%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM858+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Sun Sep 27 08:14:00 AM UTC 2026
% Result : Theorem 118.05s 29.62s
% Output : CNFRefutation 118.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 12
% Syntax : Number of formulae : 193 ( 7 unt; 0 def)
% Number of atoms : 634 ( 142 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 661 ( 220 ~; 425 |; 5 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 212 ( 2 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(lesseq_ref,axiom,
! [X0] : lesseq(X0,X0) ).
fof(lesseq_trans,axiom,
! [X0,X1,X2] :
( ( lesseq(X1,X2)
& lesseq(X0,X1) )
=> lesseq(X0,X2) ) ).
fof(lesseq_antisymmetric,axiom,
! [X0,X1] :
( ( lesseq(X1,X0)
& lesseq(X0,X1) )
=> X0 = X1 ) ).
fof(lesseq_total,axiom,
! [X0,X1] :
( lesseq(X1,X0)
| lesseq(X0,X1) ) ).
fof(max_1,axiom,
! [X0,X1] :
( ~ lesseq(X1,X0)
| max(X0,X1) = X0 ) ).
fof(max_2,axiom,
! [X0,X1] :
( ~ lesseq(X0,X1)
| max(X0,X1) = X1 ) ).
fof(ub,axiom,
! [X0,X1,X2] :
( ub(X0,X1,X2)
<=> ( lesseq(X1,X2)
& lesseq(X0,X2) ) ) ).
fof(model_max_1,axiom,
! [X0,X1,X2] :
( 'model$umax'(X0,X1,X2)
<=> X2 = max(X0,X1) ) ).
fof(model_ub_1,axiom,
! [X0,X1,X2] :
( 'model$uub'(X0,X1,X2)
<=> ub(X0,X1,X2) ) ).
fof(minsol_model_max,axiom,
! [X0,X1,X2] :
( 'minsol$umodel$umax'(X0,X1,X2)
<=> ( ! [X3] :
( 'model$umax'(X0,X1,X3)
=> lesseq(X2,X3) )
& 'model$umax'(X0,X1,X2) ) ) ).
fof(minsol_model_ub,axiom,
! [X0,X1,X2] :
( 'minsol$umodel$uub'(X0,X1,X2)
<=> ( ! [X3] :
( 'model$uub'(X0,X1,X3)
=> lesseq(X2,X3) )
& 'model$uub'(X0,X1,X2) ) ) ).
fof(max_is_ub_1,conjecture,
! [X0,X1,X2] :
( 'minsol$umodel$uub'(X0,X1,X2)
<=> 'minsol$umodel$umax'(X0,X1,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( 'minsol$umodel$uub'(X0,X1,X2)
<=> 'minsol$umodel$umax'(X0,X1,X2) ),
inference(negate_conjecture,[status(cth)],[max_is_ub_1]) ).
cnf(c0,plain,
lesseq(X0,X0),
inference(clausification,[status(esa)],[lesseq_ref]) ).
cnf(c1,plain,
( lesseq(X0,X2)
| ~ lesseq(X1,X2)
| ~ lesseq(X0,X1) ),
inference(clausification,[status(esa)],[lesseq_trans]) ).
cnf(c2,plain,
( X0 = X1
| ~ lesseq(X1,X0)
| ~ lesseq(X0,X1) ),
inference(clausification,[status(esa)],[lesseq_antisymmetric]) ).
cnf(c3,plain,
( lesseq(X1,X0)
| lesseq(X0,X1) ),
inference(clausification,[status(esa)],[lesseq_total]) ).
cnf(c8,plain,
( ~ lesseq(X1,X0)
| max(X0,X1) = X0 ),
inference(clausification,[status(esa)],[max_1]) ).
cnf(c9,plain,
( ~ lesseq(X0,X1)
| max(X0,X1) = X1 ),
inference(clausification,[status(esa)],[max_2]) ).
cnf(c10,plain,
( lesseq(X0,X2)
| ~ ub(X0,X1,X2) ),
inference(clausification,[status(esa)],[ub]) ).
cnf(c11,plain,
( lesseq(X1,X2)
| ~ ub(X0,X1,X2) ),
inference(clausification,[status(esa)],[ub]) ).
cnf(c12,plain,
( ~ lesseq(X1,X2)
| ~ lesseq(X0,X2)
| ub(X0,X1,X2) ),
inference(clausification,[status(esa)],[ub]) ).
cnf(c13,plain,
( X2 = max(X0,X1)
| ~ 'model$umax'(X0,X1,X2) ),
inference(clausification,[status(esa)],[model_max_1]) ).
cnf(c14,plain,
( X2 != max(X0,X1)
| 'model$umax'(X0,X1,X2) ),
inference(clausification,[status(esa)],[model_max_1]) ).
cnf(c15,plain,
( ub(X0,X1,X2)
| ~ 'model$uub'(X0,X1,X2) ),
inference(clausification,[status(esa)],[model_ub_1]) ).
cnf(c16,plain,
( ~ ub(X0,X1,X2)
| 'model$uub'(X0,X1,X2) ),
inference(clausification,[status(esa)],[model_ub_1]) ).
cnf(c17,plain,
( 'model$umax'(X0,X1,X2)
| ~ 'minsol$umodel$umax'(X0,X1,X2) ),
inference(clausification,[status(esa)],[minsol_model_max]) ).
cnf(c18,plain,
( lesseq(X2,X3)
| ~ 'model$umax'(X0,X1,X3)
| ~ 'minsol$umodel$umax'(X0,X1,X2) ),
inference(clausification,[status(esa)],[minsol_model_max]) ).
cnf(c19,plain,
( 'model$umax'(X0,X1,sK30(X0,X1,X2))
| ~ 'model$umax'(X0,X1,X2)
| 'minsol$umodel$umax'(X0,X1,X2) ),
inference(clausification,[status(esa)],[minsol_model_max]) ).
cnf(c20,plain,
( ~ lesseq(X2,sK30(X0,X1,X2))
| ~ 'model$umax'(X0,X1,X2)
| 'minsol$umodel$umax'(X0,X1,X2) ),
inference(clausification,[status(esa)],[minsol_model_max]) ).
cnf(c21,plain,
( 'model$uub'(X0,X1,X2)
| ~ 'minsol$umodel$uub'(X0,X1,X2) ),
inference(clausification,[status(esa)],[minsol_model_ub]) ).
cnf(c22,plain,
( lesseq(X2,X3)
| ~ 'model$uub'(X0,X1,X3)
| ~ 'minsol$umodel$uub'(X0,X1,X2) ),
inference(clausification,[status(esa)],[minsol_model_ub]) ).
cnf(c23,plain,
( 'model$uub'(X0,X1,sK35(X0,X1,X2))
| ~ 'model$uub'(X0,X1,X2)
| 'minsol$umodel$uub'(X0,X1,X2) ),
inference(clausification,[status(esa)],[minsol_model_ub]) ).
cnf(c24,plain,
( ~ lesseq(X2,sK35(X0,X1,X2))
| ~ 'model$uub'(X0,X1,X2)
| 'minsol$umodel$uub'(X0,X1,X2) ),
inference(clausification,[status(esa)],[minsol_model_ub]) ).
cnf(c26,plain,
( 'minsol$umodel$umax'(sK36,sK37,sK38)
| 'minsol$umodel$uub'(sK36,sK37,sK38) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c27,plain,
( ~ 'minsol$umodel$uub'(sK36,sK37,sK38)
| ~ 'minsol$umodel$umax'(sK36,sK37,sK38) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'model$umax'(X0,X1,max(X0,X1)),
inference(equality_resolution,[status(thm)],[c14]) ).
cnf(d1,plain,
( ~ lesseq(X1,X0)
| 'model$umax'(X0,X1,X0) ),
inference(superposition,[status(thm)],[c8,d0]) ).
cnf(d2,plain,
( 'minsol$umodel$umax'(sK36,sK37,sK38)
| 'model$uub'(sK36,sK37,sK38) ),
inference(resolution,[status(thm)],[c21,c26]) ).
cnf(d3,plain,
( 'model$umax'(sK36,sK37,sK38)
| 'model$uub'(sK36,sK37,sK38) ),
inference(resolution,[status(thm)],[d2,c17]) ).
cnf(d4,plain,
( ub(sK36,sK37,sK38)
| 'model$umax'(sK36,sK37,sK38) ),
inference(resolution,[status(thm)],[d3,c15]) ).
cnf(d5,plain,
( ~ 'model$umax'(X0,X1,X2)
| ~ 'model$umax'(X0,X1,X3)
| X3 = X2 ),
inference(superposition,[status(thm)],[c13,c13]) ).
cnf(d6,plain,
( ub(sK36,sK37,sK38)
| ~ 'model$umax'(sK36,sK37,X0)
| X0 = sK38 ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( ~ lesseq(sK37,sK36)
| ub(sK36,sK37,sK38)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( lesseq(sK36,sK38)
| ~ lesseq(sK37,sK36)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d7,c10]) ).
cnf(d9,plain,
( lesseq(sK36,sK37)
| lesseq(sK36,sK38)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
( ~ lesseq(X0,X1)
| 'model$umax'(X0,X1,X1) ),
inference(superposition,[status(thm)],[c9,d0]) ).
cnf(d11,plain,
( ~ lesseq(sK36,sK37)
| ub(sK36,sK37,sK38)
| sK37 = sK38 ),
inference(resolution,[status(thm)],[d6,d10]) ).
cnf(d12,plain,
( lesseq(sK36,sK38)
| ~ lesseq(sK36,sK37)
| sK37 = sK38 ),
inference(resolution,[status(thm)],[d11,c10]) ).
cnf(d13,plain,
( lesseq(sK37,sK36)
| lesseq(sK36,sK38)
| sK37 = sK38 ),
inference(resolution,[status(thm)],[d12,c3]) ).
cnf(d14,plain,
( lesseq(sK36,sK38)
| sK37 = sK38
| lesseq(sK36,sK38)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d8,d13]) ).
cnf(d15,plain,
( ~ lesseq(sK38,sK36)
| sK36 = sK38
| sK37 = sK38
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
( lesseq(sK37,sK38)
| ~ lesseq(sK36,sK37)
| sK37 = sK38 ),
inference(resolution,[status(thm)],[d11,c11]) ).
cnf(d17,plain,
( lesseq(X1,X2)
| ~ lesseq(X0,X2)
| lesseq(X0,X1) ),
inference(resolution,[status(thm)],[c1,c3]) ).
cnf(d18,plain,
( ub(sK36,sK37,sK38)
| max(sK36,sK37) = sK38 ),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d19,plain,
( ub(sK36,sK37,sK38)
| ~ lesseq(sK37,sK36)
| sK38 = sK36 ),
inference(superposition,[status(thm)],[d18,c8]) ).
cnf(d20,plain,
( lesseq(sK36,sK38)
| ~ lesseq(sK37,sK36)
| sK38 = sK36 ),
inference(resolution,[status(thm)],[d19,c10]) ).
cnf(d21,plain,
( lesseq(sK36,sK38)
| sK37 = sK38
| lesseq(sK36,sK38)
| sK38 = sK36 ),
inference(resolution,[status(thm)],[d20,d13]) ).
cnf(d22,plain,
( lesseq(sK36,X0)
| lesseq(X0,sK38)
| sK38 = sK36
| sK37 = sK38 ),
inference(resolution,[status(thm)],[d21,d17]) ).
cnf(d23,plain,
( lesseq(sK37,sK38)
| sK37 = sK38
| lesseq(sK37,sK38)
| sK38 = sK36
| sK37 = sK38 ),
inference(resolution,[status(thm)],[d22,d16]) ).
cnf(d24,plain,
( ~ lesseq(sK38,sK37)
| sK37 = sK38
| sK38 = sK36
| sK37 = sK38 ),
inference(resolution,[status(thm)],[d23,c2]) ).
cnf(d25,plain,
( ~ 'model$umax'(X0,X1,X2)
| ~ lesseq(X0,X1)
| X2 = X1 ),
inference(superposition,[status(thm)],[c13,c9]) ).
cnf(d26,plain,
( ub(sK36,sK37,sK38)
| ~ lesseq(sK36,sK37)
| sK38 = sK37 ),
inference(resolution,[status(thm)],[d25,d4]) ).
cnf(d27,plain,
( lesseq(sK36,sK38)
| ~ lesseq(sK36,sK37)
| sK38 = sK37 ),
inference(resolution,[status(thm)],[d26,c10]) ).
cnf(d28,plain,
( lesseq(sK37,sK36)
| lesseq(sK36,sK38)
| sK38 = sK37 ),
inference(resolution,[status(thm)],[d27,c3]) ).
cnf(d29,plain,
( lesseq(sK36,sK38)
| sK38 = sK37
| lesseq(sK36,sK38)
| sK38 = sK36 ),
inference(resolution,[status(thm)],[d20,d28]) ).
cnf(d30,plain,
( lesseq(sK37,sK38)
| ~ lesseq(sK36,sK37)
| sK38 = sK37 ),
inference(resolution,[status(thm)],[d26,c11]) ).
cnf(d31,plain,
( lesseq(sK37,sK36)
| lesseq(sK37,sK38)
| sK38 = sK37 ),
inference(resolution,[status(thm)],[d30,c3]) ).
cnf(d32,plain,
( 'minsol$umodel$umax'(sK36,sK37,sK38)
| ~ 'model$uub'(sK36,sK37,X0)
| lesseq(sK38,X0) ),
inference(resolution,[status(thm)],[c22,c26]) ).
cnf(d33,plain,
( 'model$uub'(X2,X0,X1)
| ~ lesseq(X2,X1)
| ~ lesseq(X0,X1) ),
inference(resolution,[status(thm)],[c12,c16]) ).
cnf(d34,plain,
( 'minsol$umodel$umax'(sK36,sK37,sK38)
| lesseq(sK38,X0)
| ~ lesseq(sK37,X0)
| ~ lesseq(sK36,X0) ),
inference(resolution,[status(thm)],[d33,d32]) ).
cnf(d35,plain,
( 'model$umax'(sK36,sK37,sK38)
| lesseq(sK38,X0)
| ~ lesseq(sK37,X0)
| ~ lesseq(sK36,X0) ),
inference(resolution,[status(thm)],[d34,c17]) ).
cnf(d36,plain,
( ~ lesseq(sK36,sK37)
| sK38 = sK37
| lesseq(sK38,X0)
| ~ lesseq(sK37,X0)
| ~ lesseq(sK36,X0) ),
inference(resolution,[status(thm)],[d35,d25]) ).
cnf(d37,plain,
( lesseq(sK38,sK37)
| ~ lesseq(sK36,sK37)
| ~ lesseq(sK36,sK37)
| sK38 = sK37 ),
inference(resolution,[status(thm)],[d36,c0]) ).
cnf(d38,plain,
( lesseq(sK37,sK36)
| lesseq(sK38,sK37)
| sK38 = sK37 ),
inference(resolution,[status(thm)],[d37,c3]) ).
cnf(d39,plain,
( ~ lesseq(sK37,sK38)
| sK38 = sK37
| lesseq(sK37,sK36)
| sK38 = sK37 ),
inference(resolution,[status(thm)],[d38,c2]) ).
cnf(d40,plain,
( lesseq(sK37,sK36)
| sK38 = sK37
| lesseq(sK37,sK36)
| sK38 = sK37 ),
inference(resolution,[status(thm)],[d39,d31]) ).
cnf(d41,plain,
( ~ 'model$umax'(X0,X1,X2)
| ~ lesseq(X1,X0)
| X2 = X0 ),
inference(superposition,[status(thm)],[c13,c8]) ).
cnf(d42,plain,
( ~ lesseq(sK37,sK36)
| sK38 = sK36
| lesseq(sK38,X0)
| ~ lesseq(sK37,X0)
| ~ lesseq(sK36,X0) ),
inference(resolution,[status(thm)],[d35,d41]) ).
cnf(d43,plain,
( sK38 = sK37
| lesseq(sK38,X0)
| ~ lesseq(sK37,X0)
| ~ lesseq(sK36,X0)
| sK38 = sK36 ),
inference(resolution,[status(thm)],[d42,d40]) ).
cnf(d44,plain,
( sK38 = sK37
| lesseq(sK38,sK36)
| ~ lesseq(sK36,sK36)
| sK38 = sK37
| sK38 = sK36 ),
inference(resolution,[status(thm)],[d43,d40]) ).
cnf(d45,plain,
( lesseq(sK38,sK36)
| sK38 = sK37
| sK38 = sK36 ),
inference(resolution,[status(thm)],[c0,d44]) ).
cnf(d46,plain,
( ~ lesseq(sK36,sK38)
| sK38 = sK36
| sK38 = sK37
| sK38 = sK36 ),
inference(resolution,[status(thm)],[d45,c2]) ).
cnf(d47,plain,
( sK38 = sK37
| sK38 = sK36
| sK38 = sK37
| sK38 = sK36 ),
inference(resolution,[status(thm)],[d46,d29]) ).
cnf(d48,plain,
( sK38 = sK36
| sK38 = sK36
| sK37 = sK38
| ~ lesseq(sK37,sK37) ),
inference(superposition,[status(thm)],[d47,d24]) ).
cnf(d49,plain,
( sK38 = sK36
| sK37 = sK38 ),
inference(resolution,[status(thm)],[c0,d48]) ).
cnf(d50,plain,
( sK37 = sK38
| sK37 = sK38
| sK36 = sK38
| ~ lesseq(sK36,sK36) ),
inference(superposition,[status(thm)],[d49,d15]) ).
cnf(d51,plain,
( sK37 = sK38
| sK36 = sK38 ),
inference(resolution,[status(thm)],[c0,d50]) ).
cnf(d52,plain,
( sK36 = sK38
| lesseq(sK36,sK37)
| sK36 = sK38
| lesseq(sK36,sK37) ),
inference(superposition,[status(thm)],[d51,d9]) ).
cnf(d53,plain,
( 'model$uub'(sK36,sK37,sK38)
| ~ 'model$umax'(sK36,sK37,X0)
| lesseq(sK38,X0) ),
inference(resolution,[status(thm)],[c18,d2]) ).
cnf(d54,plain,
( sK36 = sK38
| ub(sK36,sK37,sK38)
| 'model$umax'(sK36,sK37,sK37) ),
inference(superposition,[status(thm)],[d51,d4]) ).
cnf(d55,plain,
( 'model$uub'(sK36,sK37,sK38)
| lesseq(sK38,sK37)
| ub(sK36,sK37,sK38)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d54,d53]) ).
cnf(d56,plain,
( ub(sK36,sK37,sK38)
| ub(sK36,sK37,sK38)
| lesseq(sK38,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d55,c15]) ).
cnf(d57,plain,
( 'model$uub'(sK36,sK37,sK38)
| lesseq(sK38,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d56,c16]) ).
cnf(d58,plain,
( lesseq(sK36,sK38)
| sK38 = sK37
| lesseq(sK36,sK38)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d8,d28]) ).
cnf(d59,plain,
( ~ lesseq(sK38,sK36)
| sK36 = sK38
| sK38 = sK37
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d58,c2]) ).
cnf(d60,plain,
( sK36 = sK38
| sK38 = sK37
| sK36 = sK38
| ~ lesseq(sK37,sK36) ),
inference(superposition,[status(thm)],[d51,d59]) ).
cnf(d61,plain,
( sK38 = sK37
| sK38 = sK37
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d60,d40]) ).
cnf(d62,plain,
( sK36 = sK38
| lesseq(sK38,sK37)
| sK36 = sK38
| 'model$uub'(sK36,sK37,sK37) ),
inference(superposition,[status(thm)],[d61,d57]) ).
cnf(d63,plain,
( 'minsol$umodel$umax'(sK36,sK37,sK38)
| lesseq(sK38,sK37)
| lesseq(sK38,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d62,d32]) ).
cnf(d64,plain,
( 'model$umax'(sK36,sK37,sK38)
| lesseq(sK38,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d63,c17]) ).
cnf(d65,plain,
( sK36 = sK38
| lesseq(sK38,sK37)
| sK36 = sK38
| 'model$umax'(sK36,sK37,sK37) ),
inference(superposition,[status(thm)],[d61,d64]) ).
cnf(d66,plain,
( ~ 'model$umax'(sK36,sK37,X0)
| lesseq(sK38,X0)
| lesseq(sK38,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d63,c18]) ).
cnf(d67,plain,
( lesseq(sK38,sK37)
| sK36 = sK38
| lesseq(sK38,sK37)
| lesseq(sK38,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d66,d65]) ).
cnf(d68,plain,
( sK36 = sK38
| ~ 'minsol$umodel$umax'(sK36,sK37,sK38)
| ~ 'minsol$umodel$uub'(sK36,sK37,sK37) ),
inference(superposition,[status(thm)],[d51,c27]) ).
cnf(d69,plain,
( ub(X0,X1,sK35(X0,X1,X2))
| 'minsol$umodel$uub'(X0,X1,X2)
| ~ 'model$uub'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c23,c15]) ).
cnf(d70,plain,
( lesseq(X1,sK35(X0,X1,X2))
| 'minsol$umodel$uub'(X0,X1,X2)
| ~ 'model$uub'(X0,X1,X2) ),
inference(resolution,[status(thm)],[d69,c11]) ).
cnf(d71,plain,
( 'minsol$umodel$umax'(sK36,sK37,X0)
| ~ 'model$umax'(sK36,sK37,X0)
| ub(sK36,sK37,sK38)
| sK30(sK36,sK37,X0) = sK38 ),
inference(resolution,[status(thm)],[d6,c19]) ).
cnf(d72,plain,
( 'minsol$umodel$umax'(sK36,sK37,X0)
| ~ 'model$umax'(sK36,sK37,X0)
| ub(sK36,sK37,sK38)
| 'minsol$umodel$umax'(sK36,sK37,X0)
| ~ 'model$umax'(sK36,sK37,X0)
| ~ lesseq(X0,sK38) ),
inference(superposition,[status(thm)],[d71,c20]) ).
cnf(d73,plain,
( 'minsol$umodel$umax'(sK36,sK37,max(sK36,sK37))
| ub(sK36,sK37,sK38)
| ~ lesseq(max(sK36,sK37),sK38) ),
inference(resolution,[status(thm)],[d72,d0]) ).
cnf(d74,plain,
( ~ lesseq(sK36,sK37)
| ub(sK36,sK37,sK38)
| ~ lesseq(max(sK36,sK37),sK38)
| 'minsol$umodel$umax'(sK36,sK37,sK37) ),
inference(superposition,[status(thm)],[c9,d73]) ).
cnf(d75,plain,
( ub(sK36,sK37,sK38)
| 'minsol$umodel$umax'(sK36,sK37,sK38)
| ub(sK36,sK37,sK38)
| ~ lesseq(sK38,sK38) ),
inference(resolution,[status(thm)],[d72,d4]) ).
cnf(d76,plain,
( 'minsol$umodel$umax'(sK36,sK37,sK38)
| ub(sK36,sK37,sK38) ),
inference(resolution,[status(thm)],[c0,d75]) ).
cnf(d77,plain,
( ~ 'model$umax'(sK36,sK37,X0)
| lesseq(sK38,X0)
| ub(sK36,sK37,sK38) ),
inference(resolution,[status(thm)],[d76,c18]) ).
cnf(d78,plain,
( ub(sK36,sK37,sK38)
| lesseq(sK38,max(sK36,sK37)) ),
inference(resolution,[status(thm)],[d77,d0]) ).
cnf(d79,plain,
( ~ lesseq(max(sK36,sK37),sK38)
| sK38 = max(sK36,sK37)
| ub(sK36,sK37,sK38) ),
inference(resolution,[status(thm)],[d78,c2]) ).
cnf(d80,plain,
( ub(sK36,sK37,sK38)
| ub(sK36,sK37,sK38)
| sK38 = max(sK36,sK37)
| ~ lesseq(sK38,sK38) ),
inference(superposition,[status(thm)],[d18,d79]) ).
cnf(d81,plain,
( ub(sK36,sK37,sK38)
| sK38 = max(sK36,sK37) ),
inference(resolution,[status(thm)],[c0,d80]) ).
cnf(d82,plain,
( ub(sK36,sK37,sK38)
| 'minsol$umodel$umax'(sK36,sK37,sK37)
| ub(sK36,sK37,sK38)
| ~ lesseq(sK36,sK37)
| ~ lesseq(sK38,sK38) ),
inference(superposition,[status(thm)],[d81,d74]) ).
cnf(d83,plain,
( 'minsol$umodel$umax'(sK36,sK37,sK37)
| ub(sK36,sK37,sK38)
| ~ lesseq(sK36,sK37) ),
inference(resolution,[status(thm)],[c0,d82]) ).
cnf(d84,plain,
( ~ 'model$umax'(sK36,sK37,X0)
| lesseq(sK37,X0)
| ub(sK36,sK37,sK38)
| ~ lesseq(sK36,sK37) ),
inference(resolution,[status(thm)],[d83,c18]) ).
cnf(d85,plain,
( ub(sK36,sK37,sK38)
| ub(sK36,sK37,sK38)
| lesseq(sK37,sK38)
| ~ lesseq(sK36,sK37) ),
inference(resolution,[status(thm)],[d84,d4]) ).
cnf(d86,plain,
( lesseq(sK37,sK38)
| lesseq(sK37,sK38)
| ~ lesseq(sK36,sK37) ),
inference(resolution,[status(thm)],[d85,c11]) ).
cnf(d87,plain,
( ~ lesseq(sK37,sK36)
| ub(sK36,sK37,sK38)
| ~ lesseq(max(sK36,sK37),sK38)
| 'minsol$umodel$umax'(sK36,sK37,sK36) ),
inference(superposition,[status(thm)],[c8,d73]) ).
cnf(d88,plain,
( ub(sK36,sK37,sK38)
| 'minsol$umodel$umax'(sK36,sK37,sK36)
| ub(sK36,sK37,sK38)
| ~ lesseq(sK37,sK36)
| ~ lesseq(sK38,sK38) ),
inference(superposition,[status(thm)],[d81,d87]) ).
cnf(d89,plain,
( 'minsol$umodel$umax'(sK36,sK37,sK36)
| ub(sK36,sK37,sK38)
| ~ lesseq(sK37,sK36) ),
inference(resolution,[status(thm)],[c0,d88]) ).
cnf(d90,plain,
( ~ 'model$umax'(sK36,sK37,X0)
| lesseq(sK36,X0)
| ub(sK36,sK37,sK38)
| ~ lesseq(sK37,sK36) ),
inference(resolution,[status(thm)],[d89,c18]) ).
cnf(d91,plain,
( ub(sK36,sK37,sK38)
| ub(sK36,sK37,sK38)
| ~ lesseq(sK37,sK36)
| lesseq(sK36,sK38) ),
inference(resolution,[status(thm)],[d90,d4]) ).
cnf(d92,plain,
( lesseq(sK36,sK38)
| ~ lesseq(sK37,sK36)
| lesseq(sK36,sK38) ),
inference(resolution,[status(thm)],[d91,c10]) ).
cnf(d93,plain,
( lesseq(sK37,sK36)
| lesseq(sK37,sK38) ),
inference(resolution,[status(thm)],[d86,c3]) ).
cnf(d94,plain,
( lesseq(sK37,X0)
| lesseq(X0,sK38)
| lesseq(sK37,sK36) ),
inference(resolution,[status(thm)],[d93,d17]) ).
cnf(d95,plain,
( lesseq(sK36,sK38)
| lesseq(sK37,X0)
| lesseq(X0,sK38) ),
inference(resolution,[status(thm)],[d94,d92]) ).
cnf(d96,plain,
( lesseq(sK36,sK38)
| lesseq(sK36,sK38)
| lesseq(sK36,sK38) ),
inference(resolution,[status(thm)],[d95,d92]) ).
cnf(d97,plain,
( lesseq(sK36,X0)
| lesseq(X0,sK38) ),
inference(resolution,[status(thm)],[d96,d17]) ).
cnf(d98,plain,
( lesseq(sK37,sK38)
| lesseq(sK37,sK38) ),
inference(resolution,[status(thm)],[d97,d86]) ).
cnf(d99,plain,
( lesseq(sK37,X0)
| lesseq(X0,sK38) ),
inference(resolution,[status(thm)],[d98,d17]) ).
cnf(d100,plain,
( 'minsol$umodel$uub'(X0,X1,sK37)
| ~ 'model$uub'(X0,X1,sK37)
| lesseq(sK35(X0,X1,sK37),sK38) ),
inference(resolution,[status(thm)],[d99,c24]) ).
cnf(d101,plain,
( ~ lesseq(sK38,sK35(X0,X1,sK37))
| sK35(X0,X1,sK37) = sK38
| 'minsol$umodel$uub'(X0,X1,sK37)
| ~ 'model$uub'(X0,X1,sK37) ),
inference(resolution,[status(thm)],[d100,c2]) ).
cnf(d102,plain,
( 'minsol$umodel$uub'(X0,sK38,sK37)
| ~ 'model$uub'(X0,sK38,sK37)
| 'minsol$umodel$uub'(X0,sK38,sK37)
| ~ 'model$uub'(X0,sK38,sK37)
| sK35(X0,sK38,sK37) = sK38 ),
inference(resolution,[status(thm)],[d101,d70]) ).
cnf(d103,plain,
( 'minsol$umodel$uub'(X0,sK38,sK37)
| ~ 'model$uub'(X0,sK38,sK37)
| 'minsol$umodel$uub'(X0,sK38,sK37)
| ~ 'model$uub'(X0,sK38,sK37)
| ~ lesseq(sK37,sK38) ),
inference(superposition,[status(thm)],[d102,c24]) ).
cnf(d104,plain,
( 'minsol$umodel$uub'(X0,sK38,sK37)
| ~ 'model$uub'(X0,sK38,sK37) ),
inference(resolution,[status(thm)],[d98,d103]) ).
cnf(d105,plain,
( sK36 = sK38
| 'minsol$umodel$uub'(X0,sK38,sK37)
| ~ 'model$uub'(X0,sK37,sK37) ),
inference(superposition,[status(thm)],[d61,d104]) ).
cnf(d106,plain,
( ~ lesseq(sK37,sK37)
| ~ lesseq(X0,sK37)
| 'minsol$umodel$uub'(X0,sK38,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d105,d33]) ).
cnf(d107,plain,
( 'minsol$umodel$uub'(X0,sK38,sK37)
| ~ lesseq(X0,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[c0,d106]) ).
cnf(d108,plain,
( sK36 = sK38
| ~ lesseq(X0,sK37)
| sK36 = sK38
| 'minsol$umodel$uub'(X0,sK37,sK37) ),
inference(superposition,[status(thm)],[d61,d107]) ).
cnf(d109,plain,
( ~ 'minsol$umodel$umax'(sK36,sK37,sK38)
| sK36 = sK38
| ~ lesseq(sK36,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d108,d68]) ).
cnf(d110,plain,
( ~ lesseq(X0,X1)
| sK30(X0,X1,X2) = X1
| 'minsol$umodel$umax'(X0,X1,X2)
| ~ 'model$umax'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c19,d25]) ).
cnf(d111,plain,
( 'minsol$umodel$umax'(X0,X1,X2)
| ~ 'model$umax'(X0,X1,X2)
| ~ lesseq(X0,X1)
| 'minsol$umodel$umax'(X0,X1,X2)
| ~ 'model$umax'(X0,X1,X2)
| ~ lesseq(X2,X1) ),
inference(superposition,[status(thm)],[d110,c20]) ).
cnf(d112,plain,
( 'minsol$umodel$umax'(X0,X1,sK37)
| ~ 'model$umax'(X0,X1,sK37)
| lesseq(sK30(X0,X1,sK37),sK38) ),
inference(resolution,[status(thm)],[d99,c20]) ).
cnf(d113,plain,
( 'minsol$umodel$umax'(X1,X2,X3)
| ~ 'model$umax'(X1,X2,X3)
| ~ 'model$umax'(X1,X2,X0)
| X0 = sK30(X1,X2,X3) ),
inference(resolution,[status(thm)],[d5,c19]) ).
cnf(d114,plain,
( 'minsol$umodel$umax'(X0,X1,sK37)
| ~ 'model$umax'(X0,X1,X2)
| ~ 'model$umax'(X0,X1,sK37)
| 'minsol$umodel$umax'(X0,X1,sK37)
| ~ 'model$umax'(X0,X1,sK37)
| lesseq(X2,sK38) ),
inference(superposition,[status(thm)],[d113,d112]) ).
cnf(d115,plain,
( ~ lesseq(X1,sK37)
| 'minsol$umodel$umax'(X1,sK37,sK37)
| ~ 'model$umax'(X1,sK37,X0)
| lesseq(X0,sK38) ),
inference(resolution,[status(thm)],[d114,d10]) ).
cnf(d116,plain,
( 'minsol$umodel$umax'(X0,sK37,sK37)
| lesseq(max(X0,sK37),sK38)
| ~ lesseq(X0,sK37) ),
inference(resolution,[status(thm)],[d115,d0]) ).
cnf(d117,plain,
( ~ lesseq(sK38,max(X0,sK37))
| max(X0,sK37) = sK38
| 'minsol$umodel$umax'(X0,sK37,sK37)
| ~ lesseq(X0,sK37) ),
inference(resolution,[status(thm)],[d116,c2]) ).
cnf(d118,plain,
( ~ 'model$umax'(X0,sK37,X1)
| 'minsol$umodel$umax'(X0,sK37,sK37)
| ~ lesseq(X0,sK37)
| max(X0,sK37) = sK38
| ~ lesseq(sK38,X1) ),
inference(superposition,[status(thm)],[c13,d117]) ).
cnf(d119,plain,
( 'minsol$umodel$umax'(X0,sK37,sK37)
| ~ 'model$umax'(X0,sK37,X1)
| ~ lesseq(sK38,X1)
| ~ lesseq(X0,sK37)
| 'model$umax'(X0,sK37,sK38) ),
inference(superposition,[status(thm)],[d118,d0]) ).
cnf(d120,plain,
( 'minsol$umodel$umax'(X0,sK37,sK37)
| 'model$umax'(X0,sK37,sK38)
| ~ lesseq(sK38,max(X0,sK37))
| ~ lesseq(X0,sK37) ),
inference(resolution,[status(thm)],[d119,d0]) ).
cnf(d121,plain,
( sK36 = sK38
| 'minsol$umodel$umax'(X0,sK37,sK37)
| 'model$umax'(X0,sK37,sK38)
| ~ lesseq(X0,sK37)
| ~ lesseq(sK37,max(X0,sK37)) ),
inference(superposition,[status(thm)],[d61,d120]) ).
cnf(d122,plain,
( ~ lesseq(X0,sK37)
| 'minsol$umodel$umax'(X0,sK37,sK37)
| 'model$umax'(X0,sK37,sK38)
| ~ lesseq(X0,sK37)
| sK36 = sK38
| ~ lesseq(sK37,sK37) ),
inference(superposition,[status(thm)],[c9,d121]) ).
cnf(d123,plain,
( 'minsol$umodel$umax'(X0,sK37,sK37)
| 'model$umax'(X0,sK37,sK38)
| ~ lesseq(X0,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[c0,d122]) ).
cnf(d124,plain,
( sK36 = sK38
| ~ lesseq(sK36,sK37)
| sK36 = sK38
| ~ 'minsol$umodel$umax'(sK36,sK37,sK37) ),
inference(superposition,[status(thm)],[d61,d109]) ).
cnf(d125,plain,
( 'model$umax'(sK36,sK37,sK38)
| ~ lesseq(sK36,sK37)
| sK36 = sK38
| ~ lesseq(sK36,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d124,d123]) ).
cnf(d126,plain,
( 'minsol$umodel$umax'(sK36,sK37,sK38)
| ~ lesseq(sK36,sK37)
| ~ lesseq(sK38,sK37)
| ~ lesseq(sK36,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d125,d111]) ).
cnf(d127,plain,
( ~ lesseq(sK36,sK37)
| sK36 = sK38
| ~ lesseq(sK38,sK37)
| ~ lesseq(sK36,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d126,d109]) ).
cnf(d128,plain,
( sK36 = sK38
| ~ lesseq(sK36,sK37)
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d127,d67]) ).
cnf(d129,plain,
( sK36 = sK38
| sK36 = sK38 ),
inference(resolution,[status(thm)],[d128,d52]) ).
cnf(d130,plain,
( ~ 'minsol$umodel$uub'(sK36,sK37,sK38)
| ~ 'minsol$umodel$umax'(sK36,sK37,sK36) ),
inference(demodulation,[status(thm)],[c27,d129]) ).
cnf(d131,plain,
( ~ 'minsol$umodel$uub'(sK36,sK37,sK36)
| ~ 'minsol$umodel$umax'(sK36,sK37,sK36) ),
inference(demodulation,[status(thm)],[d130,d129]) ).
cnf(d132,plain,
( lesseq(X0,sK35(X0,X1,X2))
| 'minsol$umodel$uub'(X0,X1,X2)
| ~ 'model$uub'(X0,X1,X2) ),
inference(resolution,[status(thm)],[d69,c10]) ).
cnf(d133,plain,
( 'minsol$umodel$uub'(X0,X1,sK36)
| ~ 'model$uub'(X0,X1,sK36)
| lesseq(sK35(X0,X1,sK36),sK38) ),
inference(resolution,[status(thm)],[d97,c24]) ).
cnf(d134,plain,
( ~ lesseq(sK38,sK35(X0,X1,sK36))
| sK35(X0,X1,sK36) = sK38
| 'minsol$umodel$uub'(X0,X1,sK36)
| ~ 'model$uub'(X0,X1,sK36) ),
inference(resolution,[status(thm)],[d133,c2]) ).
cnf(d135,plain,
( 'minsol$umodel$uub'(sK38,X0,sK36)
| ~ 'model$uub'(sK38,X0,sK36)
| 'minsol$umodel$uub'(sK38,X0,sK36)
| ~ 'model$uub'(sK38,X0,sK36)
| sK35(sK38,X0,sK36) = sK38 ),
inference(resolution,[status(thm)],[d134,d132]) ).
cnf(d136,plain,
( 'minsol$umodel$uub'(sK38,X0,sK36)
| ~ 'model$uub'(sK38,X0,sK36)
| 'minsol$umodel$uub'(sK38,X0,sK36)
| ~ 'model$uub'(sK38,X0,sK36)
| ~ lesseq(sK36,sK38) ),
inference(superposition,[status(thm)],[d135,c24]) ).
cnf(d137,plain,
( 'minsol$umodel$uub'(sK38,X0,sK36)
| ~ 'model$uub'(sK38,X0,sK36) ),
inference(resolution,[status(thm)],[d96,d136]) ).
cnf(d138,plain,
( ~ lesseq(X0,sK36)
| ~ lesseq(sK38,sK36)
| 'minsol$umodel$uub'(sK38,X0,sK36) ),
inference(resolution,[status(thm)],[d137,d33]) ).
cnf(d139,plain,
( 'minsol$umodel$uub'(sK38,X0,sK36)
| ~ lesseq(sK36,sK36)
| ~ lesseq(X0,sK36) ),
inference(demodulation,[status(thm)],[d138,d129]) ).
cnf(d140,plain,
( 'minsol$umodel$uub'(sK36,X0,sK36)
| ~ lesseq(sK36,sK36)
| ~ lesseq(X0,sK36) ),
inference(demodulation,[status(thm)],[d139,d129]) ).
cnf(d141,plain,
( 'minsol$umodel$uub'(sK36,X0,sK36)
| ~ lesseq(X0,sK36) ),
inference(resolution,[status(thm)],[c0,d140]) ).
cnf(d142,plain,
( ~ 'minsol$umodel$umax'(sK36,sK37,sK36)
| ~ lesseq(sK37,sK36) ),
inference(resolution,[status(thm)],[d141,d131]) ).
cnf(d143,plain,
lesseq(sK37,sK36),
inference(demodulation,[status(thm)],[d98,d129]) ).
cnf(d144,plain,
~ 'minsol$umodel$umax'(sK36,sK37,sK36),
inference(resolution,[status(thm)],[d143,d142]) ).
cnf(d145,plain,
( 'minsol$umodel$umax'(X0,X1,sK36)
| ~ 'model$umax'(X0,X1,sK36)
| lesseq(sK30(X0,X1,sK36),sK38) ),
inference(resolution,[status(thm)],[d97,c20]) ).
cnf(d146,plain,
( ~ lesseq(sK38,sK30(X0,X1,sK36))
| sK30(X0,X1,sK36) = sK38
| 'minsol$umodel$umax'(X0,X1,sK36)
| ~ 'model$umax'(X0,X1,sK36) ),
inference(resolution,[status(thm)],[d145,c2]) ).
cnf(d147,plain,
( 'minsol$umodel$umax'(X0,X1,X2)
| ~ 'model$umax'(X0,X1,X2)
| ~ lesseq(X1,X0)
| sK30(X0,X1,X2) = X0 ),
inference(resolution,[status(thm)],[d41,c19]) ).
cnf(d148,plain,
( 'minsol$umodel$umax'(X0,X1,sK36)
| ~ 'model$umax'(X0,X1,sK36)
| ~ lesseq(X1,X0)
| 'minsol$umodel$umax'(X0,X1,sK36)
| ~ 'model$umax'(X0,X1,sK36)
| sK30(X0,X1,sK36) = sK38
| ~ lesseq(sK38,X0) ),
inference(superposition,[status(thm)],[d147,d146]) ).
cnf(d149,plain,
( 'minsol$umodel$umax'(X0,X1,sK36)
| ~ 'model$umax'(X0,X1,sK36)
| ~ lesseq(sK38,X0)
| ~ lesseq(X1,X0)
| sK30(X0,X1,sK36) = sK36 ),
inference(demodulation,[status(thm)],[d148,d129]) ).
cnf(d150,plain,
( 'minsol$umodel$umax'(X0,X1,sK36)
| ~ 'model$umax'(X0,X1,sK36)
| ~ lesseq(sK36,X0)
| ~ lesseq(X1,X0)
| sK30(X0,X1,sK36) = sK36 ),
inference(demodulation,[status(thm)],[d149,d129]) ).
cnf(d151,plain,
( 'minsol$umodel$umax'(X0,X1,sK36)
| ~ 'model$umax'(X0,X1,sK36)
| ~ lesseq(sK36,X0)
| ~ lesseq(X1,X0)
| 'minsol$umodel$umax'(X0,X1,sK36)
| ~ 'model$umax'(X0,X1,sK36)
| ~ lesseq(sK36,sK36) ),
inference(superposition,[status(thm)],[d150,c20]) ).
cnf(d152,plain,
( 'minsol$umodel$umax'(X1,X0,sK36)
| ~ 'model$umax'(X1,X0,sK36)
| ~ lesseq(sK36,X1)
| ~ lesseq(X0,X1) ),
inference(resolution,[status(thm)],[c0,d151]) ).
cnf(d153,plain,
( ~ lesseq(X0,sK36)
| 'minsol$umodel$umax'(sK36,X0,sK36)
| ~ lesseq(sK36,sK36)
| ~ lesseq(X0,sK36) ),
inference(resolution,[status(thm)],[d152,d1]) ).
cnf(d154,plain,
( 'minsol$umodel$umax'(sK36,X0,sK36)
| ~ lesseq(X0,sK36) ),
inference(resolution,[status(thm)],[c0,d153]) ).
cnf(d155,plain,
~ lesseq(sK37,sK36),
inference(resolution,[status(thm)],[d154,d144]) ).
cnf(d156,plain,
$false,
inference(resolution,[status(thm)],[d143,d155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM858+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n018.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 04:16:06 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 118.05/29.62 % SZS status Theorem for theBenchmark.p
% 118.05/29.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------