%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC178-1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n025.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 05:18:37 PM UTC 2026
% Result : Unsatisfiable 1.45s 1.76s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 32
% Syntax : Number of clauses : 93 ( 36 unt; 12 nHn; 88 RR)
% Number of literals : 225 ( 66 equ; 130 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 81 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_12,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(co1_11,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_13,negated_conjecture,
~ neq(sk5,sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
cnf(clause102,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssItem(X1)
| ~ ssItem(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause102) ).
cnf(co1_8,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_9,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause119,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause119) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause101,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(clause47,axiom,
ssItem(skaf44(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause47) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_10,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
cnf(co1_14,negated_conjecture,
( singletonP(sk3)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause149,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(clause100,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(clause99,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(clause179,axiom,
( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ duplicatefreeP(X5)
| ~ ssList(X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).
cnf(clause120,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause65,axiom,
( duplicatefreeP(cons(X1,nil))
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause65) ).
cnf(clause152,axiom,
( segmentP(X1,X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause152) ).
cnf(co1_7,negated_conjecture,
segmentP(sk4,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(clause80,axiom,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause80) ).
cnf(clause79,axiom,
( segmentP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause79) ).
cnf(c_0_32,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
co1_12 ).
cnf(c_0_33,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_34,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_35,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk3,
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
ssList(sk8),
co1_11 ).
cnf(c_0_37,negated_conjecture,
~ neq(sk5,sk6),
co1_13 ).
cnf(c_0_38,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssItem(X1)
| ~ ssItem(X2) ),
clause102 ).
cnf(c_0_39,negated_conjecture,
ssItem(sk5),
co1_8 ).
cnf(c_0_40,negated_conjecture,
ssItem(sk6),
co1_9 ).
cnf(c_0_41,negated_conjecture,
( app(app(sk7,cons(sk5,nil)),cons(sk6,nil)) = nil
| sk3 != nil
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_42,negated_conjecture,
sk6 = sk5,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40])]) ).
cnf(c_0_43,negated_conjecture,
( app(app(sk7,cons(sk5,nil)),cons(sk5,nil)) = nil
| sk3 != nil
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_42]) ).
cnf(c_0_44,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_45,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause119 ).
cnf(c_0_46,negated_conjecture,
( app(app(sk7,cons(sk5,nil)),cons(sk5,nil)) = nil
| sk3 != nil
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_48,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
clause101 ).
cnf(c_0_49,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_50,axiom,
ssList(nil),
clause8 ).
cnf(c_0_51,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_52,negated_conjecture,
( cons(sk5,nil) = nil
| sk3 != nil
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,negated_conjecture,
ssList(sk7),
co1_10 ).
cnf(c_0_54,plain,
( tl(X1) = nil
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50])]) ).
cnf(c_0_55,negated_conjecture,
( singletonP(sk3)
| ~ neq(sk4,nil) ),
co1_14 ).
cnf(c_0_56,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_51,c_0_33]) ).
cnf(c_0_57,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_58,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_59,negated_conjecture,
( cons(sk5,nil) = nil
| sk3 != nil
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_44]),c_0_53])]) ).
cnf(c_0_60,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_61,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)),sk8) = sk3,
inference(rw,[status(thm)],[c_0_35,c_0_42]) ).
cnf(c_0_62,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_63,negated_conjecture,
( tl(sk3) = nil
| ~ neq(sk4,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).
cnf(c_0_64,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_65,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_67,negated_conjecture,
( cons(sk5,nil) = nil
| sk3 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_39]),c_0_50])]) ).
cnf(c_0_68,axiom,
( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ duplicatefreeP(X5)
| ~ ssList(X5) ),
clause179 ).
cnf(c_0_69,negated_conjecture,
( app(app(sk7,cons(sk5,nil)),app(cons(sk5,nil),sk8)) = sk3
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_36])]) ).
cnf(c_0_70,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_71,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_72,negated_conjecture,
( tl(sk3) = nil
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_50])]) ).
cnf(c_0_73,negated_conjecture,
sk3 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_39]),c_0_50])]) ).
cnf(c_0_74,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_75,plain,
( ~ ssItem(X1)
| ~ ssList(app(app(X2,cons(X1,X3)),cons(X1,X4)))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ duplicatefreeP(app(app(X2,cons(X1,X3)),cons(X1,X4))) ),
inference(er,[status(thm)],[c_0_68]) ).
cnf(c_0_76,negated_conjecture,
( app(app(sk7,cons(sk5,nil)),cons(sk5,sk8)) = sk3
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_39]),c_0_36])]) ).
cnf(c_0_77,axiom,
( duplicatefreeP(cons(X1,nil))
| ~ ssItem(X1) ),
clause65 ).
cnf(c_0_78,negated_conjecture,
( cons(hd(sk3),nil) = sk3
| sk4 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_56])]),c_0_73]) ).
cnf(c_0_79,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(sk3) ),
inference(spm,[status(thm)],[c_0_74,c_0_56]) ).
cnf(c_0_80,negated_conjecture,
( ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil))
| ~ duplicatefreeP(sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_39]),c_0_56]),c_0_36]),c_0_50]),c_0_53])]) ).
cnf(c_0_81,negated_conjecture,
( sk4 = nil
| duplicatefreeP(sk3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_82,axiom,
( segmentP(X1,X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause152 ).
cnf(c_0_83,negated_conjecture,
segmentP(sk4,sk3),
co1_7 ).
cnf(c_0_84,negated_conjecture,
( sk4 = nil
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil)) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_85,axiom,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
clause80 ).
cnf(c_0_86,negated_conjecture,
( segmentP(X1,sk3)
| ~ segmentP(X1,sk4)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_56]),c_0_65])]) ).
cnf(c_0_87,negated_conjecture,
( sk4 = nil
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_44]),c_0_53])]) ).
cnf(c_0_88,axiom,
( segmentP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
clause79 ).
cnf(c_0_89,negated_conjecture,
~ segmentP(nil,sk4),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_56]),c_0_50])]),c_0_73]) ).
cnf(c_0_90,negated_conjecture,
sk4 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_60]),c_0_39]),c_0_50])]) ).
cnf(c_0_91,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_88]),c_0_50])]) ).
cnf(c_0_92,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90]),c_0_91])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC178-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n025.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 04:31:58 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.45/1.76 % Version : CSE_E---1.7
% 1.45/1.76 % Problem : theBenchmark.p
% 1.45/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 1.45/1.76 % SZS output start CNFRefutation
% See solution above
% 1.45/1.77 % Total time : 1.372s
%------------------------------------------------------------------------------