%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC315-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 08:54:57 AM UTC 2026
% Result : Unsatisfiable 203.40s 55.71s
% Output : CNFRefutation 203.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 27
% Syntax : Number of clauses : 183 ( 21 unt; 77 nHn; 159 RR)
% Number of literals : 507 ( 206 equ; 250 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 85 ( 24 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_1,negated_conjecture,
ssList(sk1) ).
cnf(co1_2,negated_conjecture,
ssList(sk2) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4 ).
cnf(co1_6,negated_conjecture,
sk1 = sk3 ).
cnf(co1_7,negated_conjecture,
( nil != sk4
| nil = sk3 ) ).
cnf(co1_8,negated_conjecture,
( nil = sk2
| ssItem(sk5) ) ).
cnf(co1_9,negated_conjecture,
( nil != sk1
| ssItem(sk5) ) ).
cnf(co1_10,negated_conjecture,
( nil = sk2
| ssList(sk6) ) ).
cnf(co1_11,negated_conjecture,
( nil = sk2
| app(cons(sk5,nil),sk6) = sk2 ) ).
cnf(co1_12,negated_conjecture,
( nil = sk2
| app(sk6,cons(sk5,nil)) != sk1 ) ).
cnf(co1_13,negated_conjecture,
( nil != sk1
| ssList(sk6) ) ).
cnf(co1_14,negated_conjecture,
( nil != sk1
| app(cons(sk5,nil),sk6) = sk2 ) ).
cnf(co1_16,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk7) ) ).
cnf(co1_17,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk8) ) ).
cnf(co1_18,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk7,nil),sk8) = sk4 ) ).
cnf(co1_19,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk8,cons(sk7,nil)) = sk3 ) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause71,axiom,
( ~ ssItem(X0)
| ~ memberP(nil,X0) ) ).
cnf(clause72,axiom,
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ) ).
cnf(clause85,axiom,
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause96,axiom,
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause97,axiom,
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause98,axiom,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ) ).
cnf(clause100,axiom,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause120,axiom,
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ) ).
cnf(clause138,axiom,
( memberP(cons(X1,X2),X0)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| X0 != X1 ) ).
cnf(clause179,axiom,
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ) ).
cnf(c0,plain,
ssList(sk1),
inference(clausification,[status(esa)],[co1_1]) ).
cnf(c1,plain,
ssList(sk2),
inference(clausification,[status(esa)],[co1_2]) ).
cnf(c4,plain,
sk2 = sk4,
inference(clausification,[status(esa)],[co1_5]) ).
cnf(c5,plain,
sk1 = sk3,
inference(clausification,[status(esa)],[co1_6]) ).
cnf(c6,plain,
( nil != sk4
| nil = sk3 ),
inference(clausification,[status(esa)],[co1_7]) ).
cnf(c7,plain,
( nil = sk2
| ssItem(sk5) ),
inference(clausification,[status(esa)],[co1_8]) ).
cnf(c8,plain,
( nil != sk1
| ssItem(sk5) ),
inference(clausification,[status(esa)],[co1_9]) ).
cnf(c9,plain,
( nil = sk2
| ssList(sk6) ),
inference(clausification,[status(esa)],[co1_10]) ).
cnf(c10,plain,
( nil = sk2
| app(cons(sk5,nil),sk6) = sk2 ),
inference(clausification,[status(esa)],[co1_11]) ).
cnf(c11,plain,
( nil = sk2
| app(sk6,cons(sk5,nil)) != sk1 ),
inference(clausification,[status(esa)],[co1_12]) ).
cnf(c12,plain,
( nil != sk1
| ssList(sk6) ),
inference(clausification,[status(esa)],[co1_13]) ).
cnf(c13,plain,
( nil != sk1
| app(cons(sk5,nil),sk6) = sk2 ),
inference(clausification,[status(esa)],[co1_14]) ).
cnf(c15,plain,
( ~ neq(sk4,nil)
| ssItem(sk7) ),
inference(clausification,[status(esa)],[co1_16]) ).
cnf(c16,plain,
( ~ neq(sk4,nil)
| ssList(sk8) ),
inference(clausification,[status(esa)],[co1_17]) ).
cnf(c17,plain,
( ~ neq(sk4,nil)
| app(cons(sk7,nil),sk8) = sk4 ),
inference(clausification,[status(esa)],[co1_18]) ).
cnf(c18,plain,
( ~ neq(sk4,nil)
| app(sk8,cons(sk7,nil)) = sk3 ),
inference(clausification,[status(esa)],[co1_19]) ).
cnf(c26,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c89,plain,
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(clausification,[status(esa)],[clause71]) ).
cnf(c90,plain,
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause72]) ).
cnf(c103,plain,
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause85]) ).
cnf(c114,plain,
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause96]) ).
cnf(c115,plain,
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause97]) ).
cnf(c116,plain,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(clausification,[status(esa)],[clause98]) ).
cnf(c118,plain,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause100]) ).
cnf(c138,plain,
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause120]) ).
cnf(c156,plain,
( ~ ssItem(X2)
| memberP(cons(X2,X0),X1)
| ~ ssItem(X1)
| X1 != X2
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause138]) ).
cnf(c197,plain,
( ~ ssList(X4)
| app(app(X4,cons(X0,X3)),cons(X0,X2)) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ duplicatefreeP(X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause179]) ).
cnf(d0,plain,
( nil != sk4
| nil = sk1 ),
inference(demodulation,[status(thm)],[c6,c5]) ).
cnf(d1,plain,
( nil != sk2
| nil = sk1 ),
inference(demodulation,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( duplicatefreeP(app(X1,X0))
| ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c103,c90]) ).
cnf(d3,plain,
( ~ neq(sk4,nil)
| app(sk8,cons(sk7,nil)) = sk1 ),
inference(demodulation,[status(thm)],[c18,c5]) ).
cnf(d4,plain,
( ~ neq(sk2,nil)
| app(sk8,cons(sk7,nil)) = sk1 ),
inference(demodulation,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
( ~ neq(sk2,nil)
| ~ duplicatefreeP(X1)
| ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| app(sk1,cons(sk7,X0)) != X1 ),
inference(superposition,[status(thm)],[d4,c197]) ).
cnf(d6,plain,
( ~ duplicatefreeP(X1)
| ~ neq(sk2,nil)
| ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sk1,cons(sk7,X0)) != X1 ),
inference(resolution,[status(thm)],[c26,d5]) ).
cnf(d7,plain,
( ~ neq(sk2,nil)
| ssList(sk8) ),
inference(demodulation,[status(thm)],[c16,c4]) ).
cnf(d8,plain,
( ssList(sk8)
| ~ ssList(nil)
| ~ ssList(sk2)
| sk2 = nil ),
inference(resolution,[status(thm)],[c118,d7]) ).
cnf(d9,plain,
( ssList(sk8)
| ~ ssList(nil)
| sk2 = nil ),
inference(resolution,[status(thm)],[c1,d8]) ).
cnf(d10,plain,
( ssList(sk8)
| sk2 = nil ),
inference(resolution,[status(thm)],[c26,d9]) ).
cnf(d11,plain,
( ssList(sk8)
| nil = sk1
| nil != nil ),
inference(superposition,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
( ssList(sk8)
| nil = sk1 ),
inference(equality_resolution,[status(thm)],[d11]) ).
cnf(d13,plain,
( ssList(sk8)
| app(cons(sk5,nil),sk6) = sk2
| nil != nil ),
inference(superposition,[status(thm)],[d12,c13]) ).
cnf(d14,plain,
( ssList(sk8)
| app(cons(sk5,nil),sk6) = sk2 ),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| ssList(sk8)
| cons(sk5,sk6) = sk2 ),
inference(superposition,[status(thm)],[c138,d14]) ).
cnf(d16,plain,
( ssItem(sk5)
| nil = sk1
| nil != nil ),
inference(superposition,[status(thm)],[c7,d1]) ).
cnf(d17,plain,
( ssItem(sk5)
| nil = sk1 ),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
( ssItem(sk5)
| ssItem(sk5)
| nil != nil ),
inference(superposition,[status(thm)],[d17,c8]) ).
cnf(d19,plain,
ssItem(sk5),
inference(equality_resolution,[status(thm)],[d18]) ).
cnf(d20,plain,
( ssList(sk8)
| ~ ssList(sk6)
| cons(sk5,sk6) = sk2 ),
inference(resolution,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
( ssList(sk6)
| nil = sk1
| nil != nil ),
inference(superposition,[status(thm)],[c9,d1]) ).
cnf(d22,plain,
( ssList(sk6)
| nil = sk1 ),
inference(equality_resolution,[status(thm)],[d21]) ).
cnf(d23,plain,
( ssList(sk6)
| ssList(sk6)
| nil != nil ),
inference(superposition,[status(thm)],[d22,c12]) ).
cnf(d24,plain,
ssList(sk6),
inference(equality_resolution,[status(thm)],[d23]) ).
cnf(d25,plain,
( ssList(sk8)
| cons(sk5,sk6) = sk2 ),
inference(resolution,[status(thm)],[d24,d20]) ).
cnf(d26,plain,
( ssList(sk8)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| sk2 != nil ),
inference(superposition,[status(thm)],[d25,c116]) ).
cnf(d27,plain,
( ssList(sk8)
| ~ ssList(sk6)
| sk2 != nil ),
inference(resolution,[status(thm)],[d19,d26]) ).
cnf(d28,plain,
( ssList(sk8)
| sk2 != nil ),
inference(resolution,[status(thm)],[d24,d27]) ).
cnf(d29,plain,
( ssList(sk8)
| ssList(sk8)
| nil != nil ),
inference(superposition,[status(thm)],[d10,d28]) ).
cnf(d30,plain,
ssList(sk8),
inference(equality_resolution,[status(thm)],[d29]) ).
cnf(d31,plain,
( ~ duplicatefreeP(X1)
| ~ neq(sk2,nil)
| ~ ssItem(sk7)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sk1,cons(sk7,X0)) != X1 ),
inference(resolution,[status(thm)],[d30,d6]) ).
cnf(d32,plain,
( ~ neq(sk2,nil)
| ssItem(sk7) ),
inference(demodulation,[status(thm)],[c15,c4]) ).
cnf(d33,plain,
( ssItem(sk7)
| ~ ssList(nil)
| ~ ssList(sk2)
| sk2 = nil ),
inference(resolution,[status(thm)],[c118,d32]) ).
cnf(d34,plain,
( ssItem(sk7)
| ~ ssList(nil)
| sk2 = nil ),
inference(resolution,[status(thm)],[c1,d33]) ).
cnf(d35,plain,
( ssItem(sk7)
| sk2 = nil ),
inference(resolution,[status(thm)],[c26,d34]) ).
cnf(d36,plain,
( ssItem(sk7)
| nil = sk1
| nil != nil ),
inference(superposition,[status(thm)],[d35,d1]) ).
cnf(d37,plain,
( ssItem(sk7)
| nil = sk1 ),
inference(equality_resolution,[status(thm)],[d36]) ).
cnf(d38,plain,
( ssItem(sk7)
| app(cons(sk5,nil),sk6) = sk2
| nil != nil ),
inference(superposition,[status(thm)],[d37,c13]) ).
cnf(d39,plain,
( ssItem(sk7)
| app(cons(sk5,nil),sk6) = sk2 ),
inference(equality_resolution,[status(thm)],[d38]) ).
cnf(d40,plain,
( ssItem(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| sk2 = cons(sk5,sk6) ),
inference(superposition,[status(thm)],[d39,c138]) ).
cnf(d41,plain,
( ssItem(sk7)
| ~ ssList(sk6)
| sk2 = cons(sk5,sk6) ),
inference(resolution,[status(thm)],[d19,d40]) ).
cnf(d42,plain,
( ssItem(sk7)
| sk2 = cons(sk5,sk6) ),
inference(resolution,[status(thm)],[d24,d41]) ).
cnf(d43,plain,
( ssItem(sk7)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| sk2 != nil ),
inference(superposition,[status(thm)],[d42,c116]) ).
cnf(d44,plain,
( ssItem(sk7)
| ~ ssList(sk6)
| sk2 != nil ),
inference(resolution,[status(thm)],[d19,d43]) ).
cnf(d45,plain,
( ssItem(sk7)
| sk2 != nil ),
inference(resolution,[status(thm)],[d24,d44]) ).
cnf(d46,plain,
( ssItem(sk7)
| ssItem(sk7)
| nil != nil ),
inference(superposition,[status(thm)],[d35,d45]) ).
cnf(d47,plain,
ssItem(sk7),
inference(equality_resolution,[status(thm)],[d46]) ).
cnf(d48,plain,
( ~ duplicatefreeP(X1)
| ~ neq(sk2,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sk1,cons(sk7,X0)) != X1 ),
inference(resolution,[status(thm)],[d47,d31]) ).
cnf(d49,plain,
( ~ neq(sk4,nil)
| app(cons(sk7,nil),sk8) = sk2 ),
inference(demodulation,[status(thm)],[c17,c4]) ).
cnf(d50,plain,
( ~ neq(sk2,nil)
| app(cons(sk7,nil),sk8) = sk2 ),
inference(demodulation,[status(thm)],[d49,c4]) ).
cnf(d51,plain,
( ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ neq(sk2,nil)
| cons(sk7,sk8) = sk2 ),
inference(superposition,[status(thm)],[c138,d50]) ).
cnf(d52,plain,
( ~ neq(sk2,nil)
| ~ ssItem(sk7)
| cons(sk7,sk8) = sk2 ),
inference(resolution,[status(thm)],[d30,d51]) ).
cnf(d53,plain,
( ~ neq(sk2,nil)
| cons(sk7,sk8) = sk2 ),
inference(resolution,[status(thm)],[d47,d52]) ).
cnf(d54,plain,
( ~ neq(sk2,nil)
| ~ duplicatefreeP(X0)
| ~ neq(sk2,nil)
| ~ ssList(sk8)
| ~ ssList(X0)
| app(sk1,sk2) != X0 ),
inference(superposition,[status(thm)],[d53,d48]) ).
cnf(d55,plain,
( ~ duplicatefreeP(X0)
| ~ neq(sk2,nil)
| ~ ssList(X0)
| app(sk1,sk2) != X0 ),
inference(resolution,[status(thm)],[d30,d54]) ).
cnf(d56,plain,
( ~ duplicatefreeP(app(sk1,sk2))
| ~ neq(sk2,nil)
| ~ ssList(app(sk1,sk2)) ),
inference(equality_resolution,[status(thm)],[d55]) ).
cnf(d57,plain,
( ssItem(X0)
| ~ ssList(sk2)
| ~ ssList(sk1)
| ~ neq(sk2,nil)
| ~ ssList(app(sk1,sk2)) ),
inference(resolution,[status(thm)],[d56,d2]) ).
cnf(d58,plain,
( ~ neq(sk2,nil)
| ssItem(X0)
| ~ ssList(app(sk1,sk2))
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c0,d57]) ).
cnf(d59,plain,
( ~ neq(sk2,nil)
| ssItem(X0)
| ~ ssList(app(sk1,sk2)) ),
inference(resolution,[status(thm)],[c1,d58]) ).
cnf(d60,plain,
( ~ ssList(sk1)
| ~ ssList(sk2)
| ~ neq(sk2,nil)
| ssItem(X0) ),
inference(resolution,[status(thm)],[d59,c103]) ).
cnf(d61,plain,
( ~ neq(sk2,nil)
| ssItem(X0)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c0,d60]) ).
cnf(d62,plain,
( ~ neq(sk2,nil)
| ssItem(X0) ),
inference(resolution,[status(thm)],[c1,d61]) ).
cnf(d63,plain,
( ~ ssList(nil)
| ~ ssList(sk2)
| sk2 = nil
| ssItem(X0) ),
inference(resolution,[status(thm)],[d62,c118]) ).
cnf(d64,plain,
( ssItem(X0)
| ~ ssList(nil)
| sk2 = nil ),
inference(resolution,[status(thm)],[c1,d63]) ).
cnf(d65,plain,
( ssItem(X0)
| sk2 = nil ),
inference(resolution,[status(thm)],[c26,d64]) ).
cnf(d66,plain,
( ssItem(X0)
| nil = sk1
| nil != nil ),
inference(superposition,[status(thm)],[d65,d1]) ).
cnf(d67,plain,
( ssItem(X0)
| nil = sk1 ),
inference(equality_resolution,[status(thm)],[d66]) ).
cnf(d68,plain,
( ssItem(X0)
| app(cons(sk5,nil),sk6) = sk2
| nil != nil ),
inference(superposition,[status(thm)],[d67,c13]) ).
cnf(d69,plain,
( ssItem(X0)
| app(cons(sk5,nil),sk6) = sk2 ),
inference(equality_resolution,[status(thm)],[d68]) ).
cnf(d70,plain,
( ssItem(X0)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| sk2 = cons(sk5,sk6) ),
inference(superposition,[status(thm)],[d69,c138]) ).
cnf(d71,plain,
( ssItem(X0)
| ~ ssList(sk6)
| sk2 = cons(sk5,sk6) ),
inference(resolution,[status(thm)],[d19,d70]) ).
cnf(d72,plain,
( ssItem(X0)
| sk2 = cons(sk5,sk6) ),
inference(resolution,[status(thm)],[d24,d71]) ).
cnf(d73,plain,
( ssItem(X0)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| sk2 != nil ),
inference(superposition,[status(thm)],[d72,c116]) ).
cnf(d74,plain,
( ssItem(X0)
| ~ ssList(sk6)
| sk2 != nil ),
inference(resolution,[status(thm)],[d19,d73]) ).
cnf(d75,plain,
( ssItem(X0)
| sk2 != nil ),
inference(resolution,[status(thm)],[d24,d74]) ).
cnf(d76,plain,
( memberP(cons(X1,X0),X1)
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[c156]) ).
cnf(d77,plain,
( ~ neq(sk2,nil)
| ~ ssItem(sk7)
| ~ ssList(sk8)
| memberP(sk2,sk7) ),
inference(superposition,[status(thm)],[d53,d76]) ).
cnf(d78,plain,
( memberP(sk2,sk7)
| ~ neq(sk2,nil)
| ~ ssItem(sk7) ),
inference(resolution,[status(thm)],[d30,d77]) ).
cnf(d79,plain,
( memberP(sk2,sk7)
| ~ neq(sk2,nil) ),
inference(resolution,[status(thm)],[d47,d78]) ).
cnf(d80,plain,
( ~ ssList(nil)
| ~ ssList(sk2)
| sk2 = nil
| memberP(sk2,sk7) ),
inference(resolution,[status(thm)],[d79,c118]) ).
cnf(d81,plain,
( memberP(sk2,sk7)
| ~ ssList(nil)
| sk2 = nil ),
inference(resolution,[status(thm)],[c1,d80]) ).
cnf(d82,plain,
( memberP(sk2,sk7)
| sk2 = nil ),
inference(resolution,[status(thm)],[c26,d81]) ).
cnf(d83,plain,
( ~ neq(sk2,nil)
| ~ ssItem(sk7)
| ~ ssList(sk8)
| tl(sk2) = sk8 ),
inference(superposition,[status(thm)],[d53,c114]) ).
cnf(d84,plain,
( ~ neq(sk2,nil)
| ~ ssItem(sk7)
| tl(sk2) = sk8 ),
inference(resolution,[status(thm)],[d30,d83]) ).
cnf(d85,plain,
( ~ neq(sk2,nil)
| tl(sk2) = sk8 ),
inference(resolution,[status(thm)],[d47,d84]) ).
cnf(d86,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| nil = sk2
| cons(sk5,sk6) = sk2 ),
inference(superposition,[status(thm)],[c138,c10]) ).
cnf(d87,plain,
( ~ ssList(sk6)
| cons(sk5,sk6) = sk2
| nil = sk2 ),
inference(resolution,[status(thm)],[d19,d86]) ).
cnf(d88,plain,
( cons(sk5,sk6) = sk2
| nil = sk2 ),
inference(resolution,[status(thm)],[d24,d87]) ).
cnf(d89,plain,
( nil = sk2
| ~ ssItem(sk5)
| ~ ssList(sk6)
| tl(sk2) = sk6 ),
inference(superposition,[status(thm)],[d88,c114]) ).
cnf(d90,plain,
( ~ ssList(sk6)
| tl(sk2) = sk6
| nil = sk2 ),
inference(resolution,[status(thm)],[d19,d89]) ).
cnf(d91,plain,
( tl(sk2) = sk6
| nil = sk2 ),
inference(resolution,[status(thm)],[d24,d90]) ).
cnf(d92,plain,
( nil = sk2
| ~ neq(sk2,nil)
| sk6 = sk8 ),
inference(superposition,[status(thm)],[d91,d85]) ).
cnf(d93,plain,
( ~ ssList(nil)
| ~ ssList(sk2)
| sk2 = nil
| sk6 = sk8
| nil = sk2 ),
inference(resolution,[status(thm)],[d92,c118]) ).
cnf(d94,plain,
( ~ ssList(nil)
| sk6 = sk8
| nil = sk2
| sk2 = nil ),
inference(resolution,[status(thm)],[c1,d93]) ).
cnf(d95,plain,
( sk6 = sk8
| nil = sk2
| sk2 = nil ),
inference(resolution,[status(thm)],[c26,d94]) ).
cnf(d96,plain,
( nil = sk2
| sk2 = nil
| ~ neq(sk2,nil)
| app(sk6,cons(sk7,nil)) = sk1 ),
inference(superposition,[status(thm)],[d95,d4]) ).
cnf(d97,plain,
( nil = sk2
| ~ ssItem(sk5)
| ~ ssList(sk6)
| hd(sk2) = sk5 ),
inference(superposition,[status(thm)],[d88,c115]) ).
cnf(d98,plain,
( ~ ssList(sk6)
| hd(sk2) = sk5
| nil = sk2 ),
inference(resolution,[status(thm)],[d19,d97]) ).
cnf(d99,plain,
( hd(sk2) = sk5
| nil = sk2 ),
inference(resolution,[status(thm)],[d24,d98]) ).
cnf(d100,plain,
( ~ neq(sk2,nil)
| ~ ssItem(sk7)
| ~ ssList(sk8)
| hd(sk2) = sk7 ),
inference(superposition,[status(thm)],[d53,c115]) ).
cnf(d101,plain,
( ~ neq(sk2,nil)
| ~ ssItem(sk7)
| hd(sk2) = sk7 ),
inference(resolution,[status(thm)],[d30,d100]) ).
cnf(d102,plain,
( ~ neq(sk2,nil)
| hd(sk2) = sk7 ),
inference(resolution,[status(thm)],[d47,d101]) ).
cnf(d103,plain,
( ~ neq(sk2,nil)
| nil = sk2
| sk7 = sk5 ),
inference(superposition,[status(thm)],[d102,d99]) ).
cnf(d104,plain,
( ~ ssList(nil)
| ~ ssList(sk2)
| sk2 = nil
| sk7 = sk5
| nil = sk2 ),
inference(resolution,[status(thm)],[d103,c118]) ).
cnf(d105,plain,
( ~ ssList(nil)
| sk7 = sk5
| nil = sk2
| sk2 = nil ),
inference(resolution,[status(thm)],[c1,d104]) ).
cnf(d106,plain,
( sk7 = sk5
| nil = sk2
| sk2 = nil ),
inference(resolution,[status(thm)],[c26,d105]) ).
cnf(d107,plain,
( nil = sk2
| sk2 = nil
| ~ neq(sk2,nil)
| nil = sk2
| sk2 = nil
| app(sk6,cons(sk5,nil)) = sk1 ),
inference(superposition,[status(thm)],[d106,d96]) ).
cnf(d108,plain,
( ~ neq(sk2,nil)
| nil = sk2
| sk2 = nil
| nil = sk2
| sk1 != sk1 ),
inference(superposition,[status(thm)],[d107,c11]) ).
cnf(d109,plain,
( ~ neq(sk2,nil)
| nil = sk2
| sk2 = nil ),
inference(equality_resolution,[status(thm)],[d108]) ).
cnf(d110,plain,
( ~ ssList(nil)
| ~ ssList(sk2)
| sk2 = nil
| nil = sk2
| sk2 = nil ),
inference(resolution,[status(thm)],[d109,c118]) ).
cnf(d111,plain,
( ~ ssList(nil)
| nil = sk2
| sk2 = nil ),
inference(resolution,[status(thm)],[c1,d110]) ).
cnf(d112,plain,
( nil = sk2
| sk2 = nil ),
inference(resolution,[status(thm)],[c26,d111]) ).
cnf(d113,plain,
( sk2 = nil
| sk2 = nil
| memberP(nil,sk7) ),
inference(superposition,[status(thm)],[d112,d82]) ).
cnf(d114,plain,
( ~ ssItem(sk7)
| sk2 = nil ),
inference(resolution,[status(thm)],[d113,c89]) ).
cnf(d115,plain,
sk2 = nil,
inference(resolution,[status(thm)],[d47,d114]) ).
cnf(d116,plain,
ssItem(X0),
inference(resolution,[status(thm)],[d115,d75]) ).
cnf(d117,plain,
( ~ ssList(X1)
| cons(X0,X1) != nil ),
inference(resolution,[status(thm)],[d116,c116]) ).
cnf(d118,plain,
( nil != nil
| nil = sk1 ),
inference(demodulation,[status(thm)],[d1,d115]) ).
cnf(d119,plain,
nil = sk1,
inference(equality_resolution,[status(thm)],[d118]) ).
cnf(d120,plain,
( app(cons(sk5,nil),sk6) = nil
| nil != sk1 ),
inference(demodulation,[status(thm)],[c13,d115]) ).
cnf(d121,plain,
( app(cons(sk5,nil),sk6) = nil
| nil != nil ),
inference(demodulation,[status(thm)],[d120,d119]) ).
cnf(d122,plain,
app(cons(sk5,nil),sk6) = nil,
inference(equality_resolution,[status(thm)],[d121]) ).
cnf(d123,plain,
( ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
inference(resolution,[status(thm)],[d116,c138]) ).
cnf(d124,plain,
( ~ ssList(sk6)
| cons(sk5,sk6) = nil ),
inference(superposition,[status(thm)],[d123,d122]) ).
cnf(d125,plain,
cons(sk5,sk6) = nil,
inference(resolution,[status(thm)],[d24,d124]) ).
cnf(d126,plain,
( ~ ssList(sk6)
| nil != nil ),
inference(superposition,[status(thm)],[d125,d117]) ).
cnf(d127,plain,
nil != nil,
inference(resolution,[status(thm)],[d24,d126]) ).
cnf(d128,plain,
$false,
inference(equality_resolution,[status(thm)],[d127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC315-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 12:49:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 203.40/55.71 % SZS status Unsatisfiable for theBenchmark.p
% 203.40/55.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------