%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC002-1 : 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 05:17:51 PM UTC 2026
% Result : Unsatisfiable 1.22s 1.64s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 13
% Syntax : Number of clauses : 42 ( 16 unt; 1 nHn; 42 RR)
% Number of literals : 132 ( 41 equ; 93 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_21,negated_conjecture,
( geq(sk5(X3,X2,X1),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk2
| app(X2,X3) != sk1
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_21) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_26,negated_conjecture,
( app(app(sk7,cons(sk6,nil)),sk8) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_26) ).
cnf(co1_27,negated_conjecture,
( app(sk7,sk8) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_27) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_23,negated_conjecture,
( ssItem(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_23) ).
cnf(co1_25,negated_conjecture,
( ssList(sk8)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_25) ).
cnf(co1_24,negated_conjecture,
( ssList(sk7)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_24) ).
cnf(co1_20,negated_conjecture,
( memberP(sk2,sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk2
| app(X2,X3) != sk1
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_20) ).
cnf(co1_19,negated_conjecture,
( ssItem(sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk2
| app(X2,X3) != sk1
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
cnf(co1_22,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk2
| app(X2,X3) != sk1
| X1 != sk5(X3,X2,X1)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_22) ).
cnf(co1_28,negated_conjecture,
( sk6 = X1
| ~ ssItem(X1)
| ~ memberP(sk4,X1)
| ~ geq(X1,sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_28) ).
cnf(c_0_13,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_14,negated_conjecture,
( geq(sk5(X3,X2,X1),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk2
| app(X2,X3) != sk1
| ~ neq(sk4,nil) ),
co1_21 ).
cnf(c_0_15,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_16,negated_conjecture,
neq(sk2,nil),
c_0_13 ).
cnf(c_0_17,negated_conjecture,
( app(app(sk7,cons(sk6,nil)),sk8) = sk4
| ~ neq(sk4,nil) ),
co1_26 ).
cnf(c_0_18,negated_conjecture,
( app(sk7,sk8) = sk3
| ~ neq(sk4,nil) ),
co1_27 ).
cnf(c_0_19,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_20,negated_conjecture,
( ssItem(sk6)
| ~ neq(sk4,nil) ),
co1_23 ).
cnf(c_0_21,negated_conjecture,
( ssList(sk8)
| ~ neq(sk4,nil) ),
co1_25 ).
cnf(c_0_22,negated_conjecture,
( ssList(sk7)
| ~ neq(sk4,nil) ),
co1_24 ).
cnf(c_0_23,negated_conjecture,
( memberP(sk2,sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk2
| app(X2,X3) != sk1
| ~ neq(sk4,nil) ),
co1_20 ).
cnf(c_0_24,negated_conjecture,
( ssItem(sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk2
| app(X2,X3) != sk1
| ~ neq(sk4,nil) ),
co1_19 ).
cnf(c_0_25,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk2
| app(X2,X3) != sk1
| X1 != sk5(X3,X2,X1)
| ~ neq(sk4,nil) ),
co1_22 ).
cnf(c_0_26,negated_conjecture,
( sk6 = X1
| ~ ssItem(X1)
| ~ memberP(sk4,X1)
| ~ geq(X1,sk6)
| ~ neq(sk4,nil) ),
co1_28 ).
cnf(c_0_27,negated_conjecture,
( geq(sk5(X1,X2,X3),X3)
| app(app(X2,cons(X3,nil)),X1) != sk2
| app(X2,X1) != sk1
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_28,negated_conjecture,
app(app(sk7,cons(sk6,nil)),sk8) = sk2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_15]),c_0_15]),c_0_16])]) ).
cnf(c_0_29,negated_conjecture,
app(sk7,sk8) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_15]),c_0_16])]) ).
cnf(c_0_30,negated_conjecture,
ssItem(sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_15]),c_0_16])]) ).
cnf(c_0_31,negated_conjecture,
ssList(sk8),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_15]),c_0_16])]) ).
cnf(c_0_32,negated_conjecture,
ssList(sk7),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_15]),c_0_16])]) ).
cnf(c_0_33,negated_conjecture,
( memberP(sk2,sk5(X1,X2,X3))
| app(app(X2,cons(X3,nil)),X1) != sk2
| app(X2,X1) != sk1
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_15]),c_0_16])]) ).
cnf(c_0_34,negated_conjecture,
( ssItem(sk5(X1,X2,X3))
| app(app(X2,cons(X3,nil)),X1) != sk2
| app(X2,X1) != sk1
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_15]),c_0_16])]) ).
cnf(c_0_35,negated_conjecture,
( app(app(X1,cons(X2,nil)),X3) != sk2
| sk5(X3,X1,X2) != X2
| app(X1,X3) != sk1
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_15]),c_0_16])]) ).
cnf(c_0_36,negated_conjecture,
( sk6 = X1
| ~ memberP(sk2,X1)
| ~ geq(X1,sk6)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_15]),c_0_15]),c_0_16])]) ).
cnf(c_0_37,negated_conjecture,
geq(sk5(sk8,sk7,sk6),sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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]),c_0_32])]) ).
cnf(c_0_38,negated_conjecture,
memberP(sk2,sk5(sk8,sk7,sk6)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_39,negated_conjecture,
ssItem(sk5(sk8,sk7,sk6)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_40,negated_conjecture,
sk5(sk8,sk7,sk6) != sk6,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWC002-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.06 % 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
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 23:14:26 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.22/1.64 % Version : CSE_E---1.7
% 1.22/1.64 % Problem : theBenchmark.p
% 1.22/1.64 % SZS status Unsatisfiable for theBenchmark.p
% 1.22/1.64 % SZS output start CNFRefutation
% See solution above
% 1.22/1.64 % Total time : 1.363s
%------------------------------------------------------------------------------