%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG218+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 06:48:07 AM UTC 2026
% Result : Theorem 41.80s 15.98s
% Output : CNFRefutation 41.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 19
% Syntax : Number of formulae : 161 ( 49 unt; 0 def)
% Number of atoms : 812 ( 88 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 1148 ( 497 ~; 543 |; 80 &)
% ( 6 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 146 ( 11 sgn 39 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d10_xboole_0,axiom,
! [X0,X1] :
( X0 = X1
<=> ( 'r1$utarski'(X1,X0)
& 'r1$utarski'(X0,X1) ) ) ).
fof(d1_tarski,axiom,
! [X0,X1] :
( X1 = 'k1$utarski'(X0)
<=> ! [X2] :
( 'r2$uhidden'(X2,X1)
<=> X2 = X0 ) ) ).
fof(d3_tarski,axiom,
! [X0,X1] :
( 'r1$utarski'(X0,X1)
<=> ! [X2] :
( 'r2$uhidden'(X2,X0)
=> 'r2$uhidden'(X2,X1) ) ) ).
fof(dt_k1_rlvect_1,axiom,
! [X0] :
( 'l2$ustruct$u0'(X0)
=> 'm1$usubset$u1'('k1$urlvect$u1'(X0),'u1$ustruct$u0'(X0)) ) ).
fof(dt_l1_rlvect_1,axiom,
! [X0] :
( 'l1$urlvect$u1'(X0)
=> 'l2$ustruct$u0'(X0) ) ).
fof(dt_l1_vectsp_2,axiom,
! [X0] :
( 'l1$ustruct$u0'(X0)
=> ! [X1] :
( 'l1$uvectsp$u2'(X1,X0)
=> 'l1$urlvect$u1'(X1) ) ) ).
fof(dt_l2_struct_0,axiom,
! [X0] :
( 'l2$ustruct$u0'(X0)
=> 'l1$ustruct$u0'(X0) ) ).
fof(dt_l3_vectsp_1,axiom,
! [X0] :
( 'l3$uvectsp$u1'(X0)
=> ( 'l2$uvectsp$u1'(X0)
& 'l1$urlvect$u1'(X0) ) ) ).
fof(existence_m1_subset_1,axiom,
! [X0] :
? [X1] : 'm1$usubset$u1'(X1,X0) ).
fof(fc1_xboole_0,axiom,
'v1$uxboole$u0'('k1$uxboole$u0') ).
fof(rc2_subset_1,axiom,
! [X0] :
? [X1] :
( 'v1$uxboole$u0'(X1)
& 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'(X0)) ) ).
fof(redefinition_k7_rlvect_2,axiom,
! [X0,X1] :
( ( 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
& 'l1$ustruct$u0'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> 'k7$urlvect$u2'(X0,X1) = 'k1$utarski'(X1) ) ).
fof(t10_rmod_5,axiom,
! [X0,X1] :
( ( 'l3$uvectsp$u1'(X1)
& 'v2$uvectsp$u2'(X1)
& ~ 'v10$uvectsp$u1'(X1)
& 'v8$uvectsp$u1'(X1)
& 'v7$uvectsp$u1'(X1)
& 'v6$uvectsp$u1'(X1)
& 'v7$ugroup$u1'(X1)
& 'v4$ugroup$u1'(X1)
& 'v6$urlvect$u1'(X1)
& 'v5$urlvect$u1'(X1)
& 'v4$urlvect$u1'(X1)
& 'v3$urlvect$u1'(X1)
& ~ 'v3$ustruct$u0'(X1) )
=> ! [X2] :
( ( 'l1$uvectsp$u2'(X2,X1)
& 'v5$uvectsp$u2'(X2,X1)
& 'v6$urlvect$u1'(X2)
& 'v5$urlvect$u1'(X2)
& 'v4$urlvect$u1'(X2)
& 'v3$urlvect$u1'(X2)
& ~ 'v3$ustruct$u0'(X2) )
=> ! [X3] :
( 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('u1$ustruct$u0'(X2)))
=> ( 'r2$uhidden'(X0,X3)
=> 'r1$urlvect$u1'('k1$urmod$u5'(X1,X2,X3),X0) ) ) ) ) ).
fof(t2_subset,axiom,
! [X0,X1] :
( 'm1$usubset$u1'(X0,X1)
=> ( 'r2$uhidden'(X0,X1)
| 'v1$uxboole$u0'(X1) ) ) ).
fof(t3_subset,axiom,
! [X0,X1] :
( 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'(X1))
<=> 'r1$utarski'(X0,X1) ) ).
fof(t46_rmod_2,axiom,
! [X0,X1] :
( ( 'l3$uvectsp$u1'(X1)
& 'v8$uvectsp$u1'(X1)
& 'v7$uvectsp$u1'(X1)
& 'v6$uvectsp$u1'(X1)
& 'v4$ugroup$u1'(X1)
& 'v6$urlvect$u1'(X1)
& 'v5$urlvect$u1'(X1)
& 'v4$urlvect$u1'(X1)
& 'v3$urlvect$u1'(X1)
& ~ 'v3$ustruct$u0'(X1) )
=> ! [X2] :
( ( 'l1$uvectsp$u2'(X2,X1)
& 'v5$uvectsp$u2'(X2,X1)
& 'v6$urlvect$u1'(X2)
& 'v5$urlvect$u1'(X2)
& 'v4$urlvect$u1'(X2)
& 'v3$urlvect$u1'(X2)
& ~ 'v3$ustruct$u0'(X2) )
=> ( 'r1$urlvect$u1'('k1$urmod$u2'(X1,X2),X0)
<=> X0 = 'k1$urlvect$u1'(X2) ) ) ) ).
fof(t5_subset,axiom,
! [X0,X1,X2] :
~ ( 'v1$uxboole$u0'(X2)
& 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'(X2))
& 'r2$uhidden'(X0,X1) ) ).
fof(t6_boole,axiom,
! [X0] :
( 'v1$uxboole$u0'(X0)
=> X0 = 'k1$uxboole$u0' ) ).
fof(t12_rmod_5,conjecture,
! [X0] :
( ( 'l3$uvectsp$u1'(X0)
& 'v2$uvectsp$u2'(X0)
& ~ 'v10$uvectsp$u1'(X0)
& 'v8$uvectsp$u1'(X0)
& 'v7$uvectsp$u1'(X0)
& 'v6$uvectsp$u1'(X0)
& 'v7$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v6$urlvect$u1'(X0)
& 'v5$urlvect$u1'(X0)
& 'v4$urlvect$u1'(X0)
& 'v3$urlvect$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( ( 'l1$uvectsp$u2'(X1,X0)
& 'v5$uvectsp$u2'(X1,X0)
& 'v6$urlvect$u1'(X1)
& 'v5$urlvect$u1'(X1)
& 'v4$urlvect$u1'(X1)
& 'v3$urlvect$u1'(X1)
& ~ 'v3$ustruct$u0'(X1) )
=> ! [X2] :
( 'm1$usubset$u1'(X2,'k1$uzfmisc$u1'('u1$ustruct$u0'(X1)))
=> ~ ( X2 != 'k7$urlvect$u2'(X1,'k1$urlvect$u1'(X1))
& X2 != 'k1$uxboole$u0'
& 'k1$urmod$u5'(X0,X1,X2) = 'k1$urmod$u2'(X0,X1) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'l3$uvectsp$u1'(X0)
& 'v2$uvectsp$u2'(X0)
& ~ 'v10$uvectsp$u1'(X0)
& 'v8$uvectsp$u1'(X0)
& 'v7$uvectsp$u1'(X0)
& 'v6$uvectsp$u1'(X0)
& 'v7$ugroup$u1'(X0)
& 'v4$ugroup$u1'(X0)
& 'v6$urlvect$u1'(X0)
& 'v5$urlvect$u1'(X0)
& 'v4$urlvect$u1'(X0)
& 'v3$urlvect$u1'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( ( 'l1$uvectsp$u2'(X1,X0)
& 'v5$uvectsp$u2'(X1,X0)
& 'v6$urlvect$u1'(X1)
& 'v5$urlvect$u1'(X1)
& 'v4$urlvect$u1'(X1)
& 'v3$urlvect$u1'(X1)
& ~ 'v3$ustruct$u0'(X1) )
=> ! [X2] :
( 'm1$usubset$u1'(X2,'k1$uzfmisc$u1'('u1$ustruct$u0'(X1)))
=> ~ ( X2 != 'k7$urlvect$u2'(X1,'k1$urlvect$u1'(X1))
& X2 != 'k1$uxboole$u0'
& 'k1$urmod$u5'(X0,X1,X2) = 'k1$urmod$u2'(X0,X1) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t12_rmod_5]) ).
cnf(c13,plain,
( ~ 'r1$utarski'(X1,X0)
| ~ 'r1$utarski'(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[d10_xboole_0]) ).
cnf(c17,plain,
( sK14(X1,X0) = X1
| 'r2$uhidden'(sK14(X1,X0),X0)
| X0 = 'k1$utarski'(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c18,plain,
( ~ 'r2$uhidden'(sK14(X1,X0),X0)
| sK14(X1,X0) != X1
| X0 = 'k1$utarski'(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c20,plain,
( 'r2$uhidden'(X2,X1)
| ~ 'r2$uhidden'(X2,X0)
| ~ 'r1$utarski'(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c21,plain,
( 'r2$uhidden'(sK18(X0,X1),X0)
| 'r1$utarski'(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c25,plain,
( 'm1$usubset$u1'('k1$urlvect$u1'(X0),'u1$ustruct$u0'(X0))
| ~ 'l2$ustruct$u0'(X0) ),
inference(clausification,[status(esa)],[dt_k1_rlvect_1]) ).
cnf(c33,plain,
( 'l2$ustruct$u0'(X0)
| ~ 'l1$urlvect$u1'(X0) ),
inference(clausification,[status(esa)],[dt_l1_rlvect_1]) ).
cnf(c35,plain,
( 'l1$urlvect$u1'(X1)
| ~ 'l1$uvectsp$u2'(X1,X0)
| ~ 'l1$ustruct$u0'(X0) ),
inference(clausification,[status(esa)],[dt_l1_vectsp_2]) ).
cnf(c36,plain,
( 'l1$ustruct$u0'(X0)
| ~ 'l2$ustruct$u0'(X0) ),
inference(clausification,[status(esa)],[dt_l2_struct_0]) ).
cnf(c39,plain,
( 'l1$urlvect$u1'(X0)
| ~ 'l3$uvectsp$u1'(X0) ),
inference(clausification,[status(esa)],[dt_l3_vectsp_1]) ).
cnf(c67,plain,
'm1$usubset$u1'(sK67(X0),X0),
inference(clausification,[status(esa)],[existence_m1_subset_1]) ).
cnf(c73,plain,
'v1$uxboole$u0'('k1$uxboole$u0'),
inference(clausification,[status(esa)],[fc1_xboole_0]) ).
cnf(c114,plain,
'm1$usubset$u1'(sK108(X0),'k1$uzfmisc$u1'(X0)),
inference(clausification,[status(esa)],[rc2_subset_1]) ).
cnf(c115,plain,
'v1$uxboole$u0'(sK108(X0)),
inference(clausification,[status(esa)],[rc2_subset_1]) ).
cnf(c127,plain,
( 'k7$urlvect$u2'(X0,X1) = 'k1$utarski'(X1)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
| ~ 'l1$ustruct$u0'(X0)
| 'v3$ustruct$u0'(X0) ),
inference(clausification,[status(esa)],[redefinition_k7_rlvect_2]) ).
cnf(c131,plain,
( ~ 'v4$urlvect$u1'(X3)
| ~ 'v7$ugroup$u1'(X2)
| ~ 'l3$uvectsp$u1'(X2)
| 'v3$ustruct$u0'(X2)
| ~ 'v5$urlvect$u1'(X2)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('u1$ustruct$u0'(X3)))
| ~ 'v6$urlvect$u1'(X2)
| 'v3$ustruct$u0'(X3)
| ~ 'v6$urlvect$u1'(X3)
| ~ 'v4$ugroup$u1'(X2)
| ~ 'v8$uvectsp$u1'(X2)
| ~ 'v5$urlvect$u1'(X3)
| ~ 'v6$uvectsp$u1'(X2)
| 'r1$urlvect$u1'('k1$urmod$u5'(X2,X3,X1),X0)
| ~ 'v5$uvectsp$u2'(X3,X2)
| ~ 'v3$urlvect$u1'(X3)
| ~ 'v4$urlvect$u1'(X2)
| 'v10$uvectsp$u1'(X2)
| ~ 'l1$uvectsp$u2'(X3,X2)
| ~ 'v7$uvectsp$u1'(X2)
| ~ 'v3$urlvect$u1'(X2)
| ~ 'v2$uvectsp$u2'(X2)
| ~ 'r2$uhidden'(X0,X1) ),
inference(clausification,[status(esa)],[t10_rmod_5]) ).
cnf(c133,plain,
( 'r2$uhidden'(X0,X1)
| 'v1$uxboole$u0'(X1)
| ~ 'm1$usubset$u1'(X0,X1) ),
inference(clausification,[status(esa)],[t2_subset]) ).
cnf(c134,plain,
( 'r1$utarski'(X0,X1)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c135,plain,
( ~ 'r1$utarski'(X0,X1)
| 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'(X1)) ),
inference(clausification,[status(esa)],[t3_subset]) ).
cnf(c136,plain,
( ~ 'v4$ugroup$u1'(X1)
| ~ 'v5$urlvect$u1'(X0)
| ~ 'v6$uvectsp$u1'(X1)
| ~ 'v4$urlvect$u1'(X0)
| ~ 'v8$uvectsp$u1'(X1)
| ~ 'l1$uvectsp$u2'(X0,X1)
| ~ 'v3$urlvect$u1'(X1)
| X2 = 'k1$urlvect$u1'(X0)
| ~ 'v6$urlvect$u1'(X1)
| ~ 'v3$urlvect$u1'(X0)
| ~ 'v5$urlvect$u1'(X1)
| ~ 'r1$urlvect$u1'('k1$urmod$u2'(X1,X0),X2)
| 'v3$ustruct$u0'(X0)
| ~ 'v4$urlvect$u1'(X1)
| ~ 'v5$uvectsp$u2'(X0,X1)
| ~ 'l3$uvectsp$u1'(X1)
| 'v3$ustruct$u0'(X1)
| ~ 'v7$uvectsp$u1'(X1)
| ~ 'v6$urlvect$u1'(X0) ),
inference(clausification,[status(esa)],[t46_rmod_2]) ).
cnf(c139,plain,
( ~ 'v1$uxboole$u0'(X2)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'(X2))
| ~ 'r2$uhidden'(X0,X1) ),
inference(clausification,[status(esa)],[t5_subset]) ).
cnf(c140,plain,
( X0 = 'k1$uxboole$u0'
| ~ 'v1$uxboole$u0'(X0) ),
inference(clausification,[status(esa)],[t6_boole]) ).
cnf(c143,plain,
~ 'v3$ustruct$u0'(sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c144,plain,
'v3$urlvect$u1'(sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c145,plain,
'v4$urlvect$u1'(sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c146,plain,
'v5$urlvect$u1'(sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c147,plain,
'v6$urlvect$u1'(sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c148,plain,
'v4$ugroup$u1'(sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c149,plain,
'v7$ugroup$u1'(sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c150,plain,
'v6$uvectsp$u1'(sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c151,plain,
'v7$uvectsp$u1'(sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c152,plain,
'v8$uvectsp$u1'(sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c153,plain,
~ 'v10$uvectsp$u1'(sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c154,plain,
'v2$uvectsp$u2'(sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c155,plain,
'l3$uvectsp$u1'(sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c156,plain,
~ 'v3$ustruct$u0'(sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c157,plain,
'v3$urlvect$u1'(sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c158,plain,
'v4$urlvect$u1'(sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c159,plain,
'v5$urlvect$u1'(sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c160,plain,
'v6$urlvect$u1'(sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c161,plain,
'v5$uvectsp$u2'(sK150,sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c162,plain,
'l1$uvectsp$u2'(sK150,sK149),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c163,plain,
'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c164,plain,
'k1$urmod$u5'(sK149,sK150,sK151) = 'k1$urmod$u2'(sK149,sK150),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c165,plain,
sK151 != 'k1$uxboole$u0',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c166,plain,
sK151 != 'k7$urlvect$u2'(sK150,'k1$urlvect$u1'(sK150)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'v10$uvectsp$u1'(sK149)
| ~ 'v2$uvectsp$u2'(sK149)
| ~ 'v4$ugroup$u1'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v3$urlvect$u1'(sK149)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK149)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v5$urlvect$u1'(sK149)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK149)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| 'v3$ustruct$u0'(sK149)
| ~ 'v7$ugroup$u1'(sK149)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0) ),
inference(superposition,[status(thm)],[c164,c131]) ).
cnf(d1,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| 'v10$uvectsp$u1'(sK149)
| ~ 'v2$uvectsp$u2'(sK149)
| ~ 'v4$ugroup$u1'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v3$urlvect$u1'(sK149)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK149)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v5$urlvect$u1'(sK149)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK149)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v7$ugroup$u1'(sK149)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c143,d0]) ).
cnf(d2,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| 'v10$uvectsp$u1'(sK149)
| ~ 'v2$uvectsp$u2'(sK149)
| ~ 'v4$ugroup$u1'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK149)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v5$urlvect$u1'(sK149)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK149)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v7$ugroup$u1'(sK149)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c144,d1]) ).
cnf(d3,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| 'v10$uvectsp$u1'(sK149)
| ~ 'v2$uvectsp$u2'(sK149)
| ~ 'v4$ugroup$u1'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v5$urlvect$u1'(sK149)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK149)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v7$ugroup$u1'(sK149)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c145,d2]) ).
cnf(d4,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| 'v10$uvectsp$u1'(sK149)
| ~ 'v2$uvectsp$u2'(sK149)
| ~ 'v4$ugroup$u1'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK149)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v7$ugroup$u1'(sK149)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c146,d3]) ).
cnf(d5,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| 'v10$uvectsp$u1'(sK149)
| ~ 'v2$uvectsp$u2'(sK149)
| ~ 'v4$ugroup$u1'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v7$ugroup$u1'(sK149)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c147,d4]) ).
cnf(d6,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| 'v10$uvectsp$u1'(sK149)
| ~ 'v2$uvectsp$u2'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v7$ugroup$u1'(sK149)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c148,d5]) ).
cnf(d7,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| 'v10$uvectsp$u1'(sK149)
| ~ 'v2$uvectsp$u2'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c149,d6]) ).
cnf(d8,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| 'v10$uvectsp$u1'(sK149)
| ~ 'v2$uvectsp$u2'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c150,d7]) ).
cnf(d9,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| 'v10$uvectsp$u1'(sK149)
| ~ 'v2$uvectsp$u2'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c151,d8]) ).
cnf(d10,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| 'v10$uvectsp$u1'(sK149)
| ~ 'v2$uvectsp$u2'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c152,d9]) ).
cnf(d11,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| ~ 'v2$uvectsp$u2'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c153,d10]) ).
cnf(d12,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c154,d11]) ).
cnf(d13,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c155,d12]) ).
cnf(d14,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c156,d13]) ).
cnf(d15,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c157,d14]) ).
cnf(d16,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c158,d15]) ).
cnf(d17,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c159,d16]) ).
cnf(d18,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c160,d17]) ).
cnf(d19,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149) ),
inference(resolution,[status(thm)],[c161,d18]) ).
cnf(d20,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| ~ 'm1$usubset$u1'(sK151,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK150)))
| ~ 'r2$uhidden'(X0,sK151) ),
inference(resolution,[status(thm)],[c162,d19]) ).
cnf(d21,plain,
( 'r1$urlvect$u1'('k1$urmod$u2'(sK149,sK150),X0)
| ~ 'r2$uhidden'(X0,sK151) ),
inference(resolution,[status(thm)],[c163,d20]) ).
cnf(d22,plain,
( ~ 'r2$uhidden'(X0,sK151)
| ~ 'v4$ugroup$u1'(sK149)
| ~ 'v3$urlvect$u1'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK149)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c136,d21]) ).
cnf(d23,plain,
( ~ 'v4$ugroup$u1'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v3$urlvect$u1'(sK149)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK149)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v5$urlvect$u1'(sK149)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK149)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c143,d22]) ).
cnf(d24,plain,
( ~ 'v4$ugroup$u1'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK149)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v5$urlvect$u1'(sK149)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK149)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c144,d23]) ).
cnf(d25,plain,
( ~ 'v4$ugroup$u1'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v5$urlvect$u1'(sK149)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK149)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c145,d24]) ).
cnf(d26,plain,
( ~ 'v4$ugroup$u1'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK149)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c146,d25]) ).
cnf(d27,plain,
( ~ 'v4$ugroup$u1'(sK149)
| ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c147,d26]) ).
cnf(d28,plain,
( ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'v6$uvectsp$u1'(sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c148,d27]) ).
cnf(d29,plain,
( ~ 'v3$urlvect$u1'(sK150)
| ~ 'v7$uvectsp$u1'(sK149)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c150,d28]) ).
cnf(d30,plain,
( ~ 'v3$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'v8$uvectsp$u1'(sK149)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c151,d29]) ).
cnf(d31,plain,
( ~ 'v3$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'l3$uvectsp$u1'(sK149)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c152,d30]) ).
cnf(d32,plain,
( ~ 'v3$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| 'v3$ustruct$u0'(sK150)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c155,d31]) ).
cnf(d33,plain,
( ~ 'v3$urlvect$u1'(sK150)
| ~ 'v4$urlvect$u1'(sK150)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c156,d32]) ).
cnf(d34,plain,
( ~ 'v4$urlvect$u1'(sK150)
| ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c157,d33]) ).
cnf(d35,plain,
( ~ 'v5$urlvect$u1'(sK150)
| ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c158,d34]) ).
cnf(d36,plain,
( ~ 'v6$urlvect$u1'(sK150)
| ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c159,d35]) ).
cnf(d37,plain,
( ~ 'v5$uvectsp$u2'(sK150,sK149)
| ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c160,d36]) ).
cnf(d38,plain,
( ~ 'r2$uhidden'(X0,sK151)
| ~ 'l1$uvectsp$u2'(sK150,sK149)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c161,d37]) ).
cnf(d39,plain,
( ~ 'r2$uhidden'(X0,sK151)
| X0 = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[c162,d38]) ).
cnf(d40,plain,
( sK14(X0,sK151) = X0
| sK151 = 'k1$utarski'(X0)
| sK14(X0,sK151) = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d39,c17]) ).
cnf(d41,plain,
( sK151 = 'k1$utarski'(X0)
| sK14(X0,sK151) = X0
| 'k1$urlvect$u1'(sK150) != X0 ),
inference(equality_factoring,[status(thm)],[d40]) ).
cnf(d42,plain,
( sK151 = 'k1$utarski'('k1$urlvect$u1'(sK150))
| sK14('k1$urlvect$u1'(sK150),sK151) = 'k1$urlvect$u1'(sK150) ),
inference(equality_resolution,[status(thm)],[d41]) ).
cnf(d43,plain,
( 'l1$urlvect$u1'(sK150)
| ~ 'l1$ustruct$u0'(sK149) ),
inference(resolution,[status(thm)],[c35,c162]) ).
cnf(d44,plain,
'l1$urlvect$u1'(sK149),
inference(resolution,[status(thm)],[c39,c155]) ).
cnf(d45,plain,
'l2$ustruct$u0'(sK149),
inference(resolution,[status(thm)],[d44,c33]) ).
cnf(d46,plain,
'l1$ustruct$u0'(sK149),
inference(resolution,[status(thm)],[d45,c36]) ).
cnf(d47,plain,
'l1$urlvect$u1'(sK150),
inference(resolution,[status(thm)],[d46,d43]) ).
cnf(d48,plain,
'l2$ustruct$u0'(sK150),
inference(resolution,[status(thm)],[d47,c33]) ).
cnf(d49,plain,
( ~ 'l2$ustruct$u0'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'l1$ustruct$u0'(X0)
| 'k7$urlvect$u2'(X0,'k1$urlvect$u1'(X0)) = 'k1$utarski'('k1$urlvect$u1'(X0)) ),
inference(resolution,[status(thm)],[c127,c25]) ).
cnf(d50,plain,
( 'v3$ustruct$u0'(sK150)
| ~ 'l1$ustruct$u0'(sK150)
| 'k7$urlvect$u2'(sK150,'k1$urlvect$u1'(sK150)) = 'k1$utarski'('k1$urlvect$u1'(sK150)) ),
inference(resolution,[status(thm)],[d49,d48]) ).
cnf(d51,plain,
( ~ 'l1$ustruct$u0'(sK150)
| 'k7$urlvect$u2'(sK150,'k1$urlvect$u1'(sK150)) = 'k1$utarski'('k1$urlvect$u1'(sK150)) ),
inference(resolution,[status(thm)],[c156,d50]) ).
cnf(d52,plain,
'l1$ustruct$u0'(sK150),
inference(resolution,[status(thm)],[d48,c36]) ).
cnf(d53,plain,
'k7$urlvect$u2'(sK150,'k1$urlvect$u1'(sK150)) = 'k1$utarski'('k1$urlvect$u1'(sK150)),
inference(resolution,[status(thm)],[d52,d51]) ).
cnf(d54,plain,
sK151 != 'k1$utarski'('k1$urlvect$u1'(sK150)),
inference(demodulation,[status(thm)],[c166,d53]) ).
cnf(d55,plain,
sK14('k1$urlvect$u1'(sK150),sK151) = 'k1$urlvect$u1'(sK150),
inference(resolution,[status(thm)],[d54,d42]) ).
cnf(d56,plain,
( ~ 'r2$uhidden'(sK14('k1$urlvect$u1'(sK150),sK151),sK151)
| sK151 = 'k1$utarski'('k1$urlvect$u1'(sK150))
| 'k1$urlvect$u1'(sK150) != 'k1$urlvect$u1'(sK150) ),
inference(superposition,[status(thm)],[d55,c18]) ).
cnf(d57,plain,
( ~ 'r2$uhidden'('k1$urlvect$u1'(sK150),sK151)
| sK151 = 'k1$utarski'('k1$urlvect$u1'(sK150))
| 'k1$urlvect$u1'(sK150) != 'k1$urlvect$u1'(sK150) ),
inference(demodulation,[status(thm)],[d56,d55]) ).
cnf(d58,plain,
( ~ 'r2$uhidden'('k1$urlvect$u1'(sK150),sK151)
| 'k1$urlvect$u1'(sK150) != 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d54,d57]) ).
cnf(d59,plain,
( 'v1$uxboole$u0'(X0)
| 'r2$uhidden'(sK67(X0),X0) ),
inference(resolution,[status(thm)],[c133,c67]) ).
cnf(d60,plain,
( 'v1$uxboole$u0'(sK151)
| sK67(sK151) = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d39,d59]) ).
cnf(d61,plain,
( sK151 = 'k1$uxboole$u0'
| sK67(sK151) = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d60,c140]) ).
cnf(d62,plain,
sK67(sK151) = 'k1$urlvect$u1'(sK150),
inference(resolution,[status(thm)],[c165,d61]) ).
cnf(d63,plain,
( 'v1$uxboole$u0'(sK151)
| 'r2$uhidden'('k1$urlvect$u1'(sK150),sK151) ),
inference(superposition,[status(thm)],[d62,d59]) ).
cnf(d64,plain,
( ~ 'r1$utarski'(X1,X2)
| ~ 'v1$uxboole$u0'(X2)
| ~ 'r2$uhidden'(X0,X1) ),
inference(resolution,[status(thm)],[c139,c135]) ).
cnf(d65,plain,
( 'r1$utarski'(sK151,X0)
| sK18(sK151,X0) = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d39,c21]) ).
cnf(d66,plain,
( ~ 'v1$uxboole$u0'(X0)
| ~ 'r2$uhidden'(X1,sK151)
| sK18(sK151,X0) = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d65,d64]) ).
cnf(d67,plain,
( 'v1$uxboole$u0'(sK151)
| ~ 'v1$uxboole$u0'(X0)
| sK18(sK151,X0) = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d66,d63]) ).
cnf(d68,plain,
( 'v1$uxboole$u0'(sK151)
| sK18(sK151,'k1$uxboole$u0') = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d67,c73]) ).
cnf(d69,plain,
( sK151 = 'k1$uxboole$u0'
| sK18(sK151,'k1$uxboole$u0') = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d68,c140]) ).
cnf(d70,plain,
sK18(sK151,'k1$uxboole$u0') = 'k1$urlvect$u1'(sK150),
inference(resolution,[status(thm)],[c165,d69]) ).
cnf(d71,plain,
sK108(X0) = 'k1$uxboole$u0',
inference(resolution,[status(thm)],[c140,c115]) ).
cnf(d72,plain,
'm1$usubset$u1'('k1$uxboole$u0','k1$uzfmisc$u1'(X0)),
inference(demodulation,[status(thm)],[c114,d71]) ).
cnf(d73,plain,
'r1$utarski'('k1$uxboole$u0',X0),
inference(resolution,[status(thm)],[c134,d72]) ).
cnf(d74,plain,
( ~ 'r1$utarski'(X0,sK151)
| sK151 = X0
| sK18(sK151,X0) = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d65,c13]) ).
cnf(d75,plain,
( sK151 = 'k1$uxboole$u0'
| sK18(sK151,'k1$uxboole$u0') = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d74,d73]) ).
cnf(d76,plain,
( sK151 = 'k1$uxboole$u0'
| 'k1$urlvect$u1'(sK150) = 'k1$urlvect$u1'(sK150) ),
inference(demodulation,[status(thm)],[d75,d70]) ).
cnf(d77,plain,
'k1$urlvect$u1'(sK150) = 'k1$urlvect$u1'(sK150),
inference(resolution,[status(thm)],[c165,d76]) ).
cnf(d78,plain,
~ 'r2$uhidden'('k1$urlvect$u1'(sK150),sK151),
inference(resolution,[status(thm)],[d77,d58]) ).
cnf(d79,plain,
( ~ 'v1$uxboole$u0'(X1)
| ~ 'r2$uhidden'(X0,sK67('k1$uzfmisc$u1'(X1))) ),
inference(resolution,[status(thm)],[c139,c67]) ).
cnf(d80,plain,
( ~ 'r2$uhidden'(X1,sK151)
| 'r2$uhidden'(X1,X0)
| sK18(sK151,X0) = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d65,c20]) ).
cnf(d81,plain,
( 'v1$uxboole$u0'(sK151)
| 'r2$uhidden'('k1$urlvect$u1'(sK150),X0)
| sK18(sK151,X0) = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d80,d63]) ).
cnf(d82,plain,
( ~ 'v1$uxboole$u0'(X0)
| 'v1$uxboole$u0'(sK151)
| sK18(sK151,sK67('k1$uzfmisc$u1'(X0))) = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d81,d79]) ).
cnf(d83,plain,
( 'v1$uxboole$u0'(sK151)
| sK18(sK151,sK67('k1$uzfmisc$u1'('k1$uxboole$u0'))) = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d82,c73]) ).
cnf(d84,plain,
( sK151 = 'k1$uxboole$u0'
| sK18(sK151,sK67('k1$uzfmisc$u1'('k1$uxboole$u0'))) = 'k1$urlvect$u1'(sK150) ),
inference(resolution,[status(thm)],[d83,c140]) ).
cnf(d85,plain,
sK18(sK151,sK67('k1$uzfmisc$u1'('k1$uxboole$u0'))) = 'k1$urlvect$u1'(sK150),
inference(resolution,[status(thm)],[c165,d84]) ).
cnf(d86,plain,
( 'r1$utarski'(sK151,sK67('k1$uzfmisc$u1'('k1$uxboole$u0')))
| 'r2$uhidden'('k1$urlvect$u1'(sK150),sK151) ),
inference(superposition,[status(thm)],[d85,c21]) ).
cnf(d87,plain,
( ~ 'r2$uhidden'(X0,sK151)
| 'r2$uhidden'(X0,sK67('k1$uzfmisc$u1'('k1$uxboole$u0')))
| 'r2$uhidden'('k1$urlvect$u1'(sK150),sK151) ),
inference(resolution,[status(thm)],[d86,c20]) ).
cnf(d88,plain,
( ~ 'v1$uxboole$u0'('k1$uxboole$u0')
| 'r2$uhidden'('k1$urlvect$u1'(sK150),sK151)
| ~ 'r2$uhidden'(X0,sK151) ),
inference(resolution,[status(thm)],[d87,d79]) ).
cnf(d89,plain,
( 'r2$uhidden'('k1$urlvect$u1'(sK150),sK151)
| ~ 'r2$uhidden'(X0,sK151) ),
inference(resolution,[status(thm)],[c73,d88]) ).
cnf(d90,plain,
( 'r1$utarski'(sK151,X0)
| 'r2$uhidden'('k1$urlvect$u1'(sK150),sK151) ),
inference(resolution,[status(thm)],[d89,c21]) ).
cnf(d91,plain,
( ~ 'r1$utarski'(X0,sK151)
| sK151 = X0
| 'r2$uhidden'('k1$urlvect$u1'(sK150),sK151) ),
inference(resolution,[status(thm)],[d90,c13]) ).
cnf(d92,plain,
( 'r2$uhidden'('k1$urlvect$u1'(sK150),sK151)
| sK151 = 'k1$uxboole$u0' ),
inference(resolution,[status(thm)],[d91,d73]) ).
cnf(d93,plain,
'r2$uhidden'('k1$urlvect$u1'(sK150),sK151),
inference(resolution,[status(thm)],[c165,d92]) ).
cnf(d94,plain,
$false,
inference(resolution,[status(thm)],[d93,d78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG218+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/10.62 % Computer : n013.cluster.edu
% 0.13/10.62 % Model : x86_64 x86_64
% 0.13/10.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.62 % Memory : 8046.5625MB
% 0.13/10.62 % OS : Linux 6.8.0-71-generic
% 0.13/10.62 % CPULimit : 300
% 0.13/10.62 % WCLimit : 300
% 0.13/10.62 % DateTime : Sat Sep 26 21:29:20 UTC 2026
% 0.13/10.62 % CPUTime :
% 0.13/10.62 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.80/15.98 % SZS status Theorem for theBenchmark.p
% 41.80/15.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------