%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC220-1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:18:47 PM UTC 2026
% Result : Unsatisfiable 1.47s 1.71s
% Output : CNFRefutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of clauses : 35 ( 14 unt; 10 nHn; 35 RR)
% Number of literals : 97 ( 27 equ; 58 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 33 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_16,negated_conjecture,
( nil = sk3
| app(app(sk7,cons(sk6,nil)),sk8) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_7,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_13,negated_conjecture,
( nil = sk3
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_15,negated_conjecture,
( nil = sk3
| ssList(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
cnf(co1_14,negated_conjecture,
( nil = sk3
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_17,negated_conjecture,
( nil = sk3
| leq(X1,sk6)
| ~ ssItem(X1)
| ~ memberP(sk7,X1)
| ~ memberP(sk8,X1)
| ~ leq(sk6,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
cnf(co1_10,negated_conjecture,
( memberP(X3,sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(co1_11,negated_conjecture,
( leq(X1,sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_8,negated_conjecture,
( ssItem(sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_12,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk1
| ~ leq(sk5(X3,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(co1_9,negated_conjecture,
( memberP(X2,sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(c_0_12,negated_conjecture,
( nil = sk3
| app(app(sk7,cons(sk6,nil)),sk8) = sk3 ),
co1_16 ).
cnf(c_0_13,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_14,negated_conjecture,
nil != sk1,
co1_7 ).
cnf(c_0_15,negated_conjecture,
( nil = sk3
| ssItem(sk6) ),
co1_13 ).
cnf(c_0_16,negated_conjecture,
( nil = sk3
| ssList(sk8) ),
co1_15 ).
cnf(c_0_17,negated_conjecture,
( nil = sk3
| ssList(sk7) ),
co1_14 ).
cnf(c_0_18,negated_conjecture,
( nil = sk3
| leq(X1,sk6)
| ~ ssItem(X1)
| ~ memberP(sk7,X1)
| ~ memberP(sk8,X1)
| ~ leq(sk6,X1) ),
co1_17 ).
cnf(c_0_19,negated_conjecture,
( memberP(X3,sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk1 ),
co1_10 ).
cnf(c_0_20,negated_conjecture,
app(app(sk7,cons(sk6,nil)),sk8) = sk1,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]),c_0_14]) ).
cnf(c_0_21,negated_conjecture,
ssItem(sk6),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_13]),c_0_14]) ).
cnf(c_0_22,negated_conjecture,
ssList(sk8),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_13]),c_0_14]) ).
cnf(c_0_23,negated_conjecture,
ssList(sk7),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_13]),c_0_14]) ).
cnf(c_0_24,negated_conjecture,
( leq(X1,sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk1 ),
co1_11 ).
cnf(c_0_25,negated_conjecture,
( ssItem(sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk1 ),
co1_8 ).
cnf(c_0_26,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk1
| ~ leq(sk5(X3,X2,X1),X1) ),
co1_12 ).
cnf(c_0_27,negated_conjecture,
( leq(X1,sk6)
| ~ memberP(sk7,X1)
| ~ memberP(sk8,X1)
| ~ leq(sk6,X1)
| ~ ssItem(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_13]),c_0_14]) ).
cnf(c_0_28,negated_conjecture,
memberP(sk8,sk5(sk8,sk7,sk6)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_29,negated_conjecture,
leq(sk6,sk5(sk8,sk7,sk6)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_30,negated_conjecture,
ssItem(sk5(sk8,sk7,sk6)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_31,negated_conjecture,
~ leq(sk5(sk8,sk7,sk6),sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_32,negated_conjecture,
( memberP(X2,sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk1 ),
co1_9 ).
cnf(c_0_33,negated_conjecture,
~ memberP(sk7,sk5(sk8,sk7,sk6)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_20]),c_0_21]),c_0_22]),c_0_23])]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SWC220-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.08 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.09/0.27 % Computer : n024.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Mon May 4 23:35:26 EDT 2026
% 0.09/0.27 % CPUTime :
% 0.09/0.28 % start to proof: theBenchmark
% 1.47/1.71 % Version : CSE_E---1.7
% 1.47/1.71 % Problem : theBenchmark.p
% 1.47/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.47/1.71 % SZS output start CNFRefutation
% See solution above
% 1.47/1.71 % Total time : 1.367s
%------------------------------------------------------------------------------