],[t61208,t17]) ).

cnf(t61469,plain,
    join(X1,meet(sFlat1,join(sFlat0,X1))) = join(X1,meet(sFlat0,sFlat1)),
    inference(orient,[status(thm)],[t61212]) ).

cnf(t84,plain,
    one = join(b,sFlat0),
    inference(cp,[status(thm)],[t70,t83]) ).

cnf(t62120,plain,
    one = join(sFlat0,b),
    inference(step,[status(thm)],[t84,t58]) ).

cnf(t104,plain,
    join(sFlat0,b) = one,
    inference(orient,[status(thm)],[t62120]) ).

cnf(t61479,plain,
    join(b,meet(sFlat0,sFlat1)) = join(b,meet(sFlat1,one)),
    inference(cp,[status(thm)],[t61469,t104]) ).

cnf(t63159,plain,
    join(b,meet(sFlat0,sFlat1)) = join(b,sFlat1),
    inference(step,[status(thm)],[t61479,t89]) ).

cnf(t63160,plain,
    join(b,meet(sFlat0,sFlat1)) = join(sFlat1,b),
    inference(step,[status(thm)],[t63159,t58]) ).

cnf(t63161,plain,
    join(b,meet(sFlat0,sFlat1)) = one,
    inference(step,[status(thm)],[t63160,t167]) ).

cnf(t61745,plain,
    join(b,meet(sFlat0,sFlat1)) = one,
    inference(orient,[status(thm)],[t63161]) ).

cnf(t61748,plain,
    meet(sFlat0,sFlat1) = ifeq(meet(sFlat0,meet(sFlat1,b)),zero,ifeq(one,one,complement(b),meet(sFlat0,sFlat1)),meet(sFlat0,sFlat1)),
    inference(cp,[status(thm)],[t56920,t61745]) ).

cnf(t35,plain,
    meet(X1,X2) = join(meet(X1,X2),meet(X1,meet(X2,X3))),
    inference(cp,[status(thm)],[t20,t28]) ).

cnf(t1603,plain,
    join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
    inference(orient,[status(thm)],[t35]) ).

cnf(t50,plain,
    meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
    inference(cp,[status(thm)],[t28,t48]) ).

cnf(t282,plain,
    meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
    inference(orient,[status(thm)],[t50]) ).

cnf(t296,plain,
    meet(meet(complement(X1),X2),meet(X3,X1)) = meet(X3,meet(zero,X2)),
    inference(cp,[status(thm)],[t152,t282]) ).

cnf(t62245,plain,
    meet(complement(X1),meet(X2,meet(X3,X1))) = meet(X3,meet(zero,X2)),
    inference(step,[status(thm)],[t296,t28]) ).

cnf(t294,plain,
    meet(zero,meet(complement(complement(X1)),X2)) = meet(X1,meet(zero,X2)),
    inference(cp,[status(thm)],[t282,t282]) ).

cnf(t285,plain,
    meet(zero,meet(complement(X1),X2)) = meet(X1,meet(complement(X1),X2)),
    inference(cp,[status(thm)],[t282,t121]) ).

cnf(t62163,plain,
    meet(zero,meet(complement(X1),X2)) = meet(zero,X2),
    inference(step,[status(thm)],[t285,t282]) ).

cnf(t448,plain,
    meet(zero,meet(complement(X1),X2)) = meet(zero,X2),
    inference(orient,[status(thm)],[t62163]) ).

cnf(t62205,plain,
    meet(zero,X2) = meet(X1,meet(zero,X2)),
    inference(step,[status(thm)],[t294,t448]) ).

cnf(t1017,plain,
    meet(X1,meet(zero,X2)) = meet(zero,X2),
    inference(orient,[status(thm)],[t62205]) ).

cnf(t62246,plain,
    meet(complement(X1),meet(X2,meet(X3,X1))) = meet(zero,X2),
    inference(step,[status(thm)],[t62245,t1017]) ).

cnf(t1812,plain,
    meet(complement(X1),meet(X2,meet(X3,X1))) = meet(zero,X2),
    inference(orient,[status(thm)],[t62246]) ).

cnf(t1835,plain,
    meet(complement(X1),X2) = join(meet(complement(X1),X2),meet(zero,X2)),
    inference(cp,[status(thm)],[t1603,t1812]) ).

cnf(t62344,plain,
    meet(complement(X1),X2) = join(meet(zero,X2),meet(complement(X1),X2)),
    inference(step,[status(thm)],[t1835,t58]) ).

cnf(t108,plain,
    meet(sFlat0,meet(b,X1)) = meet(zero,X1),
    inference(cp,[status(thm)],[t28,t107]) ).

cnf(t194,plain,
    meet(sFlat0,meet(b,X1)) = meet(zero,X1),
    inference(orient,[status(thm)],[t108]) ).

cnf(t198,plain,
    meet(zero,meet(b,X1)) = meet(sFlat0,meet(b,X1)),
    inference(cp,[status(thm)],[t194,t121]) ).

cnf(t62159,plain,
    meet(zero,meet(b,X1)) = meet(zero,X1),
    inference(step,[status(thm)],[t198,t194]) ).

cnf(t380,plain,
    meet(zero,meet(b,X1)) = meet(zero,X1),
    inference(orient,[status(thm)],[t62159]) ).

cnf(t1850,plain,
    meet(zero,meet(b,X1)) = meet(zero,X1),
    inference(rw,[status(thm)],[t380]) ).

cnf(t1840,plain,
    meet(meet(X1,meet(X2,X3)),meet(X4,complement(X3))) = meet(X4,meet(zero,X1)),
    inference(cp,[status(thm)],[t152,t1812]) ).

cnf(t62247,plain,
    meet(X1,meet(meet(X2,X3),meet(X4,complement(X3)))) = meet(X4,meet(zero,X1)),
    inference(step,[status(thm)],[t1840,t28]) ).

cnf(t62248,plain,
    meet(X1,meet(X2,meet(X3,meet(X4,complement(X3))))) = meet(X4,meet(zero,X1)),
    inference(step,[status(thm)],[t62247,t28]) ).

cnf(t289,plain,
    meet(zero,X1) = meet(X2,meet(X1,complement(X2))),
    inference(cp,[status(thm)],[t282,t27]) ).

cnf(t439,plain,
    meet(X1,meet(X2,complement(X1))) = meet(zero,X2),
    inference(orient,[status(thm)],[t289]) ).

cnf(t62249,plain,
    meet(X1,meet(X2,meet(zero,X4))) = meet(X4,meet(zero,X1)),
    inference(step,[status(thm)],[t62248,t439]) ).

cnf(t62250,plain,
    meet(X1,meet(zero,X4)) = meet(X4,meet(zero,X1)),
    inference(step,[status(thm)],[t62249,t1017]) ).

cnf(t62251,plain,
    meet(zero,X4) = meet(X4,meet(zero,X1)),
    inference(step,[status(thm)],[t62250,t1017]) ).

cnf(t62252,plain,
    meet(zero,X4) = meet(zero,X1),
    inference(step,[status(thm)],[t62251,t1017]) ).

cnf(t1841,plain,
    meet(zero,X1) = meet(zero,X2),
    inference(orient,[status(thm)],[t62252]) ).

cnf(t62265,plain,
    meet(zero,sFlat0) = meet(zero,X1),
    inference(step,[status(thm)],[t1850,t1841]) ).

cnf(t62266,plain,
    meet(sFlat0,zero) = meet(zero,X1),
    inference(step,[status(thm)],[t62265,t27]) ).

cnf(t123,plain,
    meet(X1,complement(X1)) = meet(X1,zero),
    inference(cp,[status(thm)],[t121,t48]) ).

cnf(t62128,plain,
    zero = meet(X1,zero),
    inference(step,[status(thm)],[t123,t48]) ).

cnf(t128,plain,
    meet(X1,zero) = zero,
    inference(orient,[status(thm)],[t62128]) ).

cnf(t62267,plain,
    zero = meet(zero,X1),
    inference(step,[status(thm)],[t62266,t128]) ).

cnf(t1853,plain,
    meet(zero,X1) = zero,
    inference(orient,[status(thm)],[t62267]) ).

cnf(t62345,plain,
    meet(complement(X1),X2) = join(zero,meet(complement(X1),X2)),
    inference(step,[status(thm)],[t62344,t1853]) ).

cnf(t3269,plain,
    join(zero,meet(complement(X1),X2)) = meet(complement(X1),X2),
    inference(orient,[status(thm)],[t62345]) ).

cnf(t3275,plain,
    meet(complement(b),X1) = join(zero,meet(sFlat0,X1)),
    inference(cp,[status(thm)],[t3269,t83]) ).

cnf(t62347,plain,
    meet(sFlat0,X1) = join(zero,meet(sFlat0,X1)),
    inference(step,[status(thm)],[t3275,t83]) ).

cnf(t3285,plain,
    join(zero,meet(sFlat0,X1)) = meet(sFlat0,X1),
    inference(orient,[status(thm)],[t62347]) ).

cnf(t34,plain,
    meet(X1,meet(X2,X3)) = meet(meet(X2,X1),X3),
    inference(cp,[status(thm)],[t28,t27]) ).

cnf(t62131,plain,
    meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
    inference(step,[status(thm)],[t34,t28]) ).

cnf(t158,plain,
    meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
    inference(orient,[status(thm)],[t62131]) ).

cnf(t3287,plain,
    meet(sFlat0,meet(X1,X2)) = join(zero,meet(X1,meet(sFlat0,X2))),
    inference(cp,[status(thm)],[t3285,t158]) ).

cnf(t3679,plain,
    join(zero,meet(X1,meet(sFlat0,X2))) = meet(sFlat0,meet(X1,X2)),
    inference(orient,[status(thm)],[t3287]) ).

cnf(t33,plain,
    meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
    inference(cp,[status(thm)],[t28,t18]) ).

cnf(t617,plain,
    meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
    inference(orient,[status(thm)],[t33]) ).

cnf(t623,plain,
    meet(X1,complement(join(X1,X2))) = meet(X1,zero),
    inference(cp,[status(thm)],[t617,t48]) ).

cnf(t62187,plain,
    meet(X1,complement(join(X1,X2))) = zero,
    inference(step,[status(thm)],[t623,t128]) ).

cnf(t643,plain,
    meet(X1,complement(join(X1,X2))) = zero,
    inference(orient,[status(thm)],[t62187]) ).

cnf(t650,plain,
    zero = meet(X1,complement(join(X2,join(X3,X1)))),
    inference(cp,[status(thm)],[t643,t160]) ).

cnf(t1141,plain,
    meet(X1,complement(join(X2,join(X3,X1)))) = zero,
    inference(orient,[status(thm)],[t650]) ).

cnf(t1144,plain,
    zero = meet(X1,complement(join(X2,X1))),
    inference(cp,[status(thm)],[t1141,t130]) ).

cnf(t1176,plain,
    meet(X1,complement(join(X2,X1))) = zero,
    inference(orient,[status(thm)],[t1144]) ).

cnf(t1614,plain,
    meet(X1,X2) = join(meet(X1,X2),meet(X2,meet(X3,X1))),
    inference(cp,[status(thm)],[t1603,t152]) ).

cnf(t2783,plain,
    join(meet(X1,X2),meet(X2,meet(X3,X1))) = meet(X1,X2),
    inference(orient,[status(thm)],[t1614]) ).

cnf(t115,plain,
    join(sFlat0,join(sFlat1,X1)) = join(sFlat2,X1),
    inference(cp,[status(thm)],[t59,t113]) ).

cnf(t209,plain,
    join(sFlat0,join(sFlat1,X1)) = join(sFlat2,X1),
    inference(orient,[status(thm)],[t115]) ).

cnf(t213,plain,
    join(sFlat2,sFlat1) = join(sFlat0,sFlat1),
    inference(cp,[status(thm)],[t209,t19]) ).

cnf(t62143,plain,
    join(sFlat1,sFlat2) = join(sFlat0,sFlat1),
    inference(step,[status(thm)],[t213,t58]) ).

cnf(t62144,plain,
    join(sFlat1,sFlat2) = sFlat2,
    inference(step,[status(thm)],[t62143,t113]) ).

cnf(t228,plain,
    join(sFlat1,sFlat2) = sFlat2,
    inference(orient,[status(thm)],[t62144]) ).

cnf(t229,plain,
    sFlat1 = meet(sFlat1,sFlat2),
    inference(cp,[status(thm)],[t18,t228]) ).

cnf(t233,plain,
    meet(sFlat1,sFlat2) = sFlat1,
    inference(orient,[status(thm)],[t229]) ).

cnf(t2824,plain,
    meet(sFlat2,X1) = join(meet(sFlat2,X1),meet(X1,sFlat1)),
    inference(cp,[status(thm)],[t2783,t233]) ).

cnf(t2839,plain,
    join(meet(sFlat2,X1),meet(X1,sFlat1)) = meet(sFlat2,X1),
    inference(orient,[status(thm)],[t2824]) ).

cnf(t2860,plain,
    zero = meet(meet(X1,sFlat1),complement(meet(sFlat2,X1))),
    inference(cp,[status(thm)],[t1176,t2839]) ).

cnf(t62343,plain,
    zero = meet(X1,meet(sFlat1,complement(meet(sFlat2,X1)))),
    inference(step,[status(thm)],[t2860,t28]) ).

cnf(t3161,plain,
    meet(X1,meet(sFlat1,complement(meet(sFlat2,X1)))) = zero,
    inference(orient,[status(thm)],[t62343]) ).

cnf(t3170,plain,
    zero = meet(X1,meet(sFlat1,complement(meet(X1,sFlat2)))),
    inference(cp,[status(thm)],[t3161,t27]) ).

cnf(t4357,plain,
    meet(X1,meet(sFlat1,complement(meet(X1,sFlat2)))) = zero,
    inference(orient,[status(thm)],[t3170]) ).

cnf(t4361,plain,
    meet(sFlat0,meet(X1,meet(sFlat1,complement(meet(sFlat0,sFlat2))))) = join(zero,meet(X1,zero)),
    inference(cp,[status(thm)],[t3679,t4357]) ).

cnf(t62381,plain,
    meet(sFlat0,meet(X1,meet(sFlat1,complement(sFlat0)))) = join(zero,meet(X1,zero)),
    inference(step,[status(thm)],[t4361,t117]) ).

cnf(t109,plain,
    b = ifeq(zero,zero,ifeq(join(sFlat0,b),one,complement(sFlat0),b),b),
    inference(cp,[status(thm)],[t22,t107]) ).

cnf(t5,plain,
    ifeq(X1,X1,X2,X3) = X2,
    introduced(definition) ).

cnf(t21,plain,
    ifeq(X1,X1,X2,X3) = X2,
    inference(orient,[status(thm)],[t5]) ).

cnf(t62122,plain,
    b = ifeq(join(sFlat0,b),one,complement(sFlat0),b),
    inference(step,[status(thm)],[t109,t21]) ).

cnf(t62123,plain,
    b = ifeq(one,one,complement(sFlat0),b),
    inference(step,[status(thm)],[t62122,t104]) ).

cnf(t62124,plain,
    b = complement(sFlat0),
    inference(step,[status(thm)],[t62123,t21]) ).

cnf(t111,plain,
    complement(sFlat0) = b,
    inference(orient,[status(thm)],[t62124]) ).

cnf(t62382,plain,
    meet(sFlat0,meet(X1,meet(sFlat1,b))) = join(zero,meet(X1,zero)),
    inference(step,[status(thm)],[t62381,t111]) ).

cnf(t62383,plain,
    meet(sFlat0,meet(X1,meet(sFlat1,b))) = zero,
    inference(step,[status(thm)],[t62382,t752]) ).

cnf(t4370,plain,
    meet(sFlat0,meet(X1,meet(sFlat1,b))) = zero,
    inference(orient,[status(thm)],[t62383]) ).

cnf(t4371,plain,
    zero = meet(sFlat0,meet(sFlat1,b)),
    inference(cp,[status(thm)],[t4370,t359]) ).

cnf(t4387,plain,
    meet(sFlat0,meet(sFlat1,b)) = zero,
    inference(orient,[status(thm)],[t4371]) ).

cnf(t63162,plain,
    meet(sFlat0,sFlat1) = ifeq(zero,zero,ifeq(one,one,complement(b),meet(sFlat0,sFlat1)),meet(sFlat0,sFlat1)),
    inference(step,[status(thm)],[t61748,t4387]) ).

cnf(t63163,plain,
    meet(sFlat0,sFlat1) = ifeq(one,one,complement(b),meet(sFlat0,sFlat1)),
    inference(step,[status(thm)],[t63162,t21]) ).

cnf(t63164,plain,
    meet(sFlat0,sFlat1) = complement(b),
    inference(step,[status(thm)],[t63163,t21]) ).

cnf(t63165,plain,
    meet(sFlat0,sFlat1) = sFlat0,
    inference(step,[status(thm)],[t63164,t83]) ).

cnf(t61756,plain,
    meet(sFlat0,sFlat1) = sFlat0,
    inference(orient,[status(thm)],[t63165]) ).

cnf(t61767,plain,
    meet(sFlat1,join(X1,sFlat2)) = join(sFlat0,meet(sFlat1,join(X1,sFlat2))),
    inference(cp,[status(thm)],[t45671,t61756]) ).

cnf(t214,plain,
    join(sFlat2,join(sFlat1,X1)) = join(sFlat0,join(sFlat1,X1)),
    inference(cp,[status(thm)],[t209,t130]) ).

cnf(t65,plain,
    join(X1,join(X2,X3)) = join(join(X2,X1),X3),
    inference(cp,[status(thm)],[t59,t58]) ).

cnf(t62132,plain,
    join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
    inference(step,[status(thm)],[t65,t59]) ).

cnf(t163,plain,
    join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
    inference(orient,[status(thm)],[t62132]) ).

cnf(t62160,plain,
    join(sFlat1,join(sFlat2,X1)) = join(sFlat0,join(sFlat1,X1)),
    inference(step,[status(thm)],[t214,t163]) ).

cnf(t62161,plain,
    join(sFlat1,join(sFlat2,X1)) = join(sFlat2,X1),
    inference(step,[status(thm)],[t62160,t209]) ).

cnf(t384,plain,
    join(sFlat1,join(sFlat2,X1)) = join(sFlat2,X1),
    inference(orient,[status(thm)],[t62161]) ).

cnf(t385,plain,
    sFlat1 = meet(sFlat1,join(sFlat2,X1)),
    inference(cp,[status(thm)],[t18,t384]) ).

cnf(t430,plain,
    meet(sFlat1,join(sFlat2,X1)) = sFlat1,
    inference(orient,[status(thm)],[t385]) ).

cnf(t431,plain,
    sFlat1 = meet(sFlat1,join(X1,sFlat2)),
    inference(cp,[status(thm)],[t430,t58]) ).

cnf(t686,plain,
    meet(sFlat1,join(X1,sFlat2)) = sFlat1,
    inference(orient,[status(thm)],[t431]) ).

cnf(t63172,plain,
    sFlat1 = join(sFlat0,meet(sFlat1,join(X1,sFlat2))),
    inference(step,[status(thm)],[t61767,t686]) ).

cnf(t63173,plain,
    sFlat1 = join(sFlat0,sFlat1),
    inference(step,[status(thm)],[t63172,t686]) ).

cnf(t63174,plain,
    sFlat1 = sFlat2,
    inference(step,[status(thm)],[t63173,t113]) ).

cnf(t61835,plain,
    sFlat2 = sFlat1,
    inference(orient,[status(thm)],[t63174]) ).

cnf(t63175,plain,
    join(sFlat0,sFlat1) = sFlat1,
    inference(step,[status(thm)],[t113,t61835]) ).

cnf(t61836,plain,
    join(sFlat0,sFlat1) = sFlat1,
    inference(orient,[status(thm)],[t63175]) ).

cnf(f13,negated_conjecture,
    join(complement(b),complement(a)) != complement(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).

fof(f13_nnf,plain,
    join(complement(b),complement(a)) != complement(a),
    inference(nnf_transformation,[status(thm)],[f13]) ).

fof(f13_sk,plain,
    join(complement(b),complement(a)) != complement(a),
    inference(skolemisation,[status(esa)],[f13_nnf]) ).

cnf(c13,plain,
    join(complement(b),complement(a)) != complement(a),
    inference(cnf_transformation,[status(esa)],[f13_sk]) ).

cnf(goal_0,negated_conjecture,
    join(complement(b),complement(a)) != complement(a),
    inference(equality_encoding,[status(esa)],[c13]) ).

cnf(g0_0,plain,
    join(sFlat0,complement(a)) != complement(a),
    inference(rw,[status(thm)],[goal_0,t83]) ).

cnf(g0_1,plain,
    join(sFlat0,sFlat1) != complement(a),
    inference(rw,[status(thm)],[g0_0,t78]) ).

cnf(g0_2,plain,
    sFlat1 != complement(a),
    inference(rw,[status(thm)],[g0_1,t61836]) ).

cnf(g0_3,plain,
    sFlat1 != sFlat1,
    inference(rw,[status(thm)],[g0_2,t78]) ).

cnf(contradiction_0,plain,
    $false,
    inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : LAT218-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07  % Command  : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43  % Computer : n007.cluster.edu
% 0.17/0.43  % Model    : x86_64 x86_64
% 0.17/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43  % Memory   : 8046.5625MB
% 0.17/0.43  % OS       : Linux 6.8.0-71-generic
% 0.17/0.43  % CPULimit : 300
% 0.17/0.44  % WCLimit  : 300
% 0.17/0.44  % DateTime : Wed Sep 23 20:33:23 UTC 2026
% 0.17/0.44  % CPUTime  : 
% 0.17/0.44  Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 198.09/29.05  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 198.09/29.05  % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------