%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT247-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 01:56:24 PM UTC 2026
% Result : Unsatisfiable 114.97s 15.01s
% Output : Proof 114.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 17
% Syntax : Number of formulae : 187 ( 183 unt; 0 def)
% Number of atoms : 195 ( 194 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 : 7 ( 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 : 252 ( 42 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t14,axiom,
sFlat0 = complement(b),
introduced(definition) ).
cnf(t93,plain,
complement(b) = sFlat0,
inference(orient,[status(thm)],[t14]) ).
cnf(t15,axiom,
sFlat1 = complement(a),
introduced(definition) ).
cnf(t88,plain,
complement(a) = sFlat1,
inference(orient,[status(thm)],[t15]) ).
cnf(t16,axiom,
sFlat2 = join(complement(b),complement(a)),
introduced(definition) ).
cnf(t59,plain,
join(complement(b),complement(a)) = sFlat2,
inference(orient,[status(thm)],[t16]) ).
cnf(t224416,plain,
join(complement(b),sFlat1) = sFlat2,
inference(step,[status(thm)],[t59,t88]) ).
cnf(t92,plain,
join(complement(b),sFlat1) = sFlat2,
inference(rw,[status(thm)],[t224416]) ).
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(t27,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t224427,plain,
join(sFlat1,complement(b)) = sFlat2,
inference(step,[status(thm)],[t92,t27]) ).
cnf(t224428,plain,
join(sFlat1,sFlat0) = sFlat2,
inference(step,[status(thm)],[t224427,t93]) ).
cnf(t224429,plain,
join(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t224428,t27]) ).
cnf(t159,plain,
join(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t224429]) ).
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(t30,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
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(t17,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t34,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t30,t17]) ).
cnf(t202,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t34]) ).
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(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(t68,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
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(t20,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t28,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t20,t27]) ).
cnf(t168,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t28]) ).
cnf(t175,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(cp,[status(thm)],[t68,t168]) ).
cnf(t2226,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t175]) ).
cnf(f11,axiom,
meet(join(X,Y),join(X,Z)) = join(X,meet(join(X,Y),join(meet(X,Y),Z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H61) ).
fof(f11_nnf,plain,
! [X,Y,Z] : meet(join(X,Y),join(X,Z)) = join(X,meet(join(X,Y),join(meet(X,Y),Z))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z] : meet(join(X,Y),join(X,Z)) = join(X,meet(join(X,Y),join(meet(X,Y),Z))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(join(X0,X1),join(X0,X2)) = join(X0,meet(join(X0,X1),join(meet(X0,X1),X2))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
join(X1,meet(join(X1,X2),join(meet(X1,X2),X3))) = meet(join(X1,X2),join(X1,X3)),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t39,plain,
join(X1,meet(join(X1,X2),join(meet(X1,X2),X3))) = meet(join(X1,X2),join(X1,X3)),
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(t78,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t94,plain,
zero = meet(b,sFlat0),
inference(cp,[status(thm)],[t78,t93]) ).
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(t64,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t224422,plain,
zero = meet(sFlat0,b),
inference(step,[status(thm)],[t94,t64]) ).
cnf(t120,plain,
meet(sFlat0,b) = zero,
inference(orient,[status(thm)],[t224422]) ).
cnf(t121,plain,
meet(sFlat0,meet(b,X1)) = meet(zero,X1),
inference(cp,[status(thm)],[t68,t120]) ).
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(t18,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t80,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t18,t78]) ).
cnf(t102,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t80]) ).
cnf(t103,plain,
X1 = join(zero,X1),
inference(cp,[status(thm)],[t102,t27]) ).
cnf(t138,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t103]) ).
cnf(t140,plain,
meet(zero,X1) = zero,
inference(cp,[status(thm)],[t138,t18]) ).
cnf(t150,plain,
meet(zero,X1) = zero,
inference(orient,[status(thm)],[t140]) ).
cnf(t224445,plain,
meet(sFlat0,meet(b,X1)) = zero,
inference(step,[status(thm)],[t121,t150]) ).
cnf(t275,plain,
meet(sFlat0,meet(b,X1)) = zero,
inference(orient,[status(thm)],[t224445]) ).
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(t83,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t276,plain,
zero = meet(sFlat0,a),
inference(cp,[status(thm)],[t275,t83]) ).
cnf(t281,plain,
meet(sFlat0,a) = zero,
inference(orient,[status(thm)],[t276]) ).
cnf(t284,plain,
meet(join(sFlat0,a),join(sFlat0,X1)) = join(sFlat0,meet(join(sFlat0,a),join(zero,X1))),
inference(cp,[status(thm)],[t39,t281]) ).
cnf(t224996,plain,
meet(join(sFlat0,a),join(sFlat0,X1)) = join(sFlat0,meet(join(sFlat0,a),X1)),
inference(step,[status(thm)],[t284,t138]) ).
cnf(t27019,plain,
join(sFlat0,meet(join(sFlat0,a),X1)) = meet(join(sFlat0,a),join(sFlat0,X1)),
inference(orient,[status(thm)],[t224996]) ).
cnf(t170,plain,
meet(X1,X2) = meet(meet(X1,X2),X1),
inference(cp,[status(thm)],[t168,t18]) ).
cnf(t224455,plain,
meet(X1,X2) = meet(X1,meet(X2,X1)),
inference(step,[status(thm)],[t170,t68]) ).
cnf(t396,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t224455]) ).
cnf(t81,plain,
meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
inference(cp,[status(thm)],[t68,t78]) ).
cnf(t224549,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(step,[status(thm)],[t81,t150]) ).
cnf(t1233,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(orient,[status(thm)],[t224549]) ).
cnf(t1237,plain,
meet(meet(complement(X1),X2),X1) = meet(meet(complement(X1),X2),zero),
inference(cp,[status(thm)],[t396,t1233]) ).
cnf(t224551,plain,
meet(complement(X1),meet(X2,X1)) = meet(meet(complement(X1),X2),zero),
inference(step,[status(thm)],[t1237,t68]) ).
cnf(t224552,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),meet(X2,zero)),
inference(step,[status(thm)],[t224551,t68]) ).
cnf(t151,plain,
zero = meet(X1,zero),
inference(cp,[status(thm)],[t150,t64]) ).
cnf(t157,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t151]) ).
cnf(t224553,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),zero),
inference(step,[status(thm)],[t224552,t157]) ).
cnf(t224554,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(step,[status(thm)],[t224553,t157]) ).
cnf(t1310,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t224554]) ).
cnf(t1316,plain,
zero = meet(complement(join(X1,X2)),X2),
inference(cp,[status(thm)],[t1310,t168]) ).
cnf(t224556,plain,
zero = meet(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t1316,t64]) ).
cnf(t1359,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t224556]) ).
cnf(t65,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t18,t64]) ).
cnf(t183,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t65]) ).
cnf(t185,plain,
join(X1,X2) = join(join(X1,X2),X1),
inference(cp,[status(thm)],[t183,t20]) ).
cnf(t224471,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(step,[status(thm)],[t185,t30]) ).
cnf(t507,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t224471]) ).
cnf(t1361,plain,
zero = meet(join(X1,X2),complement(join(X2,X1))),
inference(cp,[status(thm)],[t1359,t507]) ).
cnf(t6857,plain,
meet(join(X1,X2),complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t1361]) ).
cnf(t27029,plain,
meet(join(sFlat0,a),join(sFlat0,complement(join(a,sFlat0)))) = join(sFlat0,zero),
inference(cp,[status(thm)],[t27019,t6857]) ).
cnf(t225700,plain,
meet(join(sFlat0,a),join(sFlat0,complement(join(sFlat0,a)))) = join(sFlat0,zero),
inference(step,[status(thm)],[t27029,t27]) ).
cnf(t225701,plain,
meet(join(sFlat0,a),join(sFlat0,complement(join(sFlat0,a)))) = sFlat0,
inference(step,[status(thm)],[t225700,t102]) ).
cnf(t223586,plain,
meet(join(sFlat0,a),join(sFlat0,complement(join(sFlat0,a)))) = sFlat0,
inference(orient,[status(thm)],[t225701]) ).
cnf(t223635,plain,
meet(a,join(sFlat0,complement(join(sFlat0,a)))) = meet(a,sFlat0),
inference(cp,[status(thm)],[t2226,t223586]) ).
cnf(t225702,plain,
meet(a,join(sFlat0,complement(join(sFlat0,a)))) = meet(sFlat0,a),
inference(step,[status(thm)],[t223635,t64]) ).
cnf(t225703,plain,
meet(a,join(sFlat0,complement(join(sFlat0,a)))) = zero,
inference(step,[status(thm)],[t225702,t281]) ).
cnf(t223707,plain,
meet(a,join(sFlat0,complement(join(sFlat0,a)))) = zero,
inference(orient,[status(thm)],[t225703]) ).
cnf(t223711,plain,
join(sFlat0,complement(join(sFlat0,a))) = ifeq(zero,zero,ifeq(join(a,join(sFlat0,complement(join(sFlat0,a)))),one,complement(a),join(sFlat0,complement(join(sFlat0,a)))),join(sFlat0,complement(join(sFlat0,a)))),
inference(cp,[status(thm)],[t22,t223707]) ).
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(t225704,plain,
join(sFlat0,complement(join(sFlat0,a))) = ifeq(join(a,join(sFlat0,complement(join(sFlat0,a)))),one,complement(a),join(sFlat0,complement(join(sFlat0,a)))),
inference(step,[status(thm)],[t223711,t21]) ).
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(t52,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t54,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(cp,[status(thm)],[t30,t52]) ).
cnf(t55,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t20,t52]) ).
cnf(t97,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t55]) ).
cnf(t98,plain,
X1 = meet(one,X1),
inference(cp,[status(thm)],[t97,t64]) ).
cnf(t130,plain,
meet(one,X1) = X1,
inference(orient,[status(thm)],[t98]) ).
cnf(t132,plain,
join(one,X1) = one,
inference(cp,[status(thm)],[t130,t20]) ).
cnf(t147,plain,
join(one,X1) = one,
inference(orient,[status(thm)],[t132]) ).
cnf(t224536,plain,
join(X1,join(complement(X1),X2)) = one,
inference(step,[status(thm)],[t54,t147]) ).
cnf(t1080,plain,
join(X1,join(complement(X1),X2)) = one,
inference(orient,[status(thm)],[t224536]) ).
cnf(t1084,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),one),
inference(cp,[status(thm)],[t507,t1080]) ).
cnf(t224537,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),one),
inference(step,[status(thm)],[t1084,t30]) ).
cnf(t224538,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,one)),
inference(step,[status(thm)],[t224537,t30]) ).
cnf(t148,plain,
one = join(X1,one),
inference(cp,[status(thm)],[t147,t27]) ).
cnf(t153,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t148]) ).
cnf(t224539,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),one),
inference(step,[status(thm)],[t224538,t153]) ).
cnf(t224540,plain,
join(complement(X1),join(X2,X1)) = one,
inference(step,[status(thm)],[t224539,t153]) ).
cnf(t1096,plain,
join(complement(X1),join(X2,X1)) = one,
inference(orient,[status(thm)],[t224540]) ).
cnf(t1101,plain,
one = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t1096,t183]) ).
cnf(t224541,plain,
one = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t1101,t27]) ).
cnf(t1133,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(orient,[status(thm)],[t224541]) ).
cnf(t534,plain,
join(X1,X2) = meet(join(X1,X2),join(X2,X1)),
inference(cp,[status(thm)],[t168,t507]) ).
cnf(t2865,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t534]) ).
cnf(t2952,plain,
one = join(join(X1,X2),complement(join(X2,X1))),
inference(cp,[status(thm)],[t1133,t2865]) ).
cnf(t224742,plain,
one = join(X1,join(X2,complement(join(X2,X1)))),
inference(step,[status(thm)],[t2952,t30]) ).
cnf(t8500,plain,
join(X1,join(X2,complement(join(X2,X1)))) = one,
inference(orient,[status(thm)],[t224742]) ).
cnf(t225705,plain,
join(sFlat0,complement(join(sFlat0,a))) = ifeq(one,one,complement(a),join(sFlat0,complement(join(sFlat0,a)))),
inference(step,[status(thm)],[t225704,t8500]) ).
cnf(t225706,plain,
join(sFlat0,complement(join(sFlat0,a))) = complement(a),
inference(step,[status(thm)],[t225705,t21]) ).
cnf(t225707,plain,
join(sFlat0,complement(join(sFlat0,a))) = sFlat1,
inference(step,[status(thm)],[t225706,t88]) ).
cnf(t223775,plain,
join(sFlat0,complement(join(sFlat0,a))) = sFlat1,
inference(orient,[status(thm)],[t225707]) ).
cnf(t223780,plain,
join(sFlat0,complement(join(sFlat0,a))) = join(sFlat0,sFlat1),
inference(cp,[status(thm)],[t202,t223775]) ).
cnf(t225710,plain,
sFlat1 = join(sFlat0,sFlat1),
inference(step,[status(thm)],[t223780,t223775]) ).
cnf(t225711,plain,
sFlat1 = sFlat2,
inference(step,[status(thm)],[t225710,t159]) ).
cnf(t224008,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t225711]) ).
cnf(t225712,plain,
join(sFlat0,sFlat1) = sFlat1,
inference(step,[status(thm)],[t159,t224008]) ).
cnf(t224009,plain,
join(sFlat0,sFlat1) = sFlat1,
inference(orient,[status(thm)],[t225712]) ).
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,t93]) ).
cnf(g0_1,plain,
join(sFlat0,sFlat1) != complement(a),
inference(rw,[status(thm)],[g0_0,t88]) ).
cnf(g0_2,plain,
sFlat1 != complement(a),
inference(rw,[status(thm)],[g0_1,t224009]) ).
cnf(g0_3,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_2,t88]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT247-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 20:41:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 114.97/15.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 114.97/15.01 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------