%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT035-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 3.31s 0.88s
% Output : Proof 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 43 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 42 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f19,negated_conjecture,
( f(k(n0)) != n0
| f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',comp_join_hemimorphism) ).
fof(f19_nnf,plain,
( f(k(n0)) != n0
| f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
( f(k(n0)) != n0
| f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( f(k(n0)) != n0
| f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t24,plain,
ifeq(f(k(join(aa,bb))),join(f(k(aa)),f(k(bb))),ifeq(f(k(n0)),n0,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
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(t10,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t32,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t10]) ).
cnf(t153,plain,
ifeq(f(k(join(bb,aa))),join(f(k(aa)),f(k(bb))),ifeq(f(k(n0)),n0,false,true),true) = true,
inference(step,[status(thm)],[t24,t32]) ).
cnf(f17,axiom,
f(meet(U,V)) = join(f(U),f(V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_on_meet) ).
fof(f17_nnf,plain,
! [U,V] : f(meet(U,V)) = join(f(U),f(V)),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [U,V] : f(meet(U,V)) = join(f(U),f(V)),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
f(meet(X0,X1)) = join(f(X0),f(X1)),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t14,plain,
join(f(X1),f(X2)) = f(meet(X1,X2)),
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t103,plain,
join(f(X1),f(X2)) = f(meet(X1,X2)),
inference(orient,[status(thm)],[t14]) ).
cnf(t154,plain,
ifeq(f(k(join(bb,aa))),f(meet(k(aa),k(bb))),ifeq(f(k(n0)),n0,false,true),true) = true,
inference(step,[status(thm)],[t153,t103]) ).
cnf(f13,axiom,
k(join(U,V)) = meet(k(U),k(V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_on_join) ).
fof(f13_nnf,plain,
! [U,V] : k(join(U,V)) = meet(k(U),k(V)),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [U,V] : k(join(U,V)) = meet(k(U),k(V)),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
k(join(X0,X1)) = meet(k(X0),k(X1)),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t16,plain,
meet(k(X1),k(X2)) = k(join(X1,X2)),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t136,plain,
meet(k(X1),k(X2)) = k(join(X1,X2)),
inference(orient,[status(thm)],[t16]) ).
cnf(t155,plain,
ifeq(f(k(join(bb,aa))),f(k(join(aa,bb))),ifeq(f(k(n0)),n0,false,true),true) = true,
inference(step,[status(thm)],[t154,t136]) ).
cnf(t156,plain,
ifeq(f(k(join(bb,aa))),f(k(join(bb,aa))),ifeq(f(k(n0)),n0,false,true),true) = true,
inference(step,[status(thm)],[t155,t32]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t31,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t157,plain,
ifeq(f(k(n0)),n0,false,true) = true,
inference(step,[status(thm)],[t156,t31]) ).
cnf(f15,axiom,
k(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_on_bottom) ).
fof(f15_nnf,plain,
k(n0) = n1,
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
k(n0) = n1,
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(t1,plain,
k(n0) = n1,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t147,plain,
k(n0) = n1,
inference(orient,[status(thm)],[t1]) ).
cnf(t158,plain,
ifeq(f(n1),n0,false,true) = true,
inference(step,[status(thm)],[t157,t147]) ).
cnf(f18,axiom,
f(n1) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_on_top) ).
fof(f18_nnf,plain,
f(n1) = n0,
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
f(n1) = n0,
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(t0,plain,
f(n1) = n0,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t145,plain,
f(n1) = n0,
inference(orient,[status(thm)],[t0]) ).
cnf(t159,plain,
ifeq(n0,n0,false,true) = true,
inference(step,[status(thm)],[t158,t145]) ).
cnf(t160,plain,
false = true,
inference(step,[status(thm)],[t159,t31]) ).
cnf(t150,plain,
false = true,
inference(orient,[status(thm)],[t160]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t150]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT035-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 20:04:04 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.31/0.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.31/0.88 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------