%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT274-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 01:56:34 PM UTC 2026
% Result : Unsatisfiable 5.10s 1.11s
% Output : Proof 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 15
% Syntax : Number of formulae : 122 ( 20 unt; 0 def)
% Number of atoms : 399 ( 91 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 396 ( 119 ~; 277 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 210 ( 26 sgn 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( c_in(V_x,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),T_a)
| ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_A_h56fe1212f3ebf9b5) ).
fof(f6_nnf,plain,
! [V_x,V_b,T_a,V_r,V_a] :
( c_in(V_x,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),T_a)
| ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [V_x,V_b,T_a,V_r,V_a] :
( c_in(V_x,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),T_a)
| ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( c_in(X0,c_Tarski_Ointerval(X3,X4,X1,X2),X2)
| ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f8,axiom,
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_5_h31cb6f020cf69d83) ).
fof(f8_nnf,plain,
! [V_S,V_L,V_z] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [V_S,V_L,V_z] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( c_in(v_sko__4mi(X0,v_r,X2),X0,t_a)
| c_in(c_Pair(X1,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X2,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X1,t_a) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f13,negated_conjecture,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f13_nnf,plain,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(p24,plain,
( c_in(v_sko__4mi(v_S,v_r,X0),v_S,t_a)
| c_in(c_Pair(v_L,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X0,v_A,t_a) ),
inference(resolution,[status(thm)],[c8,c13]) ).
cnf(f10,negated_conjecture,
c_in(v_b,v_A,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f10_nnf,plain,
c_in(v_b,v_A,t_a),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
c_in(v_b,v_A,t_a),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(p25,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[p24,c10]) ).
cnf(p30,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_L,c_Tarski_Ointerval(v_r,X0,v_b,t_a),t_a)
| ~ c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c6,p25]) ).
cnf(f11,negated_conjecture,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f11_nnf,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(f0,axiom,
( V_S = c_emptyset
| c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
| c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS_h39a67a120e84c596) ).
fof(f0_nnf,plain,
! [V_S,V_A,V_a,V_L] :
( V_S = c_emptyset
| c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
| c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_S,V_A,V_a,V_L] :
( V_S = c_emptyset
| c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
| c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X0 = c_emptyset
| c_in(v_sko__4mk(X3,X0,v_r),X0,t_a)
| c_in(v_sko__4mj(X0,X2,v_r),X0,t_a)
| c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X0,X1,tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p15,plain,
( v_S = c_emptyset
| c_in(v_sko__4mk(X1,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a)
| c_in(c_Pair(X0,X1,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c11,c0]) ).
cnf(p31,plain,
( v_S = c_emptyset
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a)
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_L,c_Tarski_Ointerval(v_r,X0,v_b,t_a),t_a) ),
inference(resolution,[status(thm)],[p30,p15]) ).
cnf(f14,negated_conjecture,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f14_nnf,plain,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p32,plain,
( v_S = c_emptyset
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a)
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(resolution,[status(thm)],[p31,c14]) ).
cnf(f5,axiom,
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_Ainterva_h025c8f644970219c) ).
fof(f5_nnf,plain,
! [V_x,V_S,T_a,V_r,V_a,V_b] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_x,V_S,T_a,V_r,V_a,V_b] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_in(c_Pair(X0,X5,X2,X2),X3,tc_prod(X2,X2))
| ~ c_lessequals(X1,c_Tarski_Ointerval(X3,X4,X5,X2),tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p37,plain,
( c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),X2,t_a,t_a),X0,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(X0,X1,X2,t_a),tc_set(t_a))
| v_S = c_emptyset
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p32,c5]) ).
cnf(p61,plain,
( c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p37,c11]) ).
cnf(f9,axiom,
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_5_h31cb6e020cf69bd0) ).
fof(f9_nnf,plain,
! [V_S,V_L,V_z] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V_S,V_L,V_z] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( c_in(c_Pair(X1,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(X0,v_r,X2),X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X2,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X1,t_a) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p41,plain,
( c_in(c_Pair(v_L,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,X0),X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X0,v_A,t_a) ),
inference(resolution,[status(thm)],[c9,c13]) ).
cnf(p42,plain,
( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[p41,c10]) ).
cnf(p65,plain,
( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p61,p42]) ).
cnf(p69,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,X0,v_b,t_a),t_a)
| ~ c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p65,c6]) ).
cnf(p74,plain,
( v_S = c_emptyset
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a)
| c_in(v_L,c_Tarski_Ointerval(v_r,X0,v_b,t_a),t_a)
| v_S = c_emptyset
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p69,p15]) ).
cnf(p110,plain,
( v_S = c_emptyset
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| v_S = c_emptyset
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(factoring,[status(thm)],[p74]) ).
cnf(p118,plain,
( v_S = c_emptyset
| c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| v_S = c_emptyset
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(factoring,[status(thm)],[p110]) ).
cnf(p120,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| v_S = c_emptyset
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(factoring,[status(thm)],[p118]) ).
cnf(p121,plain,
( v_S = c_emptyset
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p120,c14]) ).
cnf(f7,axiom,
( c_in(c_Pair(V_y,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_y,V_S,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_5_h2f666f6d9f9463de) ).
fof(f7_nnf,plain,
! [V_S,V_L,V_y] :
( c_in(c_Pair(V_y,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_y,V_S,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [V_S,V_L,V_y] :
( c_in(c_Pair(V_y,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_y,V_S,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( c_in(c_Pair(X2,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X2,X0,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X1,t_a) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p16,plain,
( c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X0,v_S,t_a) ),
inference(resolution,[status(thm)],[c7,c13]) ).
cnf(p123,plain,
( c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p121,p16]) ).
cnf(f1,axiom,
( V_S = c_emptyset
| c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS_h39a67b120e84c749) ).
fof(f1_nnf,plain,
! [V_L,V_S,V_A,V_a] :
( V_S = c_emptyset
| c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_L,V_S,V_A,V_a] :
( V_S = c_emptyset
| c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( X1 = c_emptyset
| c_in(v_sko__4mj(X1,X3,v_r),X1,t_a)
| c_in(c_Pair(X3,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,X2,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(X0,X1,v_r),X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p126,plain,
( v_S = c_emptyset
| c_in(v_sko__4mj(v_S,X1,v_r),v_S,t_a)
| c_in(c_Pair(X1,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X0,tc_set(t_a))
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p123,c1]) ).
cnf(p165,plain,
( v_S = c_emptyset
| c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X0,tc_set(t_a))
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(factoring,[status(thm)],[p126]) ).
cnf(p167,plain,
( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X0,tc_set(t_a))
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(factoring,[status(thm)],[p165]) ).
cnf(p168,plain,
( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p167,c11]) ).
cnf(p172,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p168,p30]) ).
cnf(p174,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p172,c14]) ).
cnf(p177,plain,
( c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),X2,t_a,t_a),X0,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(X0,X1,X2,t_a),tc_set(t_a))
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p174,c5]) ).
cnf(p189,plain,
( c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p177,c11]) ).
cnf(p193,plain,
( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p189,p42]) ).
cnf(p197,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,X0,v_b,t_a),t_a)
| ~ c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p193,c6]) ).
cnf(p200,plain,
( v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a)
| c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p197,p168]) ).
cnf(p202,plain,
( v_S = c_emptyset
| c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(factoring,[status(thm)],[p200]) ).
cnf(p204,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(factoring,[status(thm)],[p202]) ).
cnf(p205,plain,
( v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p204,c14]) ).
cnf(f4,axiom,
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_Ainterva_h77f5851d30b83473) ).
fof(f4_nnf,plain,
! [V_x,V_S,T_a,V_r,V_a,V_b] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_x,V_S,T_a,V_r,V_a,V_b] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_lessequals(X1,c_Tarski_Ointerval(X3,X4,X5,X2),tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p207,plain,
( c_in(c_Pair(X1,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),X0,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(X0,X1,X2,t_a),tc_set(t_a))
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p205,c4]) ).
cnf(p216,plain,
( c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p207,c11]) ).
cnf(f3,axiom,
( V_S = c_emptyset
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS_h39a679120e84c3e3) ).
fof(f3_nnf,plain,
! [V_a,V_S,V_L,V_A] :
( V_S = c_emptyset
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_a,V_S,V_L,V_A] :
( V_S = c_emptyset
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( X1 = c_emptyset
| c_in(c_Pair(X0,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,X3,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(X2,X1,v_r),X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,v_sko__4mj(X1,X0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p220,plain,
( v_S = c_emptyset
| c_in(c_Pair(v_a,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X1,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(X0,v_S,v_r),X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p216,c3]) ).
cnf(p370,plain,
( c_in(c_Pair(v_a,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X1,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(X0,v_S,v_r),X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset ),
inference(factoring,[status(thm)],[p220]) ).
cnf(f2,axiom,
( V_S = c_emptyset
| c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS_h39a678120e84c230) ).
fof(f2_nnf,plain,
! [V_a,V_S,V_A,V_L] :
( V_S = c_emptyset
| c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_a,V_S,V_A,V_L] :
( V_S = c_emptyset
| c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( X1 = c_emptyset
| c_in(v_sko__4mk(X3,X1,v_r),X1,t_a)
| c_in(c_Pair(X0,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,X2,tc_set(t_a))
| ~ c_in(c_Pair(X0,v_sko__4mj(X1,X0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p218,plain,
( v_S = c_emptyset
| c_in(v_sko__4mk(X1,v_S,v_r),v_S,t_a)
| c_in(c_Pair(v_a,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X0,tc_set(t_a))
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p216,c2]) ).
cnf(p240,plain,
( c_in(v_sko__4mk(X1,v_S,v_r),v_S,t_a)
| c_in(c_Pair(v_a,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X0,tc_set(t_a))
| v_S = c_emptyset ),
inference(factoring,[status(thm)],[p218]) ).
cnf(p241,plain,
( c_in(v_sko__4mk(X0,v_S,v_r),v_S,t_a)
| c_in(c_Pair(v_a,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p240,c11]) ).
cnf(p247,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p241,p30]) ).
cnf(p260,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p247,c14]) ).
cnf(p263,plain,
( c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),X2,t_a,t_a),X0,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(X0,X1,X2,t_a),tc_set(t_a))
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p260,c5]) ).
cnf(p294,plain,
( c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p263,c11]) ).
cnf(p298,plain,
( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p294,p42]) ).
cnf(p303,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,X0,v_b,t_a),t_a)
| ~ c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p298,c6]) ).
cnf(p307,plain,
( c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| v_S = c_emptyset
| c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p303,p241]) ).
cnf(p316,plain,
( v_S = c_emptyset
| c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| v_S = c_emptyset ),
inference(factoring,[status(thm)],[p307]) ).
cnf(p317,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| v_S = c_emptyset ),
inference(factoring,[status(thm)],[p316]) ).
cnf(p318,plain,
( c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p317,c14]) ).
cnf(p319,plain,
( c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p318,p16]) ).
cnf(p402,plain,
( v_S = c_emptyset
| c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X0,tc_set(t_a))
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p370,p319]) ).
cnf(p403,plain,
( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X0,tc_set(t_a))
| v_S = c_emptyset ),
inference(factoring,[status(thm)],[p402]) ).
cnf(p405,plain,
( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p403,c11]) ).
cnf(p409,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p405,p30]) ).
cnf(p412,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p409,c14]) ).
cnf(p415,plain,
( c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),X2,t_a,t_a),X0,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(X0,X1,X2,t_a),tc_set(t_a))
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p412,c5]) ).
cnf(p439,plain,
( c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p415,c11]) ).
cnf(p443,plain,
( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p439,p42]) ).
cnf(p448,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,X0,v_b,t_a),t_a)
| ~ c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p443,c6]) ).
cnf(p454,plain,
( v_S = c_emptyset
| c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| v_S = c_emptyset ),
inference(resolution,[status(thm)],[p448,p405]) ).
cnf(p456,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| v_S = c_emptyset ),
inference(factoring,[status(thm)],[p454]) ).
cnf(p457,plain,
v_S = c_emptyset,
inference(resolution,[status(thm)],[p456,c14]) ).
cnf(f12,negated_conjecture,
v_S != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f12_nnf,plain,
v_S != c_emptyset,
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
v_S != c_emptyset,
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
v_S != c_emptyset,
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p459,plain,
c_emptyset != c_emptyset,
inference(demodulation,[status(thm)],[p457,c12]) ).
cnf(p469,plain,
$false,
inference(equality_resolution,[status(thm)],[p459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT274-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 20:46:21 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.10/1.11 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.10/1.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------