%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT005-6 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 01:54:59 PM UTC 2026
% Result : Unsatisfiable 4.17s 0.99s
% Output : Proof 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 106 ( 86 unt; 0 def)
% Number of atoms : 166 ( 37 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 126 ( 66 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 13 con; 0-4 aty)
% Number of variables : 160 ( 6 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f15,axiom,
( meet(Z,X1,Z1)
| ~ join(X,Y1,Z1)
| ~ meet(Y,Z,Y1)
| ~ join(X,Y,X1)
| ~ meet(X,Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modularity2) ).
fof(f15_nnf,plain,
! [X,Z,Y,X1,Y1,Z1] :
( meet(Z,X1,Z1)
| ~ join(X,Y1,Z1)
| ~ meet(Y,Z,Y1)
| ~ join(X,Y,X1)
| ~ meet(X,Z,X) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Z,Y,X1,Y1,Z1] :
( meet(Z,X1,Z1)
| ~ join(X,Y1,Z1)
| ~ meet(Y,Z,Y1)
| ~ join(X,Y,X1)
| ~ meet(X,Z,X) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( meet(X1,X3,X5)
| ~ join(X0,X4,X5)
| ~ meet(X2,X1,X4)
| ~ join(X0,X2,X3)
| ~ meet(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(meet(X0,X1,X0),true,ifeq(join(X0,X2,X3),true,ifeq(meet(X2,X1,X4),true,ifeq(join(X0,X4,X5),true,meet(X1,X3,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(f3,axiom,
meet(n0,X,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_0_and_x) ).
fof(f3_nnf,plain,
! [X] : meet(n0,X,n0),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : meet(n0,X,n0),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
meet(n0,X0,n0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
meet(n0,X0,n0) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f2,axiom,
join(n0,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_0_and_x) ).
fof(f2_nnf,plain,
! [X] : join(n0,X,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : join(n0,X,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
join(n0,X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
join(n0,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f29,negated_conjecture,
meet(r2,b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_r2_and_b) ).
fof(f29_nnf,plain,
meet(r2,b,e),
inference(nnf_transformation,[status(thm)],[f29]) ).
cnf(c29,plain,
meet(r2,b,e),
inference(cnf_transformation,[status(esa)],[f29_nnf]) ).
cnf(hi29,negated_conjecture,
meet(r2,b,e) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(h6,plain,
meet(b,r2,e) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi3,hi2,hi29,hi2]) ).
cnf(f28,negated_conjecture,
meet(c,r2,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_c_and_r2) ).
fof(f28_nnf,plain,
meet(c,r2,n0),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
meet(c,r2,n0),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(hi28,negated_conjecture,
meet(c,r2,n0) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(f21,axiom,
join(X,n0,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_x_and_0) ).
fof(f21_nnf,plain,
! [X] : join(X,n0,X),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X] : join(X,n0,X),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
join(X0,n0,X0),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi21,axiom,
join(X0,n0,X0) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(h5,plain,
meet(r2,c,n0) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi3,hi2,hi28,hi21]) ).
cnf(f10,axiom,
( meet(Xy,Z,Xyz)
| ~ meet(X,Yz,Xyz)
| ~ meet(Y,Z,Yz)
| ~ meet(X,Y,Xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet1) ).
fof(f10_nnf,plain,
! [X,Y,Xy,Z,Yz,Xyz] :
( meet(Xy,Z,Xyz)
| ~ meet(X,Yz,Xyz)
| ~ meet(Y,Z,Yz)
| ~ meet(X,Y,Xy) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,Xy,Z,Yz,Xyz] :
( meet(Xy,Z,Xyz)
| ~ meet(X,Yz,Xyz)
| ~ meet(Y,Z,Yz)
| ~ meet(X,Y,Xy) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( meet(X2,X3,X5)
| ~ meet(X0,X4,X5)
| ~ meet(X1,X3,X4)
| ~ meet(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(meet(X0,X1,X2),true,ifeq(meet(X1,X3,X4),true,ifeq(meet(X0,X4,X5),true,meet(X2,X3,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f33,negated_conjecture,
meet(r2,a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_r2_and_a) ).
fof(f33_nnf,plain,
meet(r2,a,d),
inference(nnf_transformation,[status(thm)],[f33]) ).
cnf(c33,plain,
meet(r2,a,d),
inference(cnf_transformation,[status(esa)],[f33_nnf]) ).
cnf(hi33,negated_conjecture,
meet(r2,a,d) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(f26,negated_conjecture,
meet(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_a_and_b) ).
fof(f26_nnf,plain,
meet(a,b,c),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
meet(a,b,c),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(hi26,negated_conjecture,
meet(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(h40,plain,
meet(d,b,n0) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi33,hi26,h5]) ).
cnf(f11,axiom,
( meet(X,Yz,Xyz)
| ~ meet(Xy,Z,Xyz)
| ~ meet(Y,Z,Yz)
| ~ meet(X,Y,Xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet2) ).
fof(f11_nnf,plain,
! [X,Y,Xy,Z,Yz,Xyz] :
( meet(X,Yz,Xyz)
| ~ meet(Xy,Z,Xyz)
| ~ meet(Y,Z,Yz)
| ~ meet(X,Y,Xy) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Xy,Z,Yz,Xyz] :
( meet(X,Yz,Xyz)
| ~ meet(Xy,Z,Xyz)
| ~ meet(Y,Z,Yz)
| ~ meet(X,Y,Xy) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( meet(X0,X4,X5)
| ~ meet(X2,X3,X5)
| ~ meet(X1,X3,X4)
| ~ meet(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(meet(X0,X1,X2),true,ifeq(meet(X1,X3,X4),true,ifeq(meet(X2,X3,X5),true,meet(X0,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h81,plain,
meet(d,e,n0) = true,
inference(hyper_resolution,[status(thm)],[hi11,h40,h6,hi3]) ).
cnf(f32,negated_conjecture,
meet(c2,r1,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_c2_and_r1) ).
fof(f32_nnf,plain,
meet(c2,r1,n0),
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c32,plain,
meet(c2,r1,n0),
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
cnf(hi32,negated_conjecture,
meet(c2,r1,n0) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(h16,plain,
meet(r1,c2,n0) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi3,hi2,hi32,hi21]) ).
cnf(f24,axiom,
( join(Z,X1,Z1)
| ~ meet(X,Y1,Z1)
| ~ meet(X,Y,X1)
| ~ join(Y,Z,Y1)
| ~ meet(X,Z,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modularity3) ).
fof(f24_nnf,plain,
! [X,Z,Y,Y1,X1,Z1] :
( join(Z,X1,Z1)
| ~ meet(X,Y1,Z1)
| ~ meet(X,Y,X1)
| ~ join(Y,Z,Y1)
| ~ meet(X,Z,Z) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X,Z,Y,Y1,X1,Z1] :
( join(Z,X1,Z1)
| ~ meet(X,Y1,Z1)
| ~ meet(X,Y,X1)
| ~ join(Y,Z,Y1)
| ~ meet(X,Z,Z) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( join(X1,X4,X5)
| ~ meet(X0,X3,X5)
| ~ meet(X0,X2,X4)
| ~ join(X2,X1,X3)
| ~ meet(X0,X1,X1) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi24,axiom,
ifeq(meet(X0,X1,X1),true,ifeq(join(X2,X1,X3),true,ifeq(meet(X0,X2,X4),true,ifeq(meet(X0,X3,X5),true,join(X1,X4,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(f5,axiom,
meet(n1,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_1_and_x) ).
fof(f5_nnf,plain,
! [X] : meet(n1,X,X),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : meet(n1,X,X),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
meet(n1,X0,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
meet(n1,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f34,negated_conjecture,
join(r1,e,a2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_r1_and_e) ).
fof(f34_nnf,plain,
join(r1,e,a2),
inference(nnf_transformation,[status(thm)],[f34]) ).
cnf(c34,plain,
join(r1,e,a2),
inference(cnf_transformation,[status(esa)],[f34_nnf]) ).
cnf(hi34,negated_conjecture,
join(r1,e,a2) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(h22,plain,
join(e,r1,a2) = true,
inference(hyper_resolution,[status(thm)],[hi24,hi5,hi34,hi5,hi5]) ).
cnf(f4,axiom,
meet(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_x_and_x) ).
fof(f4_nnf,plain,
! [X] : meet(X,X,X),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] : meet(X,X,X),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
meet(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
meet(X0,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h9,plain,
meet(e,b,e) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi29,hi4,hi29]) ).
cnf(f30,negated_conjecture,
join(a,b,c2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_a_and_b) ).
fof(f30_nnf,plain,
join(a,b,c2),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c30,plain,
join(a,b,c2),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(hi30,negated_conjecture,
join(a,b,c2) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(h11,plain,
join(b,a,c2) = true,
inference(hyper_resolution,[status(thm)],[hi24,hi5,hi30,hi5,hi5]) ).
cnf(f9,axiom,
( meet(X,Z,X)
| ~ join(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion2) ).
fof(f9_nnf,plain,
! [X,Y,Z] :
( meet(X,Z,X)
| ~ join(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y,Z] :
( meet(X,Z,X)
| ~ join(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( meet(X0,X2,X0)
| ~ join(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
ifeq(join(X0,X1,X2),true,meet(X0,X2,X0),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h52,plain,
meet(b,c2,b) = true,
inference(hyper_resolution,[status(thm)],[hi9,h11]) ).
cnf(h86,plain,
meet(e,c2,e) = true,
inference(hyper_resolution,[status(thm)],[hi10,h9,h52,h9]) ).
cnf(h106,plain,
meet(c2,a2,e) = true,
inference(hyper_resolution,[status(thm)],[hi15,h86,h22,h16,hi21]) ).
cnf(h14,plain,
meet(a,c2,a) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi30]) ).
cnf(h55,plain,
meet(d,c2,d) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi33,h14,hi33]) ).
cnf(h121,plain,
meet(d,a2,n0) = true,
inference(hyper_resolution,[status(thm)],[hi10,h55,h106,h81]) ).
cnf(h26,plain,
meet(r1,a2,r1) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi34]) ).
cnf(f35,negated_conjecture,
join(r1,d,b2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_r1_and_d) ).
fof(f35_nnf,plain,
join(r1,d,b2),
inference(nnf_transformation,[status(thm)],[f35]) ).
cnf(c35,plain,
join(r1,d,b2),
inference(cnf_transformation,[status(esa)],[f35_nnf]) ).
cnf(hi35,negated_conjecture,
join(r1,d,b2) = true,
inference(equality_encoding,[status(esa)],[c35]) ).
cnf(t81,plain,
meet(a2,b2,r1) = true,
inference(hyper_resolution,[status(thm)],[hi15,h26,hi35,h121,hi21]) ).
cnf(t395,plain,
meet(a2,b2,r1) = true,
inference(orient,[status(thm)],[t81]) ).
cnf(f36,negated_conjecture,
~ meet(a2,b2,r1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_a2_and_b2) ).
fof(f36_nnf,plain,
~ meet(a2,b2,r1),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
~ meet(a2,b2,r1),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c36,plain,
~ meet(a2,b2,r1),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(goal_0,negated_conjecture,
meet(a2,b2,r1) != true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t395]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT005-6 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 20:02:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.17/0.99 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.17/0.99 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------