%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC100-1 : 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 : n002.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 08:54:16 AM UTC 2026
% Result : Unsatisfiable 18.02s 12.34s
% Output : CNFRefutation 18.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 19
% Syntax : Number of clauses : 80 ( 21 unt; 19 nHn; 80 RR)
% Number of literals : 186 ( 74 equ; 91 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_1,negated_conjecture,
ssList(sk1) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4 ).
cnf(co1_6,negated_conjecture,
sk1 = sk3 ).
cnf(co1_7,negated_conjecture,
ssList(sk5) ).
cnf(co1_8,negated_conjecture,
app(sk3,sk5) = sk4 ).
cnf(co1_11,negated_conjecture,
( nil != sk3
| nil = sk4 ) ).
cnf(co1_13,negated_conjecture,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ) ).
cnf(co1_14,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ) ).
cnf(co1_15,negated_conjecture,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil)
| nil != sk1 ) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause59,axiom,
( rearsegP(X0,X0)
| ~ ssList(X0) ) ).
cnf(clause61,axiom,
( frontsegP(X0,X0)
| ~ ssList(X0) ) ).
cnf(clause73,axiom,
( app(X0,nil) = X0
| ~ ssList(X0) ) ).
cnf(clause74,axiom,
( app(nil,X0) = X0
| ~ ssList(X0) ) ).
cnf(clause82,axiom,
( nil = X0
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ).
cnf(clause84,axiom,
( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ).
cnf(clause100,axiom,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause136,axiom,
( rearsegP(app(X2,X0),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ) ).
cnf(clause137,axiom,
( frontsegP(app(X0,X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X0,X1) ) ).
cnf(c0,plain,
ssList(sk1),
inference(clausification,[status(esa)],[co1_1]) ).
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,
ssList(sk5),
inference(clausification,[status(esa)],[co1_7]) ).
cnf(c7,plain,
app(sk3,sk5) = sk4,
inference(clausification,[status(esa)],[co1_8]) ).
cnf(c10,plain,
( nil != sk3
| nil = sk4 ),
inference(clausification,[status(esa)],[co1_11]) ).
cnf(c12,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
inference(clausification,[status(esa)],[co1_13]) ).
cnf(c13,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausification,[status(esa)],[co1_14]) ).
cnf(c14,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil)
| nil != sk1 ),
inference(clausification,[status(esa)],[co1_15]) ).
cnf(c22,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c73,plain,
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause59]) ).
cnf(c75,plain,
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause61]) ).
cnf(c87,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause73]) ).
cnf(c88,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause74]) ).
cnf(c96,plain,
( nil = X0
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(clausification,[status(esa)],[clause82]) ).
cnf(c98,plain,
( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(clausification,[status(esa)],[clause84]) ).
cnf(c114,plain,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause100]) ).
cnf(c150,plain,
( ~ ssList(X2)
| rearsegP(app(X1,X0),X2)
| ~ rearsegP(X0,X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause136]) ).
cnf(c151,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X0)
| frontsegP(app(X1,X2),X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause137]) ).
cnf(d0,plain,
app(sk1,sk5) = sk4,
inference(demodulation,[status(thm)],[c7,c5]) ).
cnf(d1,plain,
app(sk1,sk5) = sk2,
inference(demodulation,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( ~ frontsegP(sk1,X0)
| ~ ssList(sk1)
| ~ ssList(X0)
| ~ ssList(sk5)
| frontsegP(sk2,X0) ),
inference(superposition,[status(thm)],[d1,c151]) ).
cnf(d3,plain,
( frontsegP(sk2,X0)
| ~ frontsegP(sk1,X0)
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c0,d2]) ).
cnf(d4,plain,
( frontsegP(sk2,X0)
| ~ frontsegP(sk1,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c6,d3]) ).
cnf(d5,plain,
( ~ ssList(sk1)
| frontsegP(sk2,sk1)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[d4,c75]) ).
cnf(d6,plain,
frontsegP(sk2,sk1),
inference(resolution,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
( ~ neq(sk1,nil)
| nil = sk2 ),
inference(resolution,[status(thm)],[d6,c12]) ).
cnf(d8,plain,
( ~ ssList(sk1)
| ~ ssList(nil)
| sk1 = nil
| nil = sk2 ),
inference(resolution,[status(thm)],[d7,c114]) ).
cnf(d9,plain,
( ~ ssList(nil)
| nil = sk2
| sk1 = nil ),
inference(resolution,[status(thm)],[c0,d8]) ).
cnf(d10,plain,
( nil = sk2
| sk1 = nil ),
inference(resolution,[status(thm)],[c22,d9]) ).
cnf(d11,plain,
( sk1 = nil
| frontsegP(nil,sk1) ),
inference(superposition,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( ~ ssList(sk1)
| nil = sk1
| sk1 = nil ),
inference(resolution,[status(thm)],[d11,c98]) ).
cnf(d13,plain,
( nil = sk1
| sk1 = nil ),
inference(resolution,[status(thm)],[c0,d12]) ).
cnf(d14,plain,
( sk1 = nil
| app(nil,sk5) = sk2 ),
inference(superposition,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
( sk1 = nil
| ~ ssList(sk5)
| sk2 = sk5 ),
inference(superposition,[status(thm)],[d14,c88]) ).
cnf(d16,plain,
( sk2 = sk5
| sk1 = nil ),
inference(resolution,[status(thm)],[c6,d15]) ).
cnf(d17,plain,
( ~ rearsegP(sk5,X0)
| ~ ssList(sk5)
| ~ ssList(X0)
| ~ ssList(sk1)
| rearsegP(sk2,X0) ),
inference(superposition,[status(thm)],[d1,c150]) ).
cnf(d18,plain,
( ~ rearsegP(sk5,X0)
| rearsegP(sk2,X0)
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c0,d17]) ).
cnf(d19,plain,
( ~ rearsegP(sk5,X0)
| rearsegP(sk2,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c6,d18]) ).
cnf(d20,plain,
( ~ ssList(sk5)
| rearsegP(sk2,sk5)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[d19,c73]) ).
cnf(d21,plain,
rearsegP(sk2,sk5),
inference(resolution,[status(thm)],[c6,d20]) ).
cnf(d22,plain,
( sk1 = nil
| rearsegP(nil,sk5) ),
inference(superposition,[status(thm)],[d10,d21]) ).
cnf(d23,plain,
( ~ ssList(sk5)
| nil = sk5
| sk1 = nil ),
inference(resolution,[status(thm)],[d22,c96]) ).
cnf(d24,plain,
( nil = sk5
| sk1 = nil ),
inference(resolution,[status(thm)],[c6,d23]) ).
cnf(d25,plain,
( sk1 = nil
| sk1 = nil
| sk2 = nil ),
inference(superposition,[status(thm)],[d24,d16]) ).
cnf(d26,plain,
( sk1 = nil
| app(sk1,nil) = sk2 ),
inference(superposition,[status(thm)],[d24,d1]) ).
cnf(d27,plain,
( sk1 = nil
| ~ ssList(sk1)
| sk2 = sk1 ),
inference(superposition,[status(thm)],[d26,c87]) ).
cnf(d28,plain,
( sk2 = sk1
| sk1 = nil ),
inference(resolution,[status(thm)],[c0,d27]) ).
cnf(d29,plain,
( sk1 = nil
| sk1 = nil
| sk1 = nil ),
inference(superposition,[status(thm)],[d28,d25]) ).
cnf(d30,plain,
( nil = sk4
| nil != sk1 ),
inference(demodulation,[status(thm)],[c10,c5]) ).
cnf(d31,plain,
( nil = sk2
| nil != sk1 ),
inference(demodulation,[status(thm)],[d30,c4]) ).
cnf(d32,plain,
( nil = sk2
| nil != nil ),
inference(demodulation,[status(thm)],[d31,d29]) ).
cnf(d33,plain,
nil = sk2,
inference(equality_resolution,[status(thm)],[d32]) ).
cnf(d34,plain,
( neq(sk2,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[c13,d29]) ).
cnf(d35,plain,
neq(sk2,nil),
inference(equality_resolution,[status(thm)],[d34]) ).
cnf(d36,plain,
neq(nil,nil),
inference(demodulation,[status(thm)],[d35,d33]) ).
cnf(d37,plain,
( ~ neq(sk1,nil)
| nil != sk1 ),
inference(resolution,[status(thm)],[d6,c14]) ).
cnf(d38,plain,
( ~ neq(sk1,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[d37,d29]) ).
cnf(d39,plain,
( ~ neq(nil,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[d38,d29]) ).
cnf(d40,plain,
~ neq(nil,nil),
inference(equality_resolution,[status(thm)],[d39]) ).
cnf(d41,plain,
$false,
inference(resolution,[status(thm)],[d40,d36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC100-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.40 % Computer : n002.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Sat Sep 26 12:17:59 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.02/12.34 % SZS status Unsatisfiable for theBenchmark.p
% 18.02/12.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------