%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG216+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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:48:07 AM UTC 2026
% Result : Theorem 7.53s 7.86s
% Output : CNFRefutation 7.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 10
% Syntax : Number of formulae : 86 ( 33 unt; 0 def)
% Number of atoms : 451 ( 47 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 655 ( 290 ~; 289 |; 55 &)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 56 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [X0,X1] : 'k2$utarski'(X0,X1) = 'k2$utarski'(X1,X0) ).
fof(dt_l1_rlvect_1,axiom,
! [X0] :
( 'l1$urlvect$u1'(X0)
=> 'l2$ustruct$u0'(X0) ) ).
fof(dt_l2_struct_0,axiom,
! [X0] :
( 'l2$ustruct$u0'(X0)
=> 'l1$ustruct$u0'(X0) ) ).
fof(commutativity_k8_rlvect_2,axiom,
! [X0,X1,X2] :
( ( 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X0))
& 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
& 'l1$ustruct$u0'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> 'k8$urlvect$u2'(X0,X1,X2) = 'k8$urlvect$u2'(X0,X2,X1) ) ).
fof(redefinition_k8_rlvect_2,axiom,
! [X0,X1,X2] :
( ( 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X0))
& 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
& 'l1$ustruct$u0'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> 'k8$urlvect$u2'(X0,X1,X2) = 'k2$utarski'(X1,X2) ) ).
fof(dt_k1_rlvect_1,axiom,
! [X0] :
( 'l2$ustruct$u0'(X0)
=> 'm1$usubset$u1'('k1$urlvect$u1'(X0),'u1$ustruct$u0'(X0)) ) ).
fof(dt_l1_vectsp_2,axiom,
! [X0] :
( 'l1$ustruct$u0'(X0)
=> ! [X1] :
( 'l1$uvectsp$u2'(X1,X0)
=> 'l1$urlvect$u1'(X1) ) ) ).
fof(dt_l3_vectsp_1,axiom,
! [X0] :
( 'l3$uvectsp$u1'(X0)
=> ( 'l2$uvectsp$u1'(X0)
& 'l1$urlvect$u1'(X0) ) ) ).
fof(t5_rmod_5,axiom,
! [X0] :
( ( 'l3$uvectsp$u1'(X0)
& 'v8$uvectsp$u1'(X0)
& 'v7$uvectsp$u1'(X0)
& 'v6$uvectsp$u1'(X0)
& 'v4$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$u1'(X2,'u1$ustruct$u0'(X1))
=> ! [X3] :
( 'm1$usubset$u1'(X3,'u1$ustruct$u0'(X1))
=> ( 'v1$urmod$u5'('k8$urlvect$u2'(X1,X2,X3),X0,X1)
=> ( ( X3 != 'k1$urlvect$u1'(X1)
& X2 != 'k1$urlvect$u1'(X1) )
| 'k1$urlvect$u1'(X0) = 'k2$ugroup$u1'(X0) ) ) ) ) ) ) ).
fof(t6_rmod_5,conjecture,
! [X0] :
( ( 'l3$uvectsp$u1'(X0)
& 'v8$uvectsp$u1'(X0)
& 'v7$uvectsp$u1'(X0)
& 'v6$uvectsp$u1'(X0)
& 'v4$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$u1'(X2,'u1$ustruct$u0'(X1))
=> ( 'k1$urlvect$u1'(X0) != 'k2$ugroup$u1'(X0)
=> ( ~ 'v1$urmod$u5'('k8$urlvect$u2'(X1,'k1$urlvect$u1'(X1),X2),X0,X1)
& ~ 'v1$urmod$u5'('k8$urlvect$u2'(X1,X2,'k1$urlvect$u1'(X1)),X0,X1) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'l3$uvectsp$u1'(X0)
& 'v8$uvectsp$u1'(X0)
& 'v7$uvectsp$u1'(X0)
& 'v6$uvectsp$u1'(X0)
& 'v4$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$u1'(X2,'u1$ustruct$u0'(X1))
=> ( 'k1$urlvect$u1'(X0) != 'k2$ugroup$u1'(X0)
=> ( ~ 'v1$urmod$u5'('k8$urlvect$u2'(X1,'k1$urlvect$u1'(X1),X2),X0,X1)
& ~ 'v1$urmod$u5'('k8$urlvect$u2'(X1,X2,'k1$urlvect$u1'(X1)),X0,X1) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t6_rmod_5]) ).
cnf(c23,plain,
'k2$utarski'(X0,X1) = 'k2$utarski'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_tarski]) ).
cnf(c30,plain,
( 'l2$ustruct$u0'(X0)
| ~ 'l1$urlvect$u1'(X0) ),
inference(clausification,[status(esa)],[dt_l1_rlvect_1]) ).
cnf(c31,plain,
( 'l1$ustruct$u0'(X0)
| ~ 'l2$ustruct$u0'(X0) ),
inference(clausification,[status(esa)],[dt_l2_struct_0]) ).
cnf(c45,plain,
( ~ 'l1$ustruct$u0'(X1)
| 'v3$ustruct$u0'(X1)
| ~ 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X1))
| 'k8$urlvect$u2'(X1,X0,X2) = 'k8$urlvect$u2'(X1,X2,X0)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(X1)) ),
inference(clausification,[status(esa)],[commutativity_k8_rlvect_2]) ).
cnf(c49,plain,
( ~ 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X1))
| 'v3$ustruct$u0'(X1)
| ~ 'l1$ustruct$u0'(X1)
| 'k8$urlvect$u2'(X1,X2,X0) = 'k2$utarski'(X2,X0)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(X1)) ),
inference(clausification,[status(esa)],[redefinition_k8_rlvect_2]) ).
cnf(c50,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(c54,plain,
( 'l1$urlvect$u1'(X1)
| ~ 'l1$uvectsp$u2'(X1,X0)
| ~ 'l1$ustruct$u0'(X0) ),
inference(clausification,[status(esa)],[dt_l1_vectsp_2]) ).
cnf(c55,plain,
( 'l1$urlvect$u1'(X0)
| ~ 'l3$uvectsp$u1'(X0) ),
inference(clausification,[status(esa)],[dt_l3_vectsp_1]) ).
cnf(c57,plain,
( X2 != 'k1$urlvect$u1'(X1)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'v3$urlvect$u1'(X1)
| ~ 'v4$urlvect$u1'(X1)
| ~ 'v6$uvectsp$u1'(X0)
| 'v3$ustruct$u0'(X1)
| ~ 'v8$uvectsp$u1'(X0)
| ~ 'v5$urlvect$u1'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'v5$urlvect$u1'(X1)
| 'k1$urlvect$u1'(X0) = 'k2$ugroup$u1'(X0)
| ~ 'v6$urlvect$u1'(X0)
| ~ 'v6$urlvect$u1'(X1)
| ~ 'v7$uvectsp$u1'(X0)
| ~ 'l1$uvectsp$u2'(X1,X0)
| ~ 'm1$usubset$u1'(X2,'u1$ustruct$u0'(X1))
| ~ 'v3$urlvect$u1'(X0)
| ~ 'm1$usubset$u1'(X3,'u1$ustruct$u0'(X1))
| ~ 'l3$uvectsp$u1'(X0)
| ~ 'v5$uvectsp$u2'(X1,X0)
| ~ 'v1$urmod$u5'('k8$urlvect$u2'(X1,X2,X3),X0,X1)
| ~ 'v4$urlvect$u1'(X0) ),
inference(clausification,[status(esa)],[t5_rmod_5]) ).
cnf(c59,plain,
~ 'v3$ustruct$u0'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c60,plain,
'v3$urlvect$u1'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c61,plain,
'v4$urlvect$u1'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c62,plain,
'v5$urlvect$u1'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c63,plain,
'v6$urlvect$u1'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c64,plain,
'v4$ugroup$u1'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c65,plain,
'v6$uvectsp$u1'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c66,plain,
'v7$uvectsp$u1'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c67,plain,
'v8$uvectsp$u1'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c68,plain,
'l3$uvectsp$u1'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c69,plain,
~ 'v3$ustruct$u0'(sK76),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c70,plain,
'v3$urlvect$u1'(sK76),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c71,plain,
'v4$urlvect$u1'(sK76),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c72,plain,
'v5$urlvect$u1'(sK76),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c73,plain,
'v6$urlvect$u1'(sK76),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c74,plain,
'v5$uvectsp$u2'(sK76,sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c75,plain,
'l1$uvectsp$u2'(sK76,sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c76,plain,
'm1$usubset$u1'(sK77,'u1$ustruct$u0'(sK76)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c77,plain,
'k1$urlvect$u1'(sK75) != 'k2$ugroup$u1'(sK75),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c78,plain,
( 'v1$urmod$u5'('k8$urlvect$u2'(sK76,'k1$urlvect$u1'(sK76),sK77),sK75,sK76)
| 'v1$urmod$u5'('k8$urlvect$u2'(sK76,sK77,'k1$urlvect$u1'(sK76)),sK75,sK76) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'v3$ustruct$u0'(sK76)
| ~ 'l1$ustruct$u0'(sK76)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK76))
| 'k8$urlvect$u2'(sK76,X0,sK77) = 'k2$utarski'(X0,sK77) ),
inference(resolution,[status(thm)],[c49,c76]) ).
cnf(d1,plain,
( ~ 'l1$ustruct$u0'(sK76)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK76))
| 'k8$urlvect$u2'(sK76,X0,sK77) = 'k2$utarski'(X0,sK77) ),
inference(resolution,[status(thm)],[c69,d0]) ).
cnf(d2,plain,
( ~ 'l1$ustruct$u0'(sK76)
| 'k8$urlvect$u2'(sK76,'k1$urlvect$u1'(sK76),sK77) = 'k2$utarski'('k1$urlvect$u1'(sK76),sK77)
| ~ 'l2$ustruct$u0'(sK76) ),
inference(resolution,[status(thm)],[c50,d1]) ).
cnf(d3,plain,
( ~ 'l2$ustruct$u0'(sK76)
| ~ 'l1$ustruct$u0'(sK76)
| 'k8$urlvect$u2'(sK76,'k1$urlvect$u1'(sK76),sK77) = 'k2$utarski'(sK77,'k1$urlvect$u1'(sK76)) ),
inference(demodulation,[status(thm)],[d2,c23]) ).
cnf(d4,plain,
( 'l1$urlvect$u1'(sK76)
| ~ 'l1$ustruct$u0'(sK75) ),
inference(resolution,[status(thm)],[c54,c75]) ).
cnf(d5,plain,
'l1$urlvect$u1'(sK75),
inference(resolution,[status(thm)],[c55,c68]) ).
cnf(d6,plain,
'l2$ustruct$u0'(sK75),
inference(resolution,[status(thm)],[d5,c30]) ).
cnf(d7,plain,
'l1$ustruct$u0'(sK75),
inference(resolution,[status(thm)],[d6,c31]) ).
cnf(d8,plain,
'l1$urlvect$u1'(sK76),
inference(resolution,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
'l2$ustruct$u0'(sK76),
inference(resolution,[status(thm)],[d8,c30]) ).
cnf(d10,plain,
( ~ 'l1$ustruct$u0'(sK76)
| 'k8$urlvect$u2'(sK76,'k1$urlvect$u1'(sK76),sK77) = 'k2$utarski'(sK77,'k1$urlvect$u1'(sK76)) ),
inference(resolution,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
'l1$ustruct$u0'(sK76),
inference(resolution,[status(thm)],[d9,c31]) ).
cnf(d12,plain,
'k8$urlvect$u2'(sK76,'k1$urlvect$u1'(sK76),sK77) = 'k2$utarski'(sK77,'k1$urlvect$u1'(sK76)),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( 'v3$ustruct$u0'(sK76)
| ~ 'l1$ustruct$u0'(sK76)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK76))
| 'k8$urlvect$u2'(sK76,sK77,X0) = 'k8$urlvect$u2'(sK76,X0,sK77) ),
inference(resolution,[status(thm)],[c45,c76]) ).
cnf(d14,plain,
( ~ 'l1$ustruct$u0'(sK76)
| ~ 'm1$usubset$u1'(X0,'u1$ustruct$u0'(sK76))
| 'k8$urlvect$u2'(sK76,sK77,X0) = 'k8$urlvect$u2'(sK76,X0,sK77) ),
inference(resolution,[status(thm)],[c69,d13]) ).
cnf(d15,plain,
( ~ 'l1$ustruct$u0'(sK76)
| 'k8$urlvect$u2'(sK76,sK77,'k1$urlvect$u1'(sK76)) = 'k8$urlvect$u2'(sK76,'k1$urlvect$u1'(sK76),sK77)
| ~ 'l2$ustruct$u0'(sK76) ),
inference(resolution,[status(thm)],[c50,d14]) ).
cnf(d16,plain,
( ~ 'l1$ustruct$u0'(sK76)
| 'k8$urlvect$u2'(sK76,sK77,'k1$urlvect$u1'(sK76)) = 'k8$urlvect$u2'(sK76,'k1$urlvect$u1'(sK76),sK77) ),
inference(resolution,[status(thm)],[d9,d15]) ).
cnf(d17,plain,
( ~ 'l1$ustruct$u0'(sK76)
| 'k8$urlvect$u2'(sK76,sK77,'k1$urlvect$u1'(sK76)) = 'k2$utarski'(sK77,'k1$urlvect$u1'(sK76)) ),
inference(demodulation,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
'k8$urlvect$u2'(sK76,sK77,'k1$urlvect$u1'(sK76)) = 'k2$utarski'(sK77,'k1$urlvect$u1'(sK76)),
inference(resolution,[status(thm)],[d11,d17]) ).
cnf(d19,plain,
( 'v1$urmod$u5'('k8$urlvect$u2'(sK76,sK77,'k1$urlvect$u1'(sK76)),sK75,sK76)
| 'v1$urmod$u5'('k2$utarski'(sK77,'k1$urlvect$u1'(sK76)),sK75,sK76) ),
inference(demodulation,[status(thm)],[c78,d12]) ).
cnf(d20,plain,
( 'v1$urmod$u5'('k2$utarski'(sK77,'k1$urlvect$u1'(sK76)),sK75,sK76)
| 'v1$urmod$u5'('k2$utarski'(sK77,'k1$urlvect$u1'(sK76)),sK75,sK76) ),
inference(demodulation,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
'v1$urmod$u5'('k2$utarski'(sK77,'k1$urlvect$u1'(sK76)),sK75,sK76),
inference(factoring,[status(thm)],[d20]) ).
cnf(d22,plain,
( ~ 'v1$urmod$u5'('k8$urlvect$u2'(X2,'k1$urlvect$u1'(X2),X1),X0,X2)
| ~ 'v7$uvectsp$u1'(X0)
| ~ 'v6$urlvect$u1'(X2)
| ~ 'v6$urlvect$u1'(X0)
| ~ 'v6$uvectsp$u1'(X0)
| ~ 'v5$uvectsp$u2'(X2,X0)
| ~ 'v3$urlvect$u1'(X2)
| ~ 'v3$urlvect$u1'(X0)
| ~ 'v8$uvectsp$u1'(X0)
| ~ 'v5$urlvect$u1'(X2)
| ~ 'v5$urlvect$u1'(X0)
| ~ 'v4$urlvect$u1'(X2)
| ~ 'v4$urlvect$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l3$uvectsp$u1'(X0)
| ~ 'l1$uvectsp$u2'(X2,X0)
| 'v3$ustruct$u0'(X2)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(X2),'u1$ustruct$u0'(X2))
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X2))
| 'k1$urlvect$u1'(X0) = 'k2$ugroup$u1'(X0) ),
inference(equality_resolution,[status(thm)],[c57]) ).
cnf(d23,plain,
( ~ 'v7$uvectsp$u1'(X0)
| ~ 'v6$urlvect$u1'(X0)
| ~ 'v6$urlvect$u1'(sK76)
| ~ 'v6$uvectsp$u1'(X0)
| ~ 'v5$uvectsp$u2'(sK76,X0)
| ~ 'v3$urlvect$u1'(X0)
| ~ 'v3$urlvect$u1'(sK76)
| ~ 'v8$uvectsp$u1'(X0)
| ~ 'v5$urlvect$u1'(X0)
| ~ 'v5$urlvect$u1'(sK76)
| ~ 'v4$urlvect$u1'(X0)
| ~ 'v4$urlvect$u1'(sK76)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l3$uvectsp$u1'(X0)
| ~ 'l1$uvectsp$u2'(sK76,X0)
| 'v3$ustruct$u0'(X0)
| 'v3$ustruct$u0'(sK76)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| ~ 'm1$usubset$u1'(sK77,'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(X0) = 'k2$ugroup$u1'(X0)
| ~ 'v1$urmod$u5'('k2$utarski'(sK77,'k1$urlvect$u1'(sK76)),X0,sK76) ),
inference(superposition,[status(thm)],[d12,d22]) ).
cnf(d24,plain,
( ~ 'v1$urmod$u5'('k2$utarski'(sK77,'k1$urlvect$u1'(sK76)),X0,sK76)
| ~ 'v7$uvectsp$u1'(X0)
| ~ 'v6$urlvect$u1'(sK76)
| ~ 'v6$urlvect$u1'(X0)
| ~ 'v6$uvectsp$u1'(X0)
| ~ 'v5$uvectsp$u2'(sK76,X0)
| ~ 'v3$urlvect$u1'(sK76)
| ~ 'v3$urlvect$u1'(X0)
| ~ 'v8$uvectsp$u1'(X0)
| ~ 'v5$urlvect$u1'(sK76)
| ~ 'v5$urlvect$u1'(X0)
| ~ 'v4$urlvect$u1'(sK76)
| ~ 'v4$urlvect$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l3$uvectsp$u1'(X0)
| ~ 'l1$uvectsp$u2'(sK76,X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'(sK77,'u1$ustruct$u0'(sK76))
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(X0) = 'k2$ugroup$u1'(X0) ),
inference(resolution,[status(thm)],[c69,d23]) ).
cnf(d25,plain,
( ~ 'v1$urmod$u5'('k2$utarski'(sK77,'k1$urlvect$u1'(sK76)),X0,sK76)
| ~ 'v7$uvectsp$u1'(X0)
| ~ 'v6$urlvect$u1'(sK76)
| ~ 'v6$urlvect$u1'(X0)
| ~ 'v6$uvectsp$u1'(X0)
| ~ 'v5$uvectsp$u2'(sK76,X0)
| ~ 'v3$urlvect$u1'(X0)
| ~ 'v8$uvectsp$u1'(X0)
| ~ 'v5$urlvect$u1'(sK76)
| ~ 'v5$urlvect$u1'(X0)
| ~ 'v4$urlvect$u1'(sK76)
| ~ 'v4$urlvect$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l3$uvectsp$u1'(X0)
| ~ 'l1$uvectsp$u2'(sK76,X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'(sK77,'u1$ustruct$u0'(sK76))
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(X0) = 'k2$ugroup$u1'(X0) ),
inference(resolution,[status(thm)],[c70,d24]) ).
cnf(d26,plain,
( ~ 'v1$urmod$u5'('k2$utarski'(sK77,'k1$urlvect$u1'(sK76)),X0,sK76)
| ~ 'v7$uvectsp$u1'(X0)
| ~ 'v6$urlvect$u1'(sK76)
| ~ 'v6$urlvect$u1'(X0)
| ~ 'v6$uvectsp$u1'(X0)
| ~ 'v5$uvectsp$u2'(sK76,X0)
| ~ 'v3$urlvect$u1'(X0)
| ~ 'v8$uvectsp$u1'(X0)
| ~ 'v5$urlvect$u1'(sK76)
| ~ 'v5$urlvect$u1'(X0)
| ~ 'v4$urlvect$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l3$uvectsp$u1'(X0)
| ~ 'l1$uvectsp$u2'(sK76,X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'(sK77,'u1$ustruct$u0'(sK76))
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(X0) = 'k2$ugroup$u1'(X0) ),
inference(resolution,[status(thm)],[c71,d25]) ).
cnf(d27,plain,
( ~ 'v1$urmod$u5'('k2$utarski'(sK77,'k1$urlvect$u1'(sK76)),X0,sK76)
| ~ 'v7$uvectsp$u1'(X0)
| ~ 'v6$urlvect$u1'(sK76)
| ~ 'v6$urlvect$u1'(X0)
| ~ 'v6$uvectsp$u1'(X0)
| ~ 'v5$uvectsp$u2'(sK76,X0)
| ~ 'v3$urlvect$u1'(X0)
| ~ 'v8$uvectsp$u1'(X0)
| ~ 'v5$urlvect$u1'(X0)
| ~ 'v4$urlvect$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l3$uvectsp$u1'(X0)
| ~ 'l1$uvectsp$u2'(sK76,X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'(sK77,'u1$ustruct$u0'(sK76))
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(X0) = 'k2$ugroup$u1'(X0) ),
inference(resolution,[status(thm)],[c72,d26]) ).
cnf(d28,plain,
( ~ 'v1$urmod$u5'('k2$utarski'(sK77,'k1$urlvect$u1'(sK76)),X0,sK76)
| ~ 'v7$uvectsp$u1'(X0)
| ~ 'v6$urlvect$u1'(X0)
| ~ 'v6$uvectsp$u1'(X0)
| ~ 'v5$uvectsp$u2'(sK76,X0)
| ~ 'v3$urlvect$u1'(X0)
| ~ 'v8$uvectsp$u1'(X0)
| ~ 'v5$urlvect$u1'(X0)
| ~ 'v4$urlvect$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l3$uvectsp$u1'(X0)
| ~ 'l1$uvectsp$u2'(sK76,X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'(sK77,'u1$ustruct$u0'(sK76))
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(X0) = 'k2$ugroup$u1'(X0) ),
inference(resolution,[status(thm)],[c73,d27]) ).
cnf(d29,plain,
( ~ 'v1$urmod$u5'('k2$utarski'(sK77,'k1$urlvect$u1'(sK76)),X0,sK76)
| ~ 'v7$uvectsp$u1'(X0)
| ~ 'v6$urlvect$u1'(X0)
| ~ 'v6$uvectsp$u1'(X0)
| ~ 'v5$uvectsp$u2'(sK76,X0)
| ~ 'v3$urlvect$u1'(X0)
| ~ 'v8$uvectsp$u1'(X0)
| ~ 'v5$urlvect$u1'(X0)
| ~ 'v4$urlvect$u1'(X0)
| ~ 'v4$ugroup$u1'(X0)
| ~ 'l3$uvectsp$u1'(X0)
| ~ 'l1$uvectsp$u2'(sK76,X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(X0) = 'k2$ugroup$u1'(X0) ),
inference(resolution,[status(thm)],[c76,d28]) ).
cnf(d30,plain,
( ~ 'v7$uvectsp$u1'(sK75)
| ~ 'v6$urlvect$u1'(sK75)
| ~ 'v6$uvectsp$u1'(sK75)
| ~ 'v5$uvectsp$u2'(sK76,sK75)
| ~ 'v3$urlvect$u1'(sK75)
| ~ 'v8$uvectsp$u1'(sK75)
| ~ 'v5$urlvect$u1'(sK75)
| ~ 'v4$urlvect$u1'(sK75)
| ~ 'v4$ugroup$u1'(sK75)
| ~ 'l3$uvectsp$u1'(sK75)
| ~ 'l1$uvectsp$u2'(sK76,sK75)
| 'v3$ustruct$u0'(sK75)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(sK75) = 'k2$ugroup$u1'(sK75) ),
inference(resolution,[status(thm)],[d29,d21]) ).
cnf(d31,plain,
( ~ 'v7$uvectsp$u1'(sK75)
| ~ 'v6$urlvect$u1'(sK75)
| ~ 'v6$uvectsp$u1'(sK75)
| ~ 'v5$uvectsp$u2'(sK76,sK75)
| ~ 'v3$urlvect$u1'(sK75)
| ~ 'v8$uvectsp$u1'(sK75)
| ~ 'v5$urlvect$u1'(sK75)
| ~ 'v4$urlvect$u1'(sK75)
| ~ 'v4$ugroup$u1'(sK75)
| ~ 'l3$uvectsp$u1'(sK75)
| ~ 'l1$uvectsp$u2'(sK76,sK75)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(sK75) = 'k2$ugroup$u1'(sK75) ),
inference(resolution,[status(thm)],[c59,d30]) ).
cnf(d32,plain,
( ~ 'v7$uvectsp$u1'(sK75)
| ~ 'v6$urlvect$u1'(sK75)
| ~ 'v6$uvectsp$u1'(sK75)
| ~ 'v5$uvectsp$u2'(sK76,sK75)
| ~ 'v8$uvectsp$u1'(sK75)
| ~ 'v5$urlvect$u1'(sK75)
| ~ 'v4$urlvect$u1'(sK75)
| ~ 'v4$ugroup$u1'(sK75)
| ~ 'l3$uvectsp$u1'(sK75)
| ~ 'l1$uvectsp$u2'(sK76,sK75)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(sK75) = 'k2$ugroup$u1'(sK75) ),
inference(resolution,[status(thm)],[c60,d31]) ).
cnf(d33,plain,
( ~ 'v7$uvectsp$u1'(sK75)
| ~ 'v6$urlvect$u1'(sK75)
| ~ 'v6$uvectsp$u1'(sK75)
| ~ 'v5$uvectsp$u2'(sK76,sK75)
| ~ 'v8$uvectsp$u1'(sK75)
| ~ 'v5$urlvect$u1'(sK75)
| ~ 'v4$ugroup$u1'(sK75)
| ~ 'l3$uvectsp$u1'(sK75)
| ~ 'l1$uvectsp$u2'(sK76,sK75)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(sK75) = 'k2$ugroup$u1'(sK75) ),
inference(resolution,[status(thm)],[c61,d32]) ).
cnf(d34,plain,
( ~ 'v7$uvectsp$u1'(sK75)
| ~ 'v6$urlvect$u1'(sK75)
| ~ 'v6$uvectsp$u1'(sK75)
| ~ 'v5$uvectsp$u2'(sK76,sK75)
| ~ 'v8$uvectsp$u1'(sK75)
| ~ 'v4$ugroup$u1'(sK75)
| ~ 'l3$uvectsp$u1'(sK75)
| ~ 'l1$uvectsp$u2'(sK76,sK75)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(sK75) = 'k2$ugroup$u1'(sK75) ),
inference(resolution,[status(thm)],[c62,d33]) ).
cnf(d35,plain,
( ~ 'v7$uvectsp$u1'(sK75)
| ~ 'v6$uvectsp$u1'(sK75)
| ~ 'v5$uvectsp$u2'(sK76,sK75)
| ~ 'v8$uvectsp$u1'(sK75)
| ~ 'v4$ugroup$u1'(sK75)
| ~ 'l3$uvectsp$u1'(sK75)
| ~ 'l1$uvectsp$u2'(sK76,sK75)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(sK75) = 'k2$ugroup$u1'(sK75) ),
inference(resolution,[status(thm)],[c63,d34]) ).
cnf(d36,plain,
( ~ 'v7$uvectsp$u1'(sK75)
| ~ 'v6$uvectsp$u1'(sK75)
| ~ 'v5$uvectsp$u2'(sK76,sK75)
| ~ 'v8$uvectsp$u1'(sK75)
| ~ 'l3$uvectsp$u1'(sK75)
| ~ 'l1$uvectsp$u2'(sK76,sK75)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(sK75) = 'k2$ugroup$u1'(sK75) ),
inference(resolution,[status(thm)],[c64,d35]) ).
cnf(d37,plain,
( ~ 'v7$uvectsp$u1'(sK75)
| ~ 'v5$uvectsp$u2'(sK76,sK75)
| ~ 'v8$uvectsp$u1'(sK75)
| ~ 'l3$uvectsp$u1'(sK75)
| ~ 'l1$uvectsp$u2'(sK76,sK75)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(sK75) = 'k2$ugroup$u1'(sK75) ),
inference(resolution,[status(thm)],[c65,d36]) ).
cnf(d38,plain,
( ~ 'v5$uvectsp$u2'(sK76,sK75)
| ~ 'v8$uvectsp$u1'(sK75)
| ~ 'l3$uvectsp$u1'(sK75)
| ~ 'l1$uvectsp$u2'(sK76,sK75)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(sK75) = 'k2$ugroup$u1'(sK75) ),
inference(resolution,[status(thm)],[c66,d37]) ).
cnf(d39,plain,
( ~ 'v5$uvectsp$u2'(sK76,sK75)
| ~ 'l3$uvectsp$u1'(sK75)
| ~ 'l1$uvectsp$u2'(sK76,sK75)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(sK75) = 'k2$ugroup$u1'(sK75) ),
inference(resolution,[status(thm)],[c67,d38]) ).
cnf(d40,plain,
( ~ 'v5$uvectsp$u2'(sK76,sK75)
| ~ 'l1$uvectsp$u2'(sK76,sK75)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(sK75) = 'k2$ugroup$u1'(sK75) ),
inference(resolution,[status(thm)],[c68,d39]) ).
cnf(d41,plain,
( ~ 'l1$uvectsp$u2'(sK76,sK75)
| ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(sK75) = 'k2$ugroup$u1'(sK75) ),
inference(resolution,[status(thm)],[c74,d40]) ).
cnf(d42,plain,
( ~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76))
| 'k1$urlvect$u1'(sK75) = 'k2$ugroup$u1'(sK75) ),
inference(resolution,[status(thm)],[c75,d41]) ).
cnf(d43,plain,
~ 'm1$usubset$u1'('k1$urlvect$u1'(sK76),'u1$ustruct$u0'(sK76)),
inference(resolution,[status(thm)],[c77,d42]) ).
cnf(d44,plain,
~ 'l2$ustruct$u0'(sK76),
inference(resolution,[status(thm)],[d43,c50]) ).
cnf(d45,plain,
$false,
inference(resolution,[status(thm)],[d9,d44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG216+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n026.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 21:31:18 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.53/7.86 % SZS status Theorem for theBenchmark.p
% 7.53/7.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------