%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC109-1 : 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 : n008.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 08:54:18 AM UTC 2026
% Result : Unsatisfiable 88.75s 20.89s
% Output : CNFRefutation 88.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 24
% Syntax : Number of clauses : 105 ( 17 unt; 58 nHn; 105 RR)
% Number of literals : 276 ( 87 equ; 112 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_3,negated_conjecture,
ssList(sk3) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4 ).
cnf(co1_6,negated_conjecture,
sk1 = sk3 ).
cnf(co1_7,negated_conjecture,
( nil = sk4
| ssItem(sk5) ) ).
cnf(co1_8,negated_conjecture,
( nil = sk3
| ssItem(sk5) ) ).
cnf(co1_9,negated_conjecture,
( nil = sk4
| ssList(sk6) ) ).
cnf(co1_10,negated_conjecture,
( nil = sk4
| ssList(sk7) ) ).
cnf(co1_11,negated_conjecture,
( nil = sk4
| cons(sk5,nil) = sk3 ) ).
cnf(co1_12,negated_conjecture,
( nil = sk4
| app(app(sk6,sk3),sk7) = sk4 ) ).
cnf(co1_15,negated_conjecture,
( nil = sk3
| ssList(sk6) ) ).
cnf(co1_16,negated_conjecture,
( nil = sk3
| ssList(sk7) ) ).
cnf(co1_17,negated_conjecture,
( nil = sk3
| cons(sk5,nil) = sk3 ) ).
cnf(co1_18,negated_conjecture,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ) ).
cnf(co1_22,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ) ).
cnf(co1_23,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause11,axiom,
~ singletonP(nil) ).
cnf(clause57,axiom,
( segmentP(X0,X0)
| ~ ssList(X0) ) ).
cnf(clause80,axiom,
( nil = X0
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ).
cnf(clause86,axiom,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(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(clause116,axiom,
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ) ).
cnf(clause172,axiom,
( segmentP(app(app(X3,X0),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ) ).
cnf(c2,plain,
ssList(sk3),
inference(clausification,[status(esa)],[co1_3]) ).
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
| ssItem(sk5) ),
inference(clausification,[status(esa)],[co1_7]) ).
cnf(c7,plain,
( nil = sk3
| ssItem(sk5) ),
inference(clausification,[status(esa)],[co1_8]) ).
cnf(c8,plain,
( nil = sk4
| ssList(sk6) ),
inference(clausification,[status(esa)],[co1_9]) ).
cnf(c9,plain,
( nil = sk4
| ssList(sk7) ),
inference(clausification,[status(esa)],[co1_10]) ).
cnf(c10,plain,
( nil = sk4
| cons(sk5,nil) = sk3 ),
inference(clausification,[status(esa)],[co1_11]) ).
cnf(c11,plain,
( nil = sk4
| app(app(sk6,sk3),sk7) = sk4 ),
inference(clausification,[status(esa)],[co1_12]) ).
cnf(c14,plain,
( nil = sk3
| ssList(sk6) ),
inference(clausification,[status(esa)],[co1_15]) ).
cnf(c15,plain,
( nil = sk3
| ssList(sk7) ),
inference(clausification,[status(esa)],[co1_16]) ).
cnf(c16,plain,
( nil = sk3
| cons(sk5,nil) = sk3 ),
inference(clausification,[status(esa)],[co1_17]) ).
cnf(c17,plain,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
inference(clausification,[status(esa)],[co1_18]) ).
cnf(c21,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
inference(clausification,[status(esa)],[co1_22]) ).
cnf(c22,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausification,[status(esa)],[co1_23]) ).
cnf(c31,plain,
ssList(nil),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c34,plain,
~ singletonP(nil),
inference(clausification,[status(esa)],[clause11]) ).
cnf(c80,plain,
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause57]) ).
cnf(c103,plain,
( nil = X0
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(clausification,[status(esa)],[clause80]) ).
cnf(c109,plain,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[clause86]) ).
cnf(c123,plain,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[clause100]) ).
cnf(c138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(clausification,[status(esa)],[clause115]) ).
cnf(c139,plain,
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
inference(clausification,[status(esa)],[clause116]) ).
cnf(c195,plain,
( ~ ssList(X3)
| ~ segmentP(X1,X3)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(app(X0,X1),X2),X3) ),
inference(clausification,[status(esa)],[clause172]) ).
cnf(d0,plain,
( ~ neq(X0,X0)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[c138]) ).
cnf(d1,plain,
( neq(sk2,nil)
| nil != sk3 ),
inference(demodulation,[status(thm)],[c22,c5]) ).
cnf(d2,plain,
( neq(sk4,nil)
| nil != sk3 ),
inference(demodulation,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(equality_resolution,[status(thm)],[c139]) ).
cnf(d4,plain,
( ~ ssItem(X0)
| ~ ssList(nil)
| singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d3,c109]) ).
cnf(d5,plain,
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c31,d4]) ).
cnf(d6,plain,
( nil = sk3
| ~ ssItem(sk5)
| singletonP(sk3) ),
inference(superposition,[status(thm)],[c16,d5]) ).
cnf(d7,plain,
( ssItem(sk5)
| neq(sk4,nil)
| nil != nil ),
inference(superposition,[status(thm)],[c7,d2]) ).
cnf(d8,plain,
( neq(sk4,nil)
| ssItem(sk5) ),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
( ssItem(sk5)
| ssItem(sk5)
| neq(nil,nil) ),
inference(superposition,[status(thm)],[c6,d8]) ).
cnf(d10,plain,
( ssItem(sk5)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[d0,d9]) ).
cnf(d11,plain,
ssItem(sk5),
inference(resolution,[status(thm)],[c31,d10]) ).
cnf(d12,plain,
( singletonP(sk3)
| nil = sk3 ),
inference(resolution,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
( singletonP(sk3)
| neq(sk4,nil)
| nil != nil ),
inference(superposition,[status(thm)],[d12,d2]) ).
cnf(d14,plain,
( singletonP(sk3)
| neq(sk4,nil) ),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
( nil = sk4
| ~ ssItem(sk5)
| singletonP(sk3) ),
inference(superposition,[status(thm)],[c10,d5]) ).
cnf(d16,plain,
( singletonP(sk3)
| nil = sk4 ),
inference(resolution,[status(thm)],[d11,d15]) ).
cnf(d17,plain,
( singletonP(sk3)
| singletonP(sk3)
| neq(nil,nil) ),
inference(superposition,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
( ~ ssList(nil)
| singletonP(sk3) ),
inference(resolution,[status(thm)],[d17,d0]) ).
cnf(d19,plain,
singletonP(sk3),
inference(resolution,[status(thm)],[c31,d18]) ).
cnf(d20,plain,
( nil = sk3
| ~ segmentP(sk3,X0)
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(sk7)
| segmentP(sk4,X0) ),
inference(superposition,[status(thm)],[c17,c195]) ).
cnf(d21,plain,
( segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssList(X0)
| nil = sk3 ),
inference(resolution,[status(thm)],[c2,d20]) ).
cnf(d22,plain,
( ssList(sk7)
| neq(sk4,nil)
| nil != nil ),
inference(superposition,[status(thm)],[c15,d2]) ).
cnf(d23,plain,
( neq(sk4,nil)
| ssList(sk7) ),
inference(equality_resolution,[status(thm)],[d22]) ).
cnf(d24,plain,
( ssList(sk7)
| ssList(sk7)
| neq(nil,nil) ),
inference(superposition,[status(thm)],[c9,d23]) ).
cnf(d25,plain,
( ssList(sk7)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[d0,d24]) ).
cnf(d26,plain,
ssList(sk7),
inference(resolution,[status(thm)],[c31,d25]) ).
cnf(d27,plain,
( segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ ssList(sk6)
| ~ ssList(X0)
| nil = sk3 ),
inference(resolution,[status(thm)],[d26,d21]) ).
cnf(d28,plain,
( ssList(sk6)
| neq(sk4,nil)
| nil != nil ),
inference(superposition,[status(thm)],[c14,d2]) ).
cnf(d29,plain,
( neq(sk4,nil)
| ssList(sk6) ),
inference(equality_resolution,[status(thm)],[d28]) ).
cnf(d30,plain,
( ssList(sk6)
| ssList(sk6)
| neq(nil,nil) ),
inference(superposition,[status(thm)],[c8,d29]) ).
cnf(d31,plain,
( ssList(sk6)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[d0,d30]) ).
cnf(d32,plain,
ssList(sk6),
inference(resolution,[status(thm)],[c31,d31]) ).
cnf(d33,plain,
( segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ ssList(X0)
| nil = sk3 ),
inference(resolution,[status(thm)],[d32,d27]) ).
cnf(d34,plain,
( ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(sk3)
| nil = sk3 ),
inference(resolution,[status(thm)],[d33,c80]) ).
cnf(d35,plain,
( segmentP(sk4,sk3)
| nil = sk3 ),
inference(resolution,[status(thm)],[c2,d34]) ).
cnf(d36,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk4 ),
inference(demodulation,[status(thm)],[c21,c4]) ).
cnf(d37,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk3,nil)
| nil = sk4 ),
inference(demodulation,[status(thm)],[d36,c5]) ).
cnf(d38,plain,
( ~ segmentP(sk4,sk1)
| ~ neq(sk3,nil)
| nil = sk4 ),
inference(demodulation,[status(thm)],[d37,c4]) ).
cnf(d39,plain,
( ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil)
| nil = sk4 ),
inference(demodulation,[status(thm)],[d38,c5]) ).
cnf(d40,plain,
( nil = sk4
| ~ segmentP(sk3,X0)
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(sk7)
| segmentP(sk4,X0) ),
inference(superposition,[status(thm)],[c11,c195]) ).
cnf(d41,plain,
( segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssList(X0)
| nil = sk4 ),
inference(resolution,[status(thm)],[c2,d40]) ).
cnf(d42,plain,
( segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ ssList(sk6)
| ~ ssList(X0)
| nil = sk4 ),
inference(resolution,[status(thm)],[d26,d41]) ).
cnf(d43,plain,
( segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ ssList(X0)
| nil = sk4 ),
inference(resolution,[status(thm)],[d32,d42]) ).
cnf(d44,plain,
( ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(sk3)
| nil = sk4 ),
inference(resolution,[status(thm)],[d43,c80]) ).
cnf(d45,plain,
( segmentP(sk4,sk3)
| nil = sk4 ),
inference(resolution,[status(thm)],[c2,d44]) ).
cnf(d46,plain,
( ~ neq(sk3,nil)
| nil = sk4
| nil = sk4 ),
inference(resolution,[status(thm)],[d45,d39]) ).
cnf(d47,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| sk3 = nil
| nil = sk4 ),
inference(resolution,[status(thm)],[d46,c123]) ).
cnf(d48,plain,
( ~ ssList(nil)
| nil = sk4
| sk3 = nil ),
inference(resolution,[status(thm)],[c2,d47]) ).
cnf(d49,plain,
( nil = sk4
| sk3 = nil ),
inference(resolution,[status(thm)],[c31,d48]) ).
cnf(d50,plain,
( sk3 = nil
| nil = sk3
| segmentP(nil,sk3) ),
inference(superposition,[status(thm)],[d49,d35]) ).
cnf(d51,plain,
( ~ ssList(sk3)
| nil = sk3
| nil = sk3
| sk3 = nil ),
inference(resolution,[status(thm)],[d50,c103]) ).
cnf(d52,plain,
( nil = sk3
| sk3 = nil ),
inference(resolution,[status(thm)],[c2,d51]) ).
cnf(d53,plain,
( sk3 = nil
| singletonP(nil) ),
inference(superposition,[status(thm)],[d52,d19]) ).
cnf(d54,plain,
sk3 = nil,
inference(resolution,[status(thm)],[c34,d53]) ).
cnf(d55,plain,
singletonP(nil),
inference(demodulation,[status(thm)],[d19,d54]) ).
cnf(d56,plain,
$false,
inference(resolution,[status(thm)],[c34,d55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC109-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/6.05 % Computer : n008.cluster.edu
% 0.13/6.05 % Model : x86_64 x86_64
% 0.13/6.05 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/6.05 % Memory : 8046.5625MB
% 0.13/6.05 % OS : Linux 6.8.0-71-generic
% 0.13/6.05 % CPULimit : 300
% 0.13/6.05 % WCLimit : 300
% 0.13/6.05 % DateTime : Sat Sep 26 12:17:07 UTC 2026
% 0.13/6.06 % CPUTime :
% 0.13/6.06 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 88.75/20.89 % SZS status Unsatisfiable for theBenchmark.p
% 88.75/20.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------