%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 01:54:56 PM UTC 2026
% Result : Unsatisfiable 68.73s 10.02s
% Output : Proof 68.73s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t19,axiom,
sFlat0 = meet(r2,b),
introduced(definition) ).
cnf(t44,plain,
meet(r2,b) = sFlat0,
inference(orient,[status(thm)],[t19]) ).
cnf(f5,axiom,
join(X,Y) = join(Y,X),
file('/export/starexec/sandbox2/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(t9,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t47,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t20,axiom,
sFlat1 = join(r1,meet(r2,b)),
introduced(definition) ).
cnf(t123763,plain,
sFlat1 = join(r1,sFlat0),
inference(step,[status(thm)],[t20,t44]) ).
cnf(t123764,plain,
sFlat1 = join(sFlat0,r1),
inference(step,[status(thm)],[t123763,t47]) ).
cnf(t91,plain,
join(sFlat0,r1) = sFlat1,
inference(orient,[status(thm)],[t123764]) ).
cnf(t21,axiom,
sFlat2 = complement(a,join(r1,meet(r2,b))),
introduced(definition) ).
cnf(t123767,plain,
sFlat2 = complement(a,join(r1,sFlat0)),
inference(step,[status(thm)],[t21,t44]) ).
cnf(t123768,plain,
sFlat2 = complement(a,join(sFlat0,r1)),
inference(step,[status(thm)],[t123767,t47]) ).
cnf(t123769,plain,
sFlat2 = complement(a,sFlat1),
inference(step,[status(thm)],[t123768,t91]) ).
cnf(t134,plain,
complement(a,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t123769]) ).
cnf(f15,axiom,
( complement(X,Y)
| join(X,Y) != n1
| meet(X,Y) != n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_join_complement) ).
fof(f15_nnf,plain,
! [X,Y] :
( complement(X,Y)
| join(X,Y) != n1
| meet(X,Y) != n0 ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y] :
( complement(X,Y)
| join(X,Y) != n1
| meet(X,Y) != n0 ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( complement(X0,X1)
| join(X0,X1) != n1
| meet(X0,X1) != n0 ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t17,plain,
ifeq(meet(X1,X2),n0,ifeq(join(X1,X2),n1,complement(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t97,plain,
ifeq(meet(X1,X2),n0,ifeq(join(X1,X2),n1,complement(X1,X2),true),true) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(f4,axiom,
meet(X,Y) = meet(Y,X),
file('/export/starexec/sandbox2/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(t11,plain,
meet(X1,X2) = meet(X2,X1),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t29,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t104,plain,
true = ifeq(meet(X1,X2),n0,ifeq(join(X2,X1),n1,complement(X2,X1),true),true),
inference(cp,[status(thm)],[t97,t29]) ).
cnf(t122669,plain,
ifeq(meet(X1,X2),n0,ifeq(join(X2,X1),n1,complement(X2,X1),true),true) = true,
inference(orient,[status(thm)],[t104]) ).
cnf(f2,axiom,
meet(X,join(X,Y)) = X,
file('/export/starexec/sandbox2/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(t12,plain,
meet(X1,join(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t23,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t12]) ).
cnf(t49,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t23,t47]) ).
cnf(t208,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t49]) ).
cnf(f7,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)),
file('/export/starexec/sandbox2/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(t15,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t76,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t15]) ).
cnf(t212,plain,
X1 = meet(X1,join(X2,join(X3,X1))),
inference(cp,[status(thm)],[t208,t76]) ).
cnf(t1247,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(orient,[status(thm)],[t212]) ).
cnf(f3,axiom,
join(X,meet(X,Y)) = X,
file('/export/starexec/sandbox2/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(t10,plain,
join(X1,meet(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t26,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t1254,plain,
meet(X1,X2) = meet(meet(X1,X2),join(X3,X1)),
inference(cp,[status(thm)],[t1247,t26]) ).
cnf(f6,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('/export/starexec/sandbox2/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(t16,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t32,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t16]) ).
cnf(t123998,plain,
meet(X1,X2) = meet(X1,meet(X2,join(X3,X1))),
inference(step,[status(thm)],[t1254,t32]) ).
cnf(t5171,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t123998]) ).
cnf(f12,axiom,
( meet(Z,join(X,Y)) = join(X,meet(Y,Z))
| meet(X,Z) != X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modular) ).
fof(f12_nnf,plain,
! [X,Z,Y] :
( meet(Z,join(X,Y)) = join(X,meet(Y,Z))
| meet(X,Z) != X ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Z,Y] :
( meet(Z,join(X,Y)) = join(X,meet(Y,Z))
| meet(X,Z) != X ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( meet(X1,join(X0,X2)) = join(X0,meet(X2,X1))
| meet(X0,X1) != X0 ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t18,plain,
ifeq(meet(X1,X2),X1,meet(X2,join(X1,X3)),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t50,plain,
ifeq(meet(X1,X2),X1,meet(X2,join(X1,X3)),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
inference(orient,[status(thm)],[t18]) ).
cnf(t54,plain,
join(X1,meet(X2,join(X1,X3))) = ifeq(X1,X1,meet(join(X1,X3),join(X1,X2)),join(X1,meet(X2,join(X1,X3)))),
inference(cp,[status(thm)],[t50,t23]) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t124018,plain,
join(X1,meet(X2,join(X1,X3))) = meet(join(X1,X3),join(X1,X2)),
inference(step,[status(thm)],[t54,t28]) ).
cnf(t6737,plain,
join(X1,meet(X2,join(X1,X3))) = meet(join(X1,X3),join(X1,X2)),
inference(orient,[status(thm)],[t124018]) ).
cnf(f13,axiom,
( meet(X,Y) = n0
| ~ complement(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_meet) ).
fof(f13_nnf,plain,
! [X,Y] :
( meet(X,Y) = n0
| ~ complement(X,Y) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y] :
( meet(X,Y) = n0
| ~ complement(X,Y) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( meet(X0,X1) = n0
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t14,plain,
ifeq(complement(X1,X2),true,meet(X1,X2),n0) = n0,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t114,plain,
ifeq(complement(X1,X2),true,meet(X1,X2),n0) = n0,
inference(orient,[status(thm)],[t14]) ).
cnf(f16,hypothesis,
complement(r1,join(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_join_b) ).
fof(f16_nnf,plain,
complement(r1,join(a,b)),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
complement(r1,join(a,b)),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(t6,plain,
complement(r1,join(a,b)) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t123766,plain,
complement(r1,join(b,a)) = true,
inference(step,[status(thm)],[t6,t47]) ).
cnf(t96,plain,
complement(r1,join(b,a)) = true,
inference(orient,[status(thm)],[t123766]) ).
cnf(t116,plain,
n0 = ifeq(true,true,meet(r1,join(b,a)),n0),
inference(cp,[status(thm)],[t114,t96]) ).
cnf(t123775,plain,
n0 = meet(r1,join(b,a)),
inference(step,[status(thm)],[t116,t28]) ).
cnf(t237,plain,
meet(r1,join(b,a)) = n0,
inference(orient,[status(thm)],[t123775]) ).
cnf(t238,plain,
meet(r1,meet(join(b,a),X1)) = meet(n0,X1),
inference(cp,[status(thm)],[t32,t237]) ).
cnf(f8,axiom,
meet(X,n0) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_meet_0) ).
fof(f8_nnf,plain,
! [X] : meet(X,n0) = n0,
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] : meet(X,n0) = n0,
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
meet(X0,n0) = n0,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t4,plain,
meet(X1,n0) = n0,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t41,plain,
meet(X1,n0) = n0,
inference(orient,[status(thm)],[t4]) ).
cnf(t42,plain,
n0 = meet(n0,X1),
inference(cp,[status(thm)],[t41,t29]) ).
cnf(t145,plain,
meet(n0,X1) = n0,
inference(orient,[status(thm)],[t42]) ).
cnf(t123851,plain,
meet(r1,meet(join(b,a),X1)) = n0,
inference(step,[status(thm)],[t238,t145]) ).
cnf(t1308,plain,
meet(r1,meet(join(b,a),X1)) = n0,
inference(orient,[status(thm)],[t123851]) ).
cnf(t1309,plain,
n0 = meet(r1,meet(X1,join(b,a))),
inference(cp,[status(thm)],[t1308,t29]) ).
cnf(t1756,plain,
meet(r1,meet(X1,join(b,a))) = n0,
inference(orient,[status(thm)],[t1309]) ).
cnf(t31,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t26,t29]) ).
cnf(t179,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t31]) ).
cnf(t45,plain,
meet(r2,meet(b,X1)) = meet(sFlat0,X1),
inference(cp,[status(thm)],[t32,t44]) ).
cnf(t261,plain,
meet(r2,meet(b,X1)) = meet(sFlat0,X1),
inference(orient,[status(thm)],[t45]) ).
cnf(t263,plain,
meet(sFlat0,join(b,X1)) = meet(r2,b),
inference(cp,[status(thm)],[t261,t23]) ).
cnf(t123788,plain,
meet(sFlat0,join(b,X1)) = sFlat0,
inference(step,[status(thm)],[t263,t44]) ).
cnf(t280,plain,
meet(sFlat0,join(b,X1)) = sFlat0,
inference(orient,[status(thm)],[t123788]) ).
cnf(t282,plain,
join(b,X1) = join(join(b,X1),sFlat0),
inference(cp,[status(thm)],[t179,t280]) ).
cnf(t123811,plain,
join(b,X1) = join(b,join(X1,sFlat0)),
inference(step,[status(thm)],[t282,t76]) ).
cnf(t618,plain,
join(b,join(X1,sFlat0)) = join(b,X1),
inference(orient,[status(thm)],[t123811]) ).
cnf(t623,plain,
join(X1,sFlat0) = meet(join(X1,sFlat0),join(b,X1)),
inference(cp,[status(thm)],[t208,t618]) ).
cnf(t4169,plain,
meet(join(X1,sFlat0),join(b,X1)) = join(X1,sFlat0),
inference(orient,[status(thm)],[t623]) ).
cnf(t4196,plain,
n0 = meet(r1,join(a,sFlat0)),
inference(cp,[status(thm)],[t1756,t4169]) ).
cnf(t123980,plain,
n0 = meet(r1,join(sFlat0,a)),
inference(step,[status(thm)],[t4196,t47]) ).
cnf(t4204,plain,
meet(r1,join(sFlat0,a)) = n0,
inference(orient,[status(thm)],[t123980]) ).
cnf(t6762,plain,
meet(join(sFlat0,a),join(sFlat0,r1)) = join(sFlat0,n0),
inference(cp,[status(thm)],[t6737,t4204]) ).
cnf(t124019,plain,
meet(join(sFlat0,r1),join(sFlat0,a)) = join(sFlat0,n0),
inference(step,[status(thm)],[t6762,t29]) ).
cnf(t124020,plain,
meet(sFlat1,join(sFlat0,a)) = join(sFlat0,n0),
inference(step,[status(thm)],[t124019,t91]) ).
cnf(f9,axiom,
join(X,n0) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_join_0) ).
fof(f9_nnf,plain,
! [X] : join(X,n0) = X,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] : join(X,n0) = X,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
join(X0,n0) = X0,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t1,plain,
join(X1,n0) = X1,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t27,plain,
join(X1,n0) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t124021,plain,
meet(sFlat1,join(sFlat0,a)) = sFlat0,
inference(step,[status(thm)],[t124020,t27]) ).
cnf(t6918,plain,
meet(sFlat1,join(sFlat0,a)) = sFlat0,
inference(orient,[status(thm)],[t124021]) ).
cnf(t6929,plain,
meet(a,sFlat1) = meet(a,sFlat0),
inference(cp,[status(thm)],[t5171,t6918]) ).
cnf(t124022,plain,
meet(sFlat1,a) = meet(a,sFlat0),
inference(step,[status(thm)],[t6929,t29]) ).
cnf(t124023,plain,
meet(sFlat1,a) = meet(sFlat0,a),
inference(step,[status(thm)],[t124022,t29]) ).
cnf(f17,hypothesis,
complement(r2,meet(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_meet_b) ).
fof(f17_nnf,plain,
complement(r2,meet(a,b)),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
complement(r2,meet(a,b)),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(t7,plain,
complement(r2,meet(a,b)) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t123765,plain,
complement(r2,meet(b,a)) = true,
inference(step,[status(thm)],[t7,t29]) ).
cnf(t95,plain,
complement(r2,meet(b,a)) = true,
inference(orient,[status(thm)],[t123765]) ).
cnf(t115,plain,
n0 = ifeq(true,true,meet(r2,meet(b,a)),n0),
inference(cp,[status(thm)],[t114,t95]) ).
cnf(t123774,plain,
n0 = meet(r2,meet(b,a)),
inference(step,[status(thm)],[t115,t28]) ).
cnf(t232,plain,
meet(r2,meet(b,a)) = n0,
inference(orient,[status(thm)],[t123774]) ).
cnf(t123787,plain,
meet(sFlat0,a) = n0,
inference(step,[status(thm)],[t232,t261]) ).
cnf(t273,plain,
meet(sFlat0,a) = n0,
inference(rw,[status(thm)],[t123787]) ).
cnf(t274,plain,
meet(sFlat0,a) = n0,
inference(orient,[status(thm)],[t273]) ).
cnf(t124024,plain,
meet(sFlat1,a) = n0,
inference(step,[status(thm)],[t124023,t274]) ).
cnf(t6941,plain,
meet(sFlat1,a) = n0,
inference(orient,[status(thm)],[t124024]) ).
cnf(t122979,plain,
true = ifeq(n0,n0,ifeq(join(a,sFlat1),n1,complement(a,sFlat1),true),true),
inference(cp,[status(thm)],[t122669,t6941]) ).
cnf(t125182,plain,
true = ifeq(join(a,sFlat1),n1,complement(a,sFlat1),true),
inference(step,[status(thm)],[t122979,t28]) ).
cnf(t125183,plain,
true = ifeq(join(sFlat1,a),n1,complement(a,sFlat1),true),
inference(step,[status(thm)],[t125182,t47]) ).
cnf(t93,plain,
join(sFlat0,join(r1,X1)) = join(sFlat1,X1),
inference(cp,[status(thm)],[t76,t91]) ).
cnf(t365,plain,
join(sFlat0,join(r1,X1)) = join(sFlat1,X1),
inference(orient,[status(thm)],[t93]) ).
cnf(t373,plain,
join(r1,X1) = meet(join(r1,X1),join(sFlat1,X1)),
inference(cp,[status(thm)],[t208,t365]) ).
cnf(t123972,plain,
join(r1,X1) = meet(join(sFlat1,X1),join(r1,X1)),
inference(step,[status(thm)],[t373,t29]) ).
cnf(t3306,plain,
meet(join(sFlat1,X1),join(r1,X1)) = join(r1,X1),
inference(orient,[status(thm)],[t123972]) ).
cnf(t3327,plain,
join(r1,X1) = meet(join(sFlat1,X1),join(X1,r1)),
inference(cp,[status(thm)],[t3306,t47]) ).
cnf(t6154,plain,
meet(join(sFlat1,X1),join(X1,r1)) = join(r1,X1),
inference(orient,[status(thm)],[t3327]) ).
cnf(t181,plain,
join(X1,X2) = join(join(X1,X2),X1),
inference(cp,[status(thm)],[t179,t23]) ).
cnf(t123794,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(step,[status(thm)],[t181,t76]) ).
cnf(t465,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t123794]) ).
cnf(f14,axiom,
( join(X,Y) = n1
| ~ complement(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_join) ).
fof(f14_nnf,plain,
! [X,Y] :
( join(X,Y) = n1
| ~ complement(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y] :
( join(X,Y) = n1
| ~ complement(X,Y) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( join(X0,X1) = n1
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t13,plain,
ifeq(complement(X1,X2),true,join(X1,X2),n1) = n1,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t124,plain,
ifeq(complement(X1,X2),true,join(X1,X2),n1) = n1,
inference(orient,[status(thm)],[t13]) ).
cnf(t126,plain,
n1 = ifeq(true,true,join(r1,join(b,a)),n1),
inference(cp,[status(thm)],[t124,t96]) ).
cnf(t123777,plain,
n1 = join(r1,join(b,a)),
inference(step,[status(thm)],[t126,t28]) ).
cnf(t247,plain,
join(r1,join(b,a)) = n1,
inference(orient,[status(thm)],[t123777]) ).
cnf(t366,plain,
join(sFlat1,join(b,a)) = join(sFlat0,n1),
inference(cp,[status(thm)],[t365,t247]) ).
cnf(f11,axiom,
join(X,n1) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_join_1) ).
fof(f11_nnf,plain,
! [X] : join(X,n1) = n1,
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : join(X,n1) = n1,
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
join(X0,n1) = n1,
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t2,plain,
join(X1,n1) = n1,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t87,plain,
join(X1,n1) = n1,
inference(orient,[status(thm)],[t2]) ).
cnf(t123791,plain,
join(sFlat1,join(b,a)) = n1,
inference(step,[status(thm)],[t366,t87]) ).
cnf(t377,plain,
join(sFlat1,join(b,a)) = n1,
inference(orient,[status(thm)],[t123791]) ).
cnf(t471,plain,
join(join(b,a),sFlat1) = join(join(b,a),n1),
inference(cp,[status(thm)],[t465,t377]) ).
cnf(t123800,plain,
join(b,join(a,sFlat1)) = join(join(b,a),n1),
inference(step,[status(thm)],[t471,t76]) ).
cnf(t123801,plain,
join(b,join(sFlat1,a)) = join(join(b,a),n1),
inference(step,[status(thm)],[t123800,t47]) ).
cnf(t123802,plain,
join(b,join(sFlat1,a)) = join(b,join(a,n1)),
inference(step,[status(thm)],[t123801,t76]) ).
cnf(t123803,plain,
join(b,join(sFlat1,a)) = join(b,n1),
inference(step,[status(thm)],[t123802,t87]) ).
cnf(t123804,plain,
join(b,join(sFlat1,a)) = n1,
inference(step,[status(thm)],[t123803,t87]) ).
cnf(t491,plain,
join(b,join(sFlat1,a)) = n1,
inference(orient,[status(thm)],[t123804]) ).
cnf(t494,plain,
join(b,join(join(sFlat1,a),X1)) = join(n1,X1),
inference(cp,[status(thm)],[t76,t491]) ).
cnf(t123861,plain,
join(b,join(sFlat1,join(a,X1))) = join(n1,X1),
inference(step,[status(thm)],[t494,t76]) ).
cnf(t88,plain,
n1 = join(n1,X1),
inference(cp,[status(thm)],[t87,t47]) ).
cnf(t162,plain,
join(n1,X1) = n1,
inference(orient,[status(thm)],[t88]) ).
cnf(t123862,plain,
join(b,join(sFlat1,join(a,X1))) = n1,
inference(step,[status(thm)],[t123861,t162]) ).
cnf(t1589,plain,
join(b,join(sFlat1,join(a,X1))) = n1,
inference(orient,[status(thm)],[t123862]) ).
cnf(t1591,plain,
join(join(sFlat1,join(a,X1)),b) = join(join(sFlat1,join(a,X1)),n1),
inference(cp,[status(thm)],[t465,t1589]) ).
cnf(t123906,plain,
join(sFlat1,join(join(a,X1),b)) = join(join(sFlat1,join(a,X1)),n1),
inference(step,[status(thm)],[t1591,t76]) ).
cnf(t123907,plain,
join(sFlat1,join(a,join(X1,b))) = join(join(sFlat1,join(a,X1)),n1),
inference(step,[status(thm)],[t123906,t76]) ).
cnf(t123908,plain,
join(sFlat1,join(a,join(X1,b))) = join(sFlat1,join(join(a,X1),n1)),
inference(step,[status(thm)],[t123907,t76]) ).
cnf(t123909,plain,
join(sFlat1,join(a,join(X1,b))) = join(sFlat1,join(a,join(X1,n1))),
inference(step,[status(thm)],[t123908,t76]) ).
cnf(t123910,plain,
join(sFlat1,join(a,join(X1,b))) = join(sFlat1,join(a,n1)),
inference(step,[status(thm)],[t123909,t87]) ).
cnf(t123911,plain,
join(sFlat1,join(a,join(X1,b))) = join(sFlat1,n1),
inference(step,[status(thm)],[t123910,t87]) ).
cnf(t123912,plain,
join(sFlat1,join(a,join(X1,b))) = n1,
inference(step,[status(thm)],[t123911,t87]) ).
cnf(t2231,plain,
join(sFlat1,join(a,join(X1,b))) = n1,
inference(orient,[status(thm)],[t123912]) ).
cnf(t2237,plain,
n1 = join(sFlat1,join(a,join(b,X1))),
inference(cp,[status(thm)],[t2231,t47]) ).
cnf(t2653,plain,
join(sFlat1,join(a,join(b,X1))) = n1,
inference(orient,[status(thm)],[t2237]) ).
cnf(t6165,plain,
join(r1,join(a,join(b,X1))) = meet(n1,join(join(a,join(b,X1)),r1)),
inference(cp,[status(thm)],[t6154,t2653]) ).
cnf(f10,axiom,
meet(X,n1) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_meet_1) ).
fof(f10_nnf,plain,
! [X] : meet(X,n1) = X,
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X] : meet(X,n1) = X,
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
meet(X0,n1) = X0,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t5,plain,
meet(X1,n1) = X1,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t24,plain,
meet(X1,n1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t30,plain,
meet(n1,X1) = X1,
inference(cp,[status(thm)],[t29,t24]) ).
cnf(t138,plain,
meet(n1,X1) = X1,
inference(orient,[status(thm)],[t30]) ).
cnf(t124008,plain,
join(r1,join(a,join(b,X1))) = join(join(a,join(b,X1)),r1),
inference(step,[status(thm)],[t6165,t138]) ).
cnf(t124009,plain,
join(r1,join(a,join(b,X1))) = join(a,join(join(b,X1),r1)),
inference(step,[status(thm)],[t124008,t76]) ).
cnf(t124010,plain,
join(r1,join(a,join(b,X1))) = join(a,join(b,join(X1,r1))),
inference(step,[status(thm)],[t124009,t76]) ).
cnf(t185,plain,
X1 = join(X1,meet(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t179,t32]) ).
cnf(t1201,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(orient,[status(thm)],[t185]) ).
cnf(t1211,plain,
join(X1,X2) = join(join(X1,X2),meet(X3,X1)),
inference(cp,[status(thm)],[t1201,t23]) ).
cnf(t123991,plain,
join(X1,X2) = join(X1,join(X2,meet(X3,X1))),
inference(step,[status(thm)],[t1211,t76]) ).
cnf(t4941,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
inference(orient,[status(thm)],[t123991]) ).
cnf(f1,axiom,
join(X,X) = X,
file('/export/starexec/sandbox2/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(t25,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t80,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t76,t25]) ).
cnf(t358,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t80]) ).
cnf(t3316,plain,
join(r1,join(sFlat1,X1)) = meet(join(sFlat1,X1),join(r1,join(sFlat1,X1))),
inference(cp,[status(thm)],[t3306,t358]) ).
cnf(t123973,plain,
join(r1,join(sFlat1,X1)) = join(sFlat1,X1),
inference(step,[status(thm)],[t3316,t208]) ).
cnf(t3341,plain,
join(r1,join(sFlat1,X1)) = join(sFlat1,X1),
inference(orient,[status(thm)],[t123973]) ).
cnf(t3359,plain,
join(sFlat1,X1) = join(r1,join(X1,sFlat1)),
inference(cp,[status(thm)],[t3341,t47]) ).
cnf(t472,plain,
join(join(r1,X1),sFlat0) = join(join(r1,X1),join(sFlat1,X1)),
inference(cp,[status(thm)],[t465,t365]) ).
cnf(t123833,plain,
join(r1,join(X1,sFlat0)) = join(join(r1,X1),join(sFlat1,X1)),
inference(step,[status(thm)],[t472,t76]) ).
cnf(t123834,plain,
join(r1,join(X1,sFlat0)) = join(r1,join(X1,join(sFlat1,X1))),
inference(step,[status(thm)],[t123833,t76]) ).
cnf(t123835,plain,
join(r1,join(X1,sFlat0)) = join(r1,join(X1,sFlat1)),
inference(step,[status(thm)],[t123834,t465]) ).
cnf(t1037,plain,
join(r1,join(X1,sFlat1)) = join(r1,join(X1,sFlat0)),
inference(orient,[status(thm)],[t123835]) ).
cnf(t123974,plain,
join(sFlat1,X1) = join(r1,join(X1,sFlat0)),
inference(step,[status(thm)],[t3359,t1037]) ).
cnf(t3365,plain,
join(r1,join(X1,sFlat0)) = join(sFlat1,X1),
inference(orient,[status(thm)],[t123974]) ).
cnf(t3375,plain,
join(sFlat1,X1) = join(r1,join(sFlat0,X1)),
inference(cp,[status(thm)],[t3365,t47]) ).
cnf(t3385,plain,
join(r1,join(sFlat0,X1)) = join(sFlat1,X1),
inference(orient,[status(thm)],[t3375]) ).
cnf(t92,plain,
sFlat0 = meet(sFlat0,sFlat1),
inference(cp,[status(thm)],[t23,t91]) ).
cnf(t167,plain,
meet(sFlat0,sFlat1) = sFlat0,
inference(orient,[status(thm)],[t92]) ).
cnf(t170,plain,
join(sFlat0,meet(X1,sFlat1)) = ifeq(sFlat0,sFlat0,meet(sFlat1,join(sFlat0,X1)),join(sFlat0,meet(X1,sFlat1))),
inference(cp,[status(thm)],[t50,t167]) ).
cnf(t123830,plain,
join(sFlat0,meet(X1,sFlat1)) = meet(sFlat1,join(sFlat0,X1)),
inference(step,[status(thm)],[t170,t28]) ).
cnf(t991,plain,
join(sFlat0,meet(X1,sFlat1)) = meet(sFlat1,join(sFlat0,X1)),
inference(orient,[status(thm)],[t123830]) ).
cnf(t996,plain,
meet(sFlat1,join(sFlat0,X1)) = join(sFlat0,meet(sFlat1,X1)),
inference(cp,[status(thm)],[t991,t29]) ).
cnf(t1099,plain,
join(sFlat0,meet(sFlat1,X1)) = meet(sFlat1,join(sFlat0,X1)),
inference(orient,[status(thm)],[t996]) ).
cnf(t3390,plain,
join(sFlat1,meet(sFlat1,X1)) = join(r1,meet(sFlat1,join(sFlat0,X1))),
inference(cp,[status(thm)],[t3385,t1099]) ).
cnf(t123977,plain,
sFlat1 = join(r1,meet(sFlat1,join(sFlat0,X1))),
inference(step,[status(thm)],[t3390,t26]) ).
cnf(t3474,plain,
join(r1,meet(sFlat1,join(sFlat0,X1))) = sFlat1,
inference(orient,[status(thm)],[t123977]) ).
cnf(t184,plain,
b = join(b,sFlat0),
inference(cp,[status(thm)],[t179,t44]) ).
cnf(t123772,plain,
b = join(sFlat0,b),
inference(step,[status(thm)],[t184,t47]) ).
cnf(t195,plain,
join(sFlat0,b) = b,
inference(orient,[status(thm)],[t123772]) ).
cnf(t198,plain,
join(sFlat0,join(b,X1)) = join(b,X1),
inference(cp,[status(thm)],[t76,t195]) ).
cnf(t504,plain,
join(sFlat0,join(b,X1)) = join(b,X1),
inference(orient,[status(thm)],[t198]) ).
cnf(t506,plain,
join(b,X1) = join(sFlat0,join(X1,b)),
inference(cp,[status(thm)],[t504,t47]) ).
cnf(t755,plain,
join(sFlat0,join(X1,b)) = join(b,X1),
inference(orient,[status(thm)],[t506]) ).
cnf(t3482,plain,
sFlat1 = join(r1,meet(sFlat1,join(b,X1))),
inference(cp,[status(thm)],[t3474,t755]) ).
cnf(t3527,plain,
join(r1,meet(sFlat1,join(b,X1))) = sFlat1,
inference(orient,[status(thm)],[t3482]) ).
cnf(t4957,plain,
join(join(b,X1),r1) = join(join(b,X1),sFlat1),
inference(cp,[status(thm)],[t4941,t3527]) ).
cnf(t123992,plain,
join(b,join(X1,r1)) = join(join(b,X1),sFlat1),
inference(step,[status(thm)],[t4957,t76]) ).
cnf(t123993,plain,
join(b,join(X1,r1)) = join(b,join(X1,sFlat1)),
inference(step,[status(thm)],[t123992,t76]) ).
cnf(t5064,plain,
join(b,join(X1,r1)) = join(b,join(X1,sFlat1)),
inference(orient,[status(thm)],[t123993]) ).
cnf(t124011,plain,
join(r1,join(a,join(b,X1))) = join(a,join(b,join(X1,sFlat1))),
inference(step,[status(thm)],[t124010,t5064]) ).
cnf(t2665,plain,
join(join(a,join(b,X1)),sFlat1) = join(join(a,join(b,X1)),n1),
inference(cp,[status(thm)],[t465,t2653]) ).
cnf(t123964,plain,
join(a,join(join(b,X1),sFlat1)) = join(join(a,join(b,X1)),n1),
inference(step,[status(thm)],[t2665,t76]) ).
cnf(t123965,plain,
join(a,join(b,join(X1,sFlat1))) = join(join(a,join(b,X1)),n1),
inference(step,[status(thm)],[t123964,t76]) ).
cnf(t123966,plain,
join(a,join(b,join(X1,sFlat1))) = join(a,join(join(b,X1),n1)),
inference(step,[status(thm)],[t123965,t76]) ).
cnf(t123967,plain,
join(a,join(b,join(X1,sFlat1))) = join(a,join(b,join(X1,n1))),
inference(step,[status(thm)],[t123966,t76]) ).
cnf(t123968,plain,
join(a,join(b,join(X1,sFlat1))) = join(a,join(b,n1)),
inference(step,[status(thm)],[t123967,t87]) ).
cnf(t123969,plain,
join(a,join(b,join(X1,sFlat1))) = join(a,n1),
inference(step,[status(thm)],[t123968,t87]) ).
cnf(t123970,plain,
join(a,join(b,join(X1,sFlat1))) = n1,
inference(step,[status(thm)],[t123969,t87]) ).
cnf(t2937,plain,
join(a,join(b,join(X1,sFlat1))) = n1,
inference(orient,[status(thm)],[t123970]) ).
cnf(t124012,plain,
join(r1,join(a,join(b,X1))) = n1,
inference(step,[status(thm)],[t124011,t2937]) ).
cnf(t6213,plain,
join(r1,join(a,join(b,X1))) = n1,
inference(orient,[status(thm)],[t124012]) ).
cnf(f0,axiom,
meet(X,X) = X,
file('/export/starexec/sandbox2/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(t3,plain,
meet(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t22,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t69,plain,
join(X1,meet(X2,X2)) = ifeq(meet(X1,X2),X1,meet(X2,join(X1,X2)),join(X1,X2)),
inference(cp,[status(thm)],[t50,t22]) ).
cnf(t124369,plain,
join(X1,X2) = ifeq(meet(X1,X2),X1,meet(X2,join(X1,X2)),join(X1,X2)),
inference(step,[status(thm)],[t69,t22]) ).
cnf(t124370,plain,
join(X1,X2) = ifeq(meet(X1,X2),X1,X2,join(X1,X2)),
inference(step,[status(thm)],[t124369,t208]) ).
cnf(t29069,plain,
ifeq(meet(X1,X2),X1,X2,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t124370]) ).
cnf(t73,plain,
join(X1,meet(r2,b)) = ifeq(meet(X1,b),X1,meet(b,join(X1,r2)),join(X1,sFlat0)),
inference(cp,[status(thm)],[t50,t44]) ).
cnf(t124445,plain,
join(X1,sFlat0) = ifeq(meet(X1,b),X1,meet(b,join(X1,r2)),join(X1,sFlat0)),
inference(step,[status(thm)],[t73,t44]) ).
cnf(t34712,plain,
ifeq(meet(X1,b),X1,meet(b,join(X1,r2)),join(X1,sFlat0)) = join(X1,sFlat0),
inference(orient,[status(thm)],[t124445]) ).
cnf(t196,plain,
sFlat0 = meet(sFlat0,b),
inference(cp,[status(thm)],[t23,t195]) ).
cnf(t201,plain,
meet(sFlat0,b) = sFlat0,
inference(orient,[status(thm)],[t196]) ).
cnf(t205,plain,
join(sFlat0,meet(X1,b)) = ifeq(sFlat0,sFlat0,meet(b,join(sFlat0,X1)),join(sFlat0,meet(X1,b))),
inference(cp,[status(thm)],[t50,t201]) ).
cnf(t123832,plain,
join(sFlat0,meet(X1,b)) = meet(b,join(sFlat0,X1)),
inference(step,[status(thm)],[t205,t28]) ).
cnf(t1021,plain,
join(sFlat0,meet(X1,b)) = meet(b,join(sFlat0,X1)),
inference(orient,[status(thm)],[t123832]) ).
cnf(t1034,plain,
join(sFlat0,join(meet(X1,b),X2)) = join(meet(b,join(sFlat0,X1)),X2),
inference(cp,[status(thm)],[t76,t1021]) ).
cnf(t43377,plain,
join(meet(b,join(sFlat0,X1)),X2) = join(sFlat0,join(meet(X1,b),X2)),
inference(orient,[status(thm)],[t1034]) ).
cnf(t43488,plain,
join(meet(b,join(sFlat0,X1)),sFlat0) = ifeq(meet(meet(b,join(sFlat0,X1)),b),meet(b,join(sFlat0,X1)),meet(b,join(sFlat0,join(meet(X1,b),r2))),join(meet(b,join(sFlat0,X1)),sFlat0)),
inference(cp,[status(thm)],[t34712,t43377]) ).
cnf(t124520,plain,
join(sFlat0,join(meet(X1,b),sFlat0)) = ifeq(meet(meet(b,join(sFlat0,X1)),b),meet(b,join(sFlat0,X1)),meet(b,join(sFlat0,join(meet(X1,b),r2))),join(meet(b,join(sFlat0,X1)),sFlat0)),
inference(step,[status(thm)],[t43488,t43377]) ).
cnf(t124521,plain,
join(sFlat0,meet(X1,b)) = ifeq(meet(meet(b,join(sFlat0,X1)),b),meet(b,join(sFlat0,X1)),meet(b,join(sFlat0,join(meet(X1,b),r2))),join(meet(b,join(sFlat0,X1)),sFlat0)),
inference(step,[status(thm)],[t124520,t465]) ).
cnf(t124522,plain,
meet(b,join(sFlat0,X1)) = ifeq(meet(meet(b,join(sFlat0,X1)),b),meet(b,join(sFlat0,X1)),meet(b,join(sFlat0,join(meet(X1,b),r2))),join(meet(b,join(sFlat0,X1)),sFlat0)),
inference(step,[status(thm)],[t124521,t1021]) ).
cnf(t124523,plain,
meet(b,join(sFlat0,X1)) = ifeq(meet(b,meet(join(sFlat0,X1),b)),meet(b,join(sFlat0,X1)),meet(b,join(sFlat0,join(meet(X1,b),r2))),join(meet(b,join(sFlat0,X1)),sFlat0)),
inference(step,[status(thm)],[t124522,t32]) ).
cnf(t210,plain,
meet(X1,X2) = meet(meet(X1,X2),X1),
inference(cp,[status(thm)],[t208,t26]) ).
cnf(t123805,plain,
meet(X1,X2) = meet(X1,meet(X2,X1)),
inference(step,[status(thm)],[t210,t32]) ).
cnf(t519,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t123805]) ).
cnf(t124524,plain,
meet(b,join(sFlat0,X1)) = ifeq(meet(b,join(sFlat0,X1)),meet(b,join(sFlat0,X1)),meet(b,join(sFlat0,join(meet(X1,b),r2))),join(meet(b,join(sFlat0,X1)),sFlat0)),
inference(step,[status(thm)],[t124523,t519]) ).
cnf(t124525,plain,
meet(b,join(sFlat0,X1)) = meet(b,join(sFlat0,join(meet(X1,b),r2))),
inference(step,[status(thm)],[t124524,t28]) ).
cnf(t46,plain,
r2 = join(r2,sFlat0),
inference(cp,[status(thm)],[t26,t44]) ).
cnf(t123770,plain,
r2 = join(sFlat0,r2),
inference(step,[status(thm)],[t46,t47]) ).
cnf(t151,plain,
join(sFlat0,r2) = r2,
inference(orient,[status(thm)],[t123770]) ).
cnf(t154,plain,
join(sFlat0,join(r2,X1)) = join(r2,X1),
inference(cp,[status(thm)],[t76,t151]) ).
cnf(t420,plain,
join(sFlat0,join(r2,X1)) = join(r2,X1),
inference(orient,[status(thm)],[t154]) ).
cnf(t421,plain,
join(r2,X1) = join(sFlat0,join(X1,r2)),
inference(cp,[status(thm)],[t420,t47]) ).
cnf(t703,plain,
join(sFlat0,join(X1,r2)) = join(r2,X1),
inference(orient,[status(thm)],[t421]) ).
cnf(t124526,plain,
meet(b,join(sFlat0,X1)) = meet(b,join(r2,meet(X1,b))),
inference(step,[status(thm)],[t124525,t703]) ).
cnf(t43571,plain,
meet(b,join(r2,meet(X1,b))) = meet(b,join(sFlat0,X1)),
inference(orient,[status(thm)],[t124526]) ).
cnf(t43579,plain,
meet(b,join(sFlat0,X1)) = meet(b,join(r2,meet(b,X1))),
inference(cp,[status(thm)],[t43571,t29]) ).
cnf(t43641,plain,
meet(b,join(r2,meet(b,X1))) = meet(b,join(sFlat0,X1)),
inference(orient,[status(thm)],[t43579]) ).
cnf(t125,plain,
n1 = ifeq(true,true,join(r2,meet(b,a)),n1),
inference(cp,[status(thm)],[t124,t95]) ).
cnf(t123776,plain,
n1 = join(r2,meet(b,a)),
inference(step,[status(thm)],[t125,t28]) ).
cnf(t243,plain,
join(r2,meet(b,a)) = n1,
inference(orient,[status(thm)],[t123776]) ).
cnf(t43642,plain,
meet(b,join(sFlat0,a)) = meet(b,n1),
inference(cp,[status(thm)],[t43641,t243]) ).
cnf(t124527,plain,
meet(b,join(sFlat0,a)) = b,
inference(step,[status(thm)],[t43642,t24]) ).
cnf(t43744,plain,
meet(b,join(sFlat0,a)) = b,
inference(orient,[status(thm)],[t124527]) ).
cnf(t43753,plain,
join(b,join(sFlat0,a)) = ifeq(b,b,join(sFlat0,a),join(b,join(sFlat0,a))),
inference(cp,[status(thm)],[t29069,t43744]) ).
cnf(t622,plain,
join(b,X1) = join(b,join(sFlat0,X1)),
inference(cp,[status(thm)],[t618,t47]) ).
cnf(t801,plain,
join(b,join(sFlat0,X1)) = join(b,X1),
inference(orient,[status(thm)],[t622]) ).
cnf(t124534,plain,
join(b,a) = ifeq(b,b,join(sFlat0,a),join(b,join(sFlat0,a))),
inference(step,[status(thm)],[t43753,t801]) ).
cnf(t124535,plain,
join(b,a) = join(sFlat0,a),
inference(step,[status(thm)],[t124534,t28]) ).
cnf(t43807,plain,
join(b,a) = join(sFlat0,a),
inference(orient,[status(thm)],[t124535]) ).
cnf(t43833,plain,
n1 = join(r1,join(a,join(sFlat0,a))),
inference(cp,[status(thm)],[t6213,t43807]) ).
cnf(t3379,plain,
join(r1,join(join(X1,sFlat0),X2)) = join(join(sFlat1,X1),X2),
inference(cp,[status(thm)],[t76,t3365]) ).
cnf(t124108,plain,
join(r1,join(X1,join(sFlat0,X2))) = join(join(sFlat1,X1),X2),
inference(step,[status(thm)],[t3379,t76]) ).
cnf(t124109,plain,
join(r1,join(X1,join(sFlat0,X2))) = join(sFlat1,join(X1,X2)),
inference(step,[status(thm)],[t124108,t76]) ).
cnf(t13501,plain,
join(r1,join(X1,join(sFlat0,X2))) = join(sFlat1,join(X1,X2)),
inference(orient,[status(thm)],[t124109]) ).
cnf(t124555,plain,
n1 = join(sFlat1,join(a,a)),
inference(step,[status(thm)],[t43833,t13501]) ).
cnf(t124556,plain,
n1 = join(sFlat1,a),
inference(step,[status(thm)],[t124555,t25]) ).
cnf(t43866,plain,
join(sFlat1,a) = n1,
inference(orient,[status(thm)],[t124556]) ).
cnf(t125184,plain,
true = ifeq(n1,n1,complement(a,sFlat1),true),
inference(step,[status(thm)],[t125183,t43866]) ).
cnf(t125185,plain,
true = complement(a,sFlat1),
inference(step,[status(thm)],[t125184,t28]) ).
cnf(t125186,plain,
true = sFlat2,
inference(step,[status(thm)],[t125185,t134]) ).
cnf(t123583,plain,
true = sFlat2,
inference(orient,[status(thm)],[t125186]) ).
cnf(f18,negated_conjecture,
~ complement(a,join(r1,meet(r2,b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_complememt) ).
fof(f18_nnf,plain,
~ complement(a,join(r1,meet(r2,b))),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
~ complement(a,join(r1,meet(r2,b))),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
~ complement(a,join(r1,meet(r2,b))),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
complement(a,join(r1,meet(r2,b))) != true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
complement(a,join(r1,sFlat0)) != true,
inference(rw,[status(thm)],[goal_0,t44]) ).
cnf(g0_1,plain,
complement(a,join(sFlat0,r1)) != true,
inference(rw,[status(thm)],[g0_0,t47]) ).
cnf(g0_2,plain,
complement(a,sFlat1) != true,
inference(rw,[status(thm)],[g0_1,t91]) ).
cnf(g0_3,plain,
sFlat2 != true,
inference(rw,[status(thm)],[g0_2,t134]) ).
cnf(g0_4,plain,
sFlat2 != sFlat2,
inference(rw,[status(thm)],[g0_3,t123583]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 19:59:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 68.73/10.02 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.73/10.02 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------