%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC327-1 : 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 : n007.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 05:19:12 PM UTC 2026
% Result : Unsatisfiable 1.57s 1.80s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of clauses : 70 ( 20 unt; 15 nHn; 70 RR)
% Number of literals : 219 ( 107 equ; 146 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_8,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_9,negated_conjecture,
equalelemsP(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(clause119,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
cnf(co1_7,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_19,negated_conjecture,
( app(cons(sk6(X1),nil),sk7(X1)) = X1
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(co1_18,negated_conjecture,
( ssList(sk7(X1))
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
cnf(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause99,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(co1_13,negated_conjecture,
( ssItem(sk6(X1))
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_11,negated_conjecture,
( nil = sk4
| nil != sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_10,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != sk5
| ~ ssList(X3)
| app(X3,cons(X1,nil)) != sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(co1_17,negated_conjecture,
( app(sk8(X1),cons(sk6(X1),nil)) = sk1
| nil = sk1
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
cnf(co1_15,negated_conjecture,
( app(cons(sk6(X1),nil),sk7(X1)) = X1
| nil = sk1
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
cnf(co1_16,negated_conjecture,
( ssList(sk8(X1))
| nil = sk1
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
cnf(co1_14,negated_conjecture,
( ssList(sk7(X1))
| nil = sk1
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_12,negated_conjecture,
( ssItem(sk6(X1))
| nil = sk1
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(c_0_21,negated_conjecture,
app(sk3,sk5) = sk4,
co1_8 ).
cnf(c_0_22,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_23,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_24,negated_conjecture,
equalelemsP(sk3),
co1_9 ).
cnf(c_0_25,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause119 ).
cnf(c_0_26,negated_conjecture,
app(sk1,sk5) = sk2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,negated_conjecture,
ssList(sk5),
co1_7 ).
cnf(c_0_28,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_29,negated_conjecture,
( app(cons(sk6(X1),nil),sk7(X1)) = X1
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1)
| nil != sk2 ),
co1_19 ).
cnf(c_0_30,negated_conjecture,
equalelemsP(sk1),
inference(rw,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_31,negated_conjecture,
( sk5 = nil
| sk2 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_32,negated_conjecture,
( app(cons(sk6(X1),nil),sk7(X1)) = X1
| app(sk1,X1) != sk2
| sk2 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_33,axiom,
ssList(nil),
clause8 ).
cnf(c_0_34,negated_conjecture,
( app(sk1,nil) = sk2
| sk2 != nil ),
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( sk7(nil) = nil
| sk2 != nil
| ~ ssList(cons(sk6(nil),nil))
| ~ ssList(sk7(nil)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_32])]),c_0_33])]),c_0_34]) ).
cnf(c_0_36,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_37,negated_conjecture,
( ssList(sk7(X1))
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1)
| nil != sk2 ),
co1_18 ).
cnf(c_0_38,negated_conjecture,
( sk7(nil) = nil
| sk2 != nil
| ~ ssItem(sk6(nil))
| ~ ssList(sk7(nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_33])]) ).
cnf(c_0_39,negated_conjecture,
( ssList(sk7(X1))
| app(sk1,X1) != sk2
| sk2 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_30])]) ).
cnf(c_0_40,negated_conjecture,
( sk7(nil) = nil
| sk2 != nil
| ~ ssItem(sk6(nil)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_33])]),c_0_34]) ).
cnf(c_0_41,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_42,negated_conjecture,
( app(cons(sk6(nil),nil),nil) = nil
| sk2 != nil
| ~ ssItem(sk6(nil)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_40]),c_0_33])]),c_0_34]) ).
cnf(c_0_43,negated_conjecture,
( cons(sk6(nil),nil) = nil
| sk2 != nil
| ~ ssItem(sk6(nil))
| ~ ssList(cons(sk6(nil),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_33])]) ).
cnf(c_0_44,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_45,negated_conjecture,
( cons(sk6(nil),nil) = nil
| sk2 != nil
| ~ ssItem(sk6(nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_36]),c_0_33])]) ).
cnf(c_0_46,negated_conjecture,
( ssItem(sk6(X1))
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1)
| nil != sk2 ),
co1_13 ).
cnf(c_0_47,negated_conjecture,
( sk2 != nil
| ~ ssItem(sk6(nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_33])]) ).
cnf(c_0_48,negated_conjecture,
( ssItem(sk6(X1))
| app(sk1,X1) != sk2
| sk2 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_30])]) ).
cnf(c_0_49,negated_conjecture,
( nil = sk4
| nil != sk3 ),
co1_11 ).
cnf(c_0_50,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != sk5
| ~ ssList(X3)
| app(X3,cons(X1,nil)) != sk3 ),
co1_10 ).
cnf(c_0_51,negated_conjecture,
( app(sk8(X1),cons(sk6(X1),nil)) = sk1
| nil = sk1
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1) ),
co1_17 ).
cnf(c_0_52,negated_conjecture,
sk2 != nil,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_33])]),c_0_34]) ).
cnf(c_0_53,negated_conjecture,
( sk2 = nil
| sk1 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_23]),c_0_22]) ).
cnf(c_0_54,negated_conjecture,
( app(X1,cons(X2,nil)) != sk1
| app(cons(X2,nil),X3) != sk5
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(rw,[status(thm)],[c_0_50,c_0_22]) ).
cnf(c_0_55,negated_conjecture,
( app(sk8(X1),cons(sk6(X1),nil)) = sk1
| sk1 = nil
| app(sk1,X1) != sk2
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_30])]) ).
cnf(c_0_56,negated_conjecture,
sk1 != nil,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
( app(cons(sk6(X1),nil),sk7(X1)) = X1
| nil = sk1
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1) ),
co1_15 ).
cnf(c_0_58,negated_conjecture,
( app(cons(sk6(X1),nil),X2) != sk5
| app(sk1,X1) != sk2
| ~ ssItem(sk6(X1))
| ~ ssList(sk8(X1))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_59,negated_conjecture,
( app(cons(sk6(X1),nil),sk7(X1)) = X1
| sk1 = nil
| app(sk1,X1) != sk2
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_30])]) ).
cnf(c_0_60,negated_conjecture,
( ssList(sk8(X1))
| nil = sk1
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1) ),
co1_16 ).
cnf(c_0_61,negated_conjecture,
( ~ ssItem(sk6(sk5))
| ~ ssList(sk8(sk5))
| ~ ssList(sk7(sk5)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_56])]),c_0_26]),c_0_27])]) ).
cnf(c_0_62,negated_conjecture,
( sk1 = nil
| ssList(sk8(X1))
| app(sk1,X1) != sk2
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_30])]) ).
cnf(c_0_63,negated_conjecture,
( ssList(sk7(X1))
| nil = sk1
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1) ),
co1_14 ).
cnf(c_0_64,negated_conjecture,
( ~ ssItem(sk6(sk5))
| ~ ssList(sk7(sk5)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_26]),c_0_27])]),c_0_56]) ).
cnf(c_0_65,negated_conjecture,
( sk1 = nil
| ssList(sk7(X1))
| app(sk1,X1) != sk2
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_30])]) ).
cnf(c_0_66,negated_conjecture,
( ssItem(sk6(X1))
| nil = sk1
| ~ ssList(X1)
| app(sk1,X1) != sk2
| ~ equalelemsP(sk1) ),
co1_12 ).
cnf(c_0_67,negated_conjecture,
~ ssItem(sk6(sk5)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_26]),c_0_27])]),c_0_56]) ).
cnf(c_0_68,negated_conjecture,
( sk1 = nil
| ssItem(sk6(X1))
| app(sk1,X1) != sk2
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_30])]) ).
cnf(c_0_69,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_67,c_0_68]),c_0_26]),c_0_27])]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC327-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n007.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 04:43:09 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.57/1.80 % Version : CSE_E---1.7
% 1.57/1.80 % Problem : theBenchmark.p
% 1.57/1.80 % SZS status Unsatisfiable for theBenchmark.p
% 1.57/1.80 % SZS output start CNFRefutation
% See solution above
% 1.57/1.81 % Total time : 1.371s
%------------------------------------------------------------------------------