%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT237-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 01:56:23 PM UTC 2026
% Result : Unsatisfiable 16.58s 2.52s
% Output : Proof 16.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 15
% Syntax : Number of formulae : 185 ( 181 unt; 0 def)
% Number of atoms : 193 ( 192 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 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 : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 323 ( 56 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,axiom,
( complement(X) = Y
| join(X,Y) != one
| meet(X,Y) != zero ),
file('/export/starexec/sandbox2/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(t19,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X1),X2),X2) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(f11,axiom,
meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(Z,join(X,Y)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H40) ).
fof(f11_nnf,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(Z,join(X,Y)))))),
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(U,meet(Z,join(X,Y)))))),
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(X3,meet(X2,join(X0,X1)))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
meet(X1,join(X2,meet(X3,join(X4,meet(X3,join(X1,X2)))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t47,plain,
meet(X1,join(X2,meet(X3,join(X4,meet(X3,join(X1,X2)))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(orient,[status(thm)],[t13]) ).
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(t16,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t50,plain,
meet(X1,join(X2,meet(X3,join(X1,meet(X3,join(X1,X2)))))) = meet(X1,join(X2,meet(X3,meet(X3,join(X1,X2))))),
inference(cp,[status(thm)],[t47,t16]) ).
cnf(t1652,plain,
meet(X1,join(X2,meet(X3,join(X1,X1)))) = meet(X1,join(X2,meet(X3,meet(X3,join(X1,X2))))),
inference(step,[status(thm)],[t50,t47]) ).
cnf(t1653,plain,
meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,meet(X3,meet(X3,join(X1,X2))))),
inference(step,[status(thm)],[t1652,t16]) ).
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(t8,plain,
meet(X1,X2) = meet(X2,X1),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t24,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t1654,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,meet(X3,join(X1,X2))))),
inference(step,[status(thm)],[t1653,t24]) ).
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(t11,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t1572,plain,
meet(X3,meet(X1,X2)) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t11,t24]) ).
cnf(t27,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)),
inference(orient,[status(thm)],[t1572]) ).
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(t1,plain,
meet(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t14,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t30,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(cp,[status(thm)],[t27,t14]) ).
cnf(t1574,plain,
meet(X1,meet(X1,X2)) = meet(X2,X1),
inference(step,[status(thm)],[t30,t27]) ).
cnf(t1575,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(step,[status(thm)],[t1574,t24]) ).
cnf(t117,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t1575]) ).
cnf(t1655,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,X2)))),
inference(step,[status(thm)],[t1654,t117]) ).
cnf(t337,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,meet(X1,X3))),
inference(orient,[status(thm)],[t1655]) ).
cnf(f8,axiom,
join(X,complement(X)) = one,
file('/export/starexec/sandbox2/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(t96,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t353,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),meet(X2,one))),
inference(cp,[status(thm)],[t337,t96]) ).
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(t9,plain,
meet(X1,join(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t15,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t97,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t15,t96]) ).
cnf(t112,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t97]) ).
cnf(t1672,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t353,t112]) ).
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(t6,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t69,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t1673,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(X2,complement(X1))),
inference(step,[status(thm)],[t1672,t69]) ).
cnf(t477,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(X2,complement(X1))),
inference(orient,[status(thm)],[t1673]) ).
cnf(f9,axiom,
meet(X,complement(X)) = zero,
file('/export/starexec/sandbox2/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(t59,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t62,plain,
meet(X1,meet(complement(X1),X2)) = meet(X2,zero),
inference(cp,[status(thm)],[t27,t59]) ).
cnf(t1584,plain,
meet(X1,meet(X2,complement(X1))) = meet(X2,zero),
inference(step,[status(thm)],[t62,t24]) ).
cnf(t120,plain,
meet(X1,complement(X1)) = meet(X1,zero),
inference(cp,[status(thm)],[t117,t59]) ).
cnf(t1576,plain,
zero = meet(X1,zero),
inference(step,[status(thm)],[t120,t59]) ).
cnf(t127,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t1576]) ).
cnf(t1585,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t1584,t127]) ).
cnf(t161,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t1585]) ).
cnf(t166,plain,
meet(X1,meet(meet(X2,complement(X1)),X3)) = meet(X3,zero),
inference(cp,[status(thm)],[t27,t161]) ).
cnf(t1594,plain,
meet(X1,meet(X3,meet(X2,complement(X1)))) = meet(X3,zero),
inference(step,[status(thm)],[t166,t24]) ).
cnf(t1595,plain,
meet(X1,meet(X2,meet(complement(X1),X3))) = meet(X3,zero),
inference(step,[status(thm)],[t1594,t27]) ).
cnf(t1596,plain,
meet(X1,meet(X2,meet(X3,complement(X1)))) = meet(X3,zero),
inference(step,[status(thm)],[t1595,t24]) ).
cnf(t1597,plain,
meet(X1,meet(X2,meet(X3,complement(X1)))) = zero,
inference(step,[status(thm)],[t1596,t127]) ).
cnf(t203,plain,
meet(X1,meet(X2,meet(X3,complement(X1)))) = zero,
inference(orient,[status(thm)],[t1597]) ).
cnf(t487,plain,
meet(X1,join(meet(X2,meet(X3,complement(X1))),complement(X1))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t477,t203]) ).
cnf(t1708,plain,
meet(X1,join(complement(X1),meet(X2,meet(X3,complement(X1))))) = meet(X1,join(complement(X1),zero)),
inference(step,[status(thm)],[t487,t69]) ).
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(t7,plain,
join(X1,meet(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t17,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t60,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t17,t59]) ).
cnf(t101,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t60]) ).
cnf(t1709,plain,
meet(X1,join(complement(X1),meet(X2,meet(X3,complement(X1))))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t1708,t101]) ).
cnf(t1710,plain,
meet(X1,join(complement(X1),meet(X2,meet(X3,complement(X1))))) = zero,
inference(step,[status(thm)],[t1709,t59]) ).
cnf(t661,plain,
meet(X1,join(complement(X1),meet(X2,meet(X3,complement(X1))))) = zero,
inference(orient,[status(thm)],[t1710]) ).
cnf(t31,plain,
meet(join(X1,X2),meet(X3,X1)) = meet(X3,X1),
inference(cp,[status(thm)],[t27,t15]) ).
cnf(t1588,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X3,X1),
inference(step,[status(thm)],[t31,t27]) ).
cnf(t1589,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X3,X1),
inference(step,[status(thm)],[t1588,t24]) ).
cnf(t1590,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X1,X3),
inference(step,[status(thm)],[t1589,t24]) ).
cnf(t176,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t1590]) ).
cnf(t493,plain,
meet(X1,join(meet(X2,join(X1,X3)),complement(X1))) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(cp,[status(thm)],[t477,t176]) ).
cnf(t1778,plain,
meet(X1,join(complement(X1),meet(X2,join(X1,X3)))) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(step,[status(thm)],[t493,t69]) ).
cnf(t1779,plain,
meet(X1,join(complement(X1),meet(X2,join(X1,X3)))) = meet(X1,join(X2,complement(X1))),
inference(step,[status(thm)],[t1778,t477]) ).
cnf(t1151,plain,
meet(X1,join(complement(X1),meet(X2,join(X1,X3)))) = meet(X1,join(X2,complement(X1))),
inference(orient,[status(thm)],[t1779]) ).
cnf(t492,plain,
meet(X1,join(meet(X2,complement(X1)),complement(X1))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t477,t161]) ).
cnf(t1694,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = meet(X1,join(complement(X1),zero)),
inference(step,[status(thm)],[t492,t69]) ).
cnf(t1695,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t1694,t101]) ).
cnf(t1696,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = zero,
inference(step,[status(thm)],[t1695,t59]) ).
cnf(t588,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = zero,
inference(orient,[status(thm)],[t1696]) ).
cnf(t1159,plain,
meet(complement(X1),join(X1,complement(complement(X1)))) = meet(complement(X1),join(complement(complement(X1)),zero)),
inference(cp,[status(thm)],[t1151,t588]) ).
cnf(t1794,plain,
meet(complement(X1),join(X1,complement(complement(X1)))) = meet(complement(X1),complement(complement(X1))),
inference(step,[status(thm)],[t1159,t101]) ).
cnf(t1795,plain,
meet(complement(X1),join(X1,complement(complement(X1)))) = zero,
inference(step,[status(thm)],[t1794,t59]) ).
cnf(t1260,plain,
meet(complement(X1),join(X1,complement(complement(X1)))) = zero,
inference(orient,[status(thm)],[t1795]) ).
cnf(t1261,plain,
join(X1,complement(complement(X1))) = ifeq(zero,zero,ifeq(join(complement(X1),join(X1,complement(complement(X1)))),one,complement(complement(X1)),join(X1,complement(complement(X1)))),join(X1,complement(complement(X1)))),
inference(cp,[status(thm)],[t19,t1260]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t1796,plain,
join(X1,complement(complement(X1))) = ifeq(join(complement(X1),join(X1,complement(complement(X1)))),one,complement(complement(X1)),join(X1,complement(complement(X1)))),
inference(step,[status(thm)],[t1261,t18]) ).
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(t10,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t1573,plain,
join(X3,join(X1,X2)) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t10,t69]) ).
cnf(t74,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(orient,[status(thm)],[t1573]) ).
cnf(t99,plain,
join(X1,join(complement(X1),X2)) = join(X2,one),
inference(cp,[status(thm)],[t74,t96]) ).
cnf(t1586,plain,
join(X1,join(X2,complement(X1))) = join(X2,one),
inference(step,[status(thm)],[t99,t69]) ).
cnf(t77,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(cp,[status(thm)],[t74,t16]) ).
cnf(t1577,plain,
join(X1,join(X1,X2)) = join(X2,X1),
inference(step,[status(thm)],[t77,t74]) ).
cnf(t1578,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(step,[status(thm)],[t1577,t69]) ).
cnf(t132,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t1578]) ).
cnf(t135,plain,
join(X1,complement(X1)) = join(X1,one),
inference(cp,[status(thm)],[t132,t96]) ).
cnf(t1579,plain,
one = join(X1,one),
inference(step,[status(thm)],[t135,t96]) ).
cnf(t143,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t1579]) ).
cnf(t1587,plain,
join(X1,join(X2,complement(X1))) = one,
inference(step,[status(thm)],[t1586,t143]) ).
cnf(t168,plain,
join(X1,join(X2,complement(X1))) = one,
inference(orient,[status(thm)],[t1587]) ).
cnf(t1797,plain,
join(X1,complement(complement(X1))) = ifeq(one,one,complement(complement(X1)),join(X1,complement(complement(X1)))),
inference(step,[status(thm)],[t1796,t168]) ).
cnf(t1798,plain,
join(X1,complement(complement(X1))) = complement(complement(X1)),
inference(step,[status(thm)],[t1797,t18]) ).
cnf(t1268,plain,
join(X1,complement(complement(X1))) = complement(complement(X1)),
inference(orient,[status(thm)],[t1798]) ).
cnf(t1269,plain,
X1 = meet(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t15,t1268]) ).
cnf(t1284,plain,
meet(X1,complement(complement(X1))) = X1,
inference(orient,[status(thm)],[t1269]) ).
cnf(t1306,plain,
zero = meet(complement(X1),join(complement(complement(X1)),meet(X2,X1))),
inference(cp,[status(thm)],[t661,t1284]) ).
cnf(t1818,plain,
zero = meet(complement(X1),join(meet(X2,X1),complement(complement(X1)))),
inference(step,[status(thm)],[t1306,t69]) ).
cnf(t1819,plain,
zero = meet(complement(X1),join(meet(X1,X2),complement(complement(X1)))),
inference(step,[status(thm)],[t1818,t24]) ).
cnf(t1453,plain,
meet(complement(X1),join(meet(X1,X2),complement(complement(X1)))) = zero,
inference(orient,[status(thm)],[t1819]) ).
cnf(t1462,plain,
join(meet(X1,X2),complement(complement(X1))) = ifeq(zero,zero,ifeq(join(complement(X1),join(meet(X1,X2),complement(complement(X1)))),one,complement(complement(X1)),join(meet(X1,X2),complement(complement(X1)))),join(meet(X1,X2),complement(complement(X1)))),
inference(cp,[status(thm)],[t19,t1453]) ).
cnf(t1820,plain,
join(meet(X1,X2),complement(complement(X1))) = ifeq(join(complement(X1),join(meet(X1,X2),complement(complement(X1)))),one,complement(complement(X1)),join(meet(X1,X2),complement(complement(X1)))),
inference(step,[status(thm)],[t1462,t18]) ).
cnf(t1821,plain,
join(meet(X1,X2),complement(complement(X1))) = ifeq(one,one,complement(complement(X1)),join(meet(X1,X2),complement(complement(X1)))),
inference(step,[status(thm)],[t1820,t168]) ).
cnf(t1822,plain,
join(meet(X1,X2),complement(complement(X1))) = complement(complement(X1)),
inference(step,[status(thm)],[t1821,t18]) ).
cnf(t1473,plain,
join(meet(X1,X2),complement(complement(X1))) = complement(complement(X1)),
inference(orient,[status(thm)],[t1822]) ).
cnf(f12,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox2/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(t64,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t1476,plain,
complement(complement(b)) = join(a,complement(complement(b))),
inference(cp,[status(thm)],[t1473,t64]) ).
cnf(t1497,plain,
join(a,complement(complement(b))) = complement(complement(b)),
inference(orient,[status(thm)],[t1476]) ).
cnf(t1498,plain,
a = meet(a,complement(complement(b))),
inference(cp,[status(thm)],[t15,t1497]) ).
cnf(t1514,plain,
meet(a,complement(complement(b))) = a,
inference(orient,[status(thm)],[t1498]) ).
cnf(t1519,plain,
zero = meet(complement(b),a),
inference(cp,[status(thm)],[t161,t1514]) ).
cnf(t1823,plain,
zero = meet(a,complement(b)),
inference(step,[status(thm)],[t1519,t24]) ).
cnf(t1537,plain,
meet(a,complement(b)) = zero,
inference(orient,[status(thm)],[t1823]) ).
cnf(t1539,plain,
meet(a,join(complement(b),complement(a))) = meet(a,join(complement(a),zero)),
inference(cp,[status(thm)],[t477,t1537]) ).
cnf(t1824,plain,
meet(a,join(complement(b),complement(a))) = meet(a,complement(a)),
inference(step,[status(thm)],[t1539,t101]) ).
cnf(t1825,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(step,[status(thm)],[t1824,t59]) ).
cnf(t1544,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(orient,[status(thm)],[t1825]) ).
cnf(t1545,plain,
join(complement(b),complement(a)) = ifeq(zero,zero,ifeq(join(a,join(complement(b),complement(a))),one,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))),
inference(cp,[status(thm)],[t19,t1544]) ).
cnf(t1826,plain,
join(complement(b),complement(a)) = ifeq(join(a,join(complement(b),complement(a))),one,complement(a),join(complement(b),complement(a))),
inference(step,[status(thm)],[t1545,t18]) ).
cnf(t1827,plain,
join(complement(b),complement(a)) = ifeq(one,one,complement(a),join(complement(b),complement(a))),
inference(step,[status(thm)],[t1826,t168]) ).
cnf(t1828,plain,
join(complement(b),complement(a)) = complement(a),
inference(step,[status(thm)],[t1827,t18]) ).
cnf(t1555,plain,
join(complement(b),complement(a)) = complement(a),
inference(orient,[status(thm)],[t1828]) ).
cnf(f13,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox2/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,
complement(a) != complement(a),
inference(rw,[status(thm)],[goal_0,t1555]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT237-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 20:41:48 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 16.58/2.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.58/2.52 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------