%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC112-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 08:54:19 AM UTC 2026
% Result : Unsatisfiable 52.19s 17.17s
% Output : CNFRefutation 52.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 23
% Syntax : Number of clauses : 99 ( 27 unt; 11 nHn; 99 RR)
% Number of literals : 250 ( 73 equ; 148 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 58 ( 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,
ssList(sk6) ).
cnf(co1_9,negated_conjecture,
app(app(sk5,sk3),sk6) = sk4 ).
cnf(co1_13,negated_conjecture,
( nil != sk3
| nil = sk4 ) ).
cnf(co1_15,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ) ).
cnf(co1_16,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ) ).
cnf(co1_17,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil != sk1 ) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause57,axiom,
( segmentP(X0,X0)
| ~ ssList(X0) ) ).
cnf(clause60,axiom,
( frontsegP(X0,nil)
| ~ ssList(X0) ) ).
cnf(clause61,axiom,
( frontsegP(X0,X0)
| ~ ssList(X0) ) ).
cnf(clause80,axiom,
( nil = X0
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ).
cnf(clause84,axiom,
( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ).
cnf(clause85,axiom,
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause100,axiom,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause115,axiom,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ) ).
cnf(clause129,axiom,
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ) ).
cnf(clause137,axiom,
( frontsegP(app(X0,X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X0,X1) ) ).
cnf(clause149,axiom,
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ).
cnf(clause172,axiom,
( segmentP(app(app(X3,X0),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(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,
ssList(sk6),
inference(clausification,[status(esa)],[co1_8]) ).
cnf(c8,plain,
app(app(sk5,sk3),sk6) = sk4,
inference(clausification,[status(esa)],[co1_9]) ).
cnf(c12,plain,
( nil != sk3
| nil = sk4 ),
inference(clausification,[status(esa)],[co1_13]) ).
cnf(c14,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
inference(clausification,[status(esa)],[co1_15]) ).
cnf(c15,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausification,[status(esa)],[co1_16]) ).
cnf(c16,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil != sk1 ),
inference(clausification,[status(esa)],[co1_17]) ).
cnf(c24,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c73,plain,
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause57]) ).
cnf(c76,plain,
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause60]) ).
cnf(c77,plain,
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause61]) ).
cnf(c96,plain,
( nil = X0
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(clausification,[status(esa)],[clause80]) ).
cnf(c100,plain,
( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(clausification,[status(esa)],[clause84]) ).
cnf(c101,plain,
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause85]) ).
cnf(c116,plain,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause100]) ).
cnf(c131,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(clausification,[status(esa)],[clause115]) ).
cnf(c145,plain,
( ~ frontsegP(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1
| ~ frontsegP(X0,X1) ),
inference(clausification,[status(esa)],[clause129]) ).
cnf(c153,plain,
( ~ ssList(X1)
| frontsegP(app(X1,X0),X2)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause137]) ).
cnf(c165,plain,
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause149]) ).
cnf(c188,plain,
( ~ ssList(X3)
| segmentP(app(app(X3,X1),X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause172]) ).
cnf(d0,plain,
( ~ neq(X0,X0)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[c131]) ).
cnf(d1,plain,
app(app(sk5,sk1),sk6) = sk4,
inference(demodulation,[status(thm)],[c8,c5]) ).
cnf(d2,plain,
app(app(sk5,sk1),sk6) = sk2,
inference(demodulation,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( ~ segmentP(sk1,X0)
| ~ ssList(sk1)
| ~ ssList(X0)
| ~ ssList(sk5)
| ~ ssList(sk6)
| segmentP(sk2,X0) ),
inference(superposition,[status(thm)],[d2,c188]) ).
cnf(d4,plain,
( segmentP(sk2,X0)
| ~ segmentP(sk1,X0)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
( segmentP(sk2,X0)
| ~ segmentP(sk1,X0)
| ~ ssList(sk6)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c6,d4]) ).
cnf(d6,plain,
( segmentP(sk2,X0)
| ~ segmentP(sk1,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c7,d5]) ).
cnf(d7,plain,
( ~ ssList(sk1)
| segmentP(sk2,sk1)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[d6,c73]) ).
cnf(d8,plain,
segmentP(sk2,sk1),
inference(resolution,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
( ~ neq(sk1,nil)
| nil = sk2 ),
inference(resolution,[status(thm)],[d8,c14]) ).
cnf(d10,plain,
( ~ ssList(sk1)
| ~ ssList(nil)
| sk1 = nil
| nil = sk2 ),
inference(resolution,[status(thm)],[d9,c116]) ).
cnf(d11,plain,
( ~ ssList(nil)
| nil = sk2
| sk1 = nil ),
inference(resolution,[status(thm)],[c0,d10]) ).
cnf(d12,plain,
( nil = sk2
| sk1 = nil ),
inference(resolution,[status(thm)],[c24,d11]) ).
cnf(d13,plain,
( sk1 = nil
| segmentP(nil,sk1) ),
inference(superposition,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( ~ ssList(sk1)
| nil = sk1
| sk1 = nil ),
inference(resolution,[status(thm)],[d13,c96]) ).
cnf(d15,plain,
( nil = sk1
| sk1 = nil ),
inference(resolution,[status(thm)],[c0,d14]) ).
cnf(d16,plain,
( sk1 = nil
| neq(sk2,nil)
| nil != nil ),
inference(superposition,[status(thm)],[d15,c15]) ).
cnf(d17,plain,
( neq(sk2,nil)
| sk1 = nil ),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
( sk1 = nil
| sk1 = nil
| neq(nil,nil) ),
inference(superposition,[status(thm)],[d12,d17]) ).
cnf(d19,plain,
( ~ ssList(nil)
| sk1 = nil ),
inference(resolution,[status(thm)],[d18,d0]) ).
cnf(d20,plain,
sk1 = nil,
inference(resolution,[status(thm)],[c24,d19]) ).
cnf(d21,plain,
( nil = sk4
| nil != sk1 ),
inference(demodulation,[status(thm)],[c12,c5]) ).
cnf(d22,plain,
( nil = sk2
| nil != sk1 ),
inference(demodulation,[status(thm)],[d21,c4]) ).
cnf(d23,plain,
( nil = sk2
| nil != nil ),
inference(demodulation,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
nil = sk2,
inference(equality_resolution,[status(thm)],[d23]) ).
cnf(d25,plain,
( neq(sk2,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[c15,d20]) ).
cnf(d26,plain,
( neq(nil,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[d25,d24]) ).
cnf(d27,plain,
( ~ ssList(sk1)
| ~ ssList(sk5)
| ~ ssList(sk6)
| app(sk5,app(sk1,sk6)) = sk2 ),
inference(superposition,[status(thm)],[c165,d2]) ).
cnf(d28,plain,
( ~ ssList(sk6)
| ~ ssList(sk5)
| app(sk5,app(sk1,sk6)) = sk2 ),
inference(resolution,[status(thm)],[c0,d27]) ).
cnf(d29,plain,
( ~ ssList(sk6)
| app(sk5,app(sk1,sk6)) = sk2 ),
inference(resolution,[status(thm)],[c6,d28]) ).
cnf(d30,plain,
app(sk5,app(sk1,sk6)) = sk2,
inference(resolution,[status(thm)],[c7,d29]) ).
cnf(d31,plain,
( ~ frontsegP(sk5,X0)
| ~ ssList(app(sk1,sk6))
| ~ ssList(sk5)
| ~ ssList(X0)
| frontsegP(sk2,X0) ),
inference(superposition,[status(thm)],[d30,c153]) ).
cnf(d32,plain,
( ~ frontsegP(sk5,X0)
| frontsegP(sk2,X0)
| ~ ssList(app(sk1,sk6))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c6,d31]) ).
cnf(d33,plain,
( ~ ssList(sk1)
| ~ ssList(sk6)
| ~ frontsegP(sk5,X0)
| frontsegP(sk2,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[d32,c101]) ).
cnf(d34,plain,
( ~ frontsegP(sk5,X0)
| frontsegP(sk2,X0)
| ~ ssList(sk6)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c0,d33]) ).
cnf(d35,plain,
( ~ frontsegP(sk5,X0)
| frontsegP(sk2,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c7,d34]) ).
cnf(d36,plain,
( ~ ssList(sk5)
| frontsegP(sk2,sk5)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[d35,c77]) ).
cnf(d37,plain,
frontsegP(sk2,sk5),
inference(resolution,[status(thm)],[c6,d36]) ).
cnf(d38,plain,
frontsegP(nil,sk5),
inference(demodulation,[status(thm)],[d37,d24]) ).
cnf(d39,plain,
( ~ ssList(sk5)
| nil = sk5 ),
inference(resolution,[status(thm)],[d38,c100]) ).
cnf(d40,plain,
nil = sk5,
inference(resolution,[status(thm)],[c6,d39]) ).
cnf(d41,plain,
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| X0 = nil ),
inference(resolution,[status(thm)],[c145,c76]) ).
cnf(d42,plain,
( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(resolution,[status(thm)],[c24,d41]) ).
cnf(d43,plain,
( ~ ssList(sk5)
| sk5 = nil ),
inference(resolution,[status(thm)],[d38,d42]) ).
cnf(d44,plain,
( ~ ssList(sk5)
| nil = nil ),
inference(demodulation,[status(thm)],[d43,d40]) ).
cnf(d45,plain,
( ~ ssList(nil)
| nil = nil ),
inference(demodulation,[status(thm)],[d44,d40]) ).
cnf(d46,plain,
nil = nil,
inference(resolution,[status(thm)],[c24,d45]) ).
cnf(d47,plain,
neq(nil,nil),
inference(resolution,[status(thm)],[d46,d26]) ).
cnf(d48,plain,
( ~ neq(sk1,nil)
| nil != sk1 ),
inference(resolution,[status(thm)],[d8,c16]) ).
cnf(d49,plain,
( ~ neq(sk1,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[d48,d20]) ).
cnf(d50,plain,
( ~ neq(nil,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[d49,d20]) ).
cnf(d51,plain,
~ neq(nil,nil),
inference(equality_resolution,[status(thm)],[d50]) ).
cnf(d52,plain,
$false,
inference(resolution,[status(thm)],[d51,d47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC112-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/10.44 % Computer : n016.cluster.edu
% 0.17/10.44 % Model : x86_64 x86_64
% 0.17/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.44 % Memory : 8046.5625MB
% 0.17/10.44 % OS : Linux 6.8.0-71-generic
% 0.17/10.44 % CPULimit : 300
% 0.17/10.44 % WCLimit : 300
% 0.17/10.44 % DateTime : Sat Sep 26 12:21:41 UTC 2026
% 0.17/10.44 % CPUTime :
% 0.17/10.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.19/17.17 % SZS status Unsatisfiable for theBenchmark.p
% 52.19/17.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------