%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT037-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 01:55:04 PM UTC 2026
% Result : Unsatisfiable 7.83s 1.56s
% Output : Proof 7.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 75 ( 75 unt; 0 def)
% Number of atoms : 75 ( 74 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,hypothesis,
join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dist_join) ).
fof(f8_nnf,plain,
! [X,Y,Z] : join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] : join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
join(X0,meet(X1,X2)) = meet(join(X0,X1),join(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t21,plain,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X2,X3)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t43,plain,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t21]) ).
cnf(f16,axiom,
join(xx,zz) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs2) ).
fof(f16_nnf,plain,
join(xx,zz) = n1,
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
join(xx,zz) = n1,
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(t4,plain,
join(xx,zz) = n1,
inference(equality_encoding,[status(esa)],[c16]) ).
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(t11,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t31,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t393,plain,
join(zz,xx) = n1,
inference(step,[status(thm)],[t4,t31]) ).
cnf(t139,plain,
join(zz,xx) = n1,
inference(orient,[status(thm)],[t393]) ).
cnf(t141,plain,
join(zz,meet(X1,xx)) = meet(join(zz,X1),n1),
inference(cp,[status(thm)],[t43,t139]) ).
cnf(f12,axiom,
meet(X,n1) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_1) ).
fof(f12_nnf,plain,
! [X] : meet(X,n1) = X,
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X] : meet(X,n1) = X,
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
meet(X0,n1) = X0,
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t7,plain,
meet(X1,n1) = X1,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t29,plain,
meet(X1,n1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t425,plain,
join(zz,meet(X1,xx)) = join(zz,X1),
inference(step,[status(thm)],[t141,t29]) ).
cnf(t377,plain,
join(zz,meet(X1,xx)) = join(zz,X1),
inference(orient,[status(thm)],[t425]) ).
cnf(f17,axiom,
meet(xx,yy) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs3) ).
fof(f17_nnf,plain,
meet(xx,yy) = n0,
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
meet(xx,yy) = n0,
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(t8,plain,
meet(xx,yy) = n0,
inference(equality_encoding,[status(esa)],[c17]) ).
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(t13,plain,
meet(X1,X2) = meet(X2,X1),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t145,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t394,plain,
meet(yy,xx) = n0,
inference(step,[status(thm)],[t8,t145]) ).
cnf(t175,plain,
meet(yy,xx) = n0,
inference(orient,[status(thm)],[t394]) ).
cnf(t378,plain,
join(zz,yy) = join(zz,n0),
inference(cp,[status(thm)],[t377,t175]) ).
cnf(f15,axiom,
join(xx,yy) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs1) ).
fof(f15_nnf,plain,
join(xx,yy) = n1,
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
join(xx,yy) = n1,
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(t3,plain,
join(xx,yy) = n1,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t392,plain,
join(yy,xx) = n1,
inference(step,[status(thm)],[t3,t31]) ).
cnf(t133,plain,
join(yy,xx) = n1,
inference(orient,[status(thm)],[t392]) ).
cnf(t135,plain,
join(yy,meet(X1,xx)) = meet(join(yy,X1),n1),
inference(cp,[status(thm)],[t43,t133]) ).
cnf(t414,plain,
join(yy,meet(X1,xx)) = join(yy,X1),
inference(step,[status(thm)],[t135,t29]) ).
cnf(t285,plain,
join(yy,meet(X1,xx)) = join(yy,X1),
inference(orient,[status(thm)],[t414]) ).
cnf(f18,axiom,
meet(xx,zz) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs4) ).
fof(f18_nnf,plain,
meet(xx,zz) = n0,
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
meet(xx,zz) = n0,
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(t9,plain,
meet(xx,zz) = n0,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t395,plain,
meet(zz,xx) = n0,
inference(step,[status(thm)],[t9,t145]) ).
cnf(t181,plain,
meet(zz,xx) = n0,
inference(orient,[status(thm)],[t395]) ).
cnf(t286,plain,
join(yy,zz) = join(yy,n0),
inference(cp,[status(thm)],[t285,t181]) ).
cnf(t415,plain,
join(zz,yy) = join(yy,n0),
inference(step,[status(thm)],[t286,t31]) ).
cnf(f11,axiom,
join(X,n0) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_0) ).
fof(f11_nnf,plain,
! [X] : join(X,n0) = X,
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : join(X,n0) = X,
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
join(X0,n0) = X0,
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t1,plain,
join(X1,n0) = X1,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t26,plain,
join(X1,n0) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t416,plain,
join(zz,yy) = yy,
inference(step,[status(thm)],[t415,t26]) ).
cnf(t296,plain,
join(zz,yy) = yy,
inference(orient,[status(thm)],[t416]) ).
cnf(t426,plain,
yy = join(zz,n0),
inference(step,[status(thm)],[t378,t296]) ).
cnf(t427,plain,
yy = zz,
inference(step,[status(thm)],[t426,t26]) ).
cnf(t388,plain,
yy = zz,
inference(orient,[status(thm)],[t427]) ).
cnf(f19,negated_conjecture,
yy != zz,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rhs) ).
fof(f19_nnf,plain,
yy != zz,
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
yy != zz,
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
yy != zz,
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(goal_0,negated_conjecture,
zz != yy,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
zz != zz,
inference(rw,[status(thm)],[goal_0,t388]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT037-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.36 % Computer : n005.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Wed Sep 23 20:04:32 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.83/1.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.83/1.56 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------