%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC022-1 : 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 : n010.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 05:17:56 PM UTC 2026
% Result : Unsatisfiable 1.50s 1.79s
% Output : CNFRefutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 24
% Syntax : Number of clauses : 83 ( 22 unt; 27 nHn; 79 RR)
% Number of literals : 236 ( 79 equ; 134 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 75 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_12,negated_conjecture,
( sk3 = X1
| ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,nil) != X1
| hd(sk4) != X2
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
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(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(clause99,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(clause171,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause171) ).
cnf(clause76,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause100,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(clause109,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
cnf(clause12,axiom,
ssItem(skaf83(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).
cnf(clause13,axiom,
ssList(skaf82(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause178,axiom,
( frontsegP(cons(X3,X1),cons(X4,X2))
| ~ frontsegP(X1,X2)
| X3 != X4
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ ssItem(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause178) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause60,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).
cnf(co1_11,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ frontsegP(sk2,X1)
| ~ frontsegP(sk1,X1)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause61,axiom,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause61) ).
cnf(clause83,axiom,
( frontsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause83) ).
cnf(c_0_24,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_25,negated_conjecture,
neq(sk2,nil),
c_0_24 ).
cnf(c_0_26,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_27,negated_conjecture,
( sk3 = X1
| ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,nil) != X1
| hd(sk4) != X2
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
co1_12 ).
cnf(c_0_28,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_29,negated_conjecture,
neq(sk4,nil),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( cons(hd(sk4),nil) = sk1
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29])])])]) ).
cnf(c_0_31,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_32,axiom,
ssList(nil),
clause8 ).
cnf(c_0_33,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_34,negated_conjecture,
( cons(hd(sk4),nil) = sk1
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_35,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_36,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_37,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
clause171 ).
cnf(c_0_38,negated_conjecture,
( hd(sk1) = hd(sk4)
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_32])]) ).
cnf(c_0_39,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_40,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_35,c_0_26]) ).
cnf(c_0_41,negated_conjecture,
( sk1 != nil
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_34]),c_0_32])]) ).
cnf(c_0_42,negated_conjecture,
( X1 = nil
| cons(X2,X1) != sk1
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_34]),c_0_32])]) ).
cnf(c_0_43,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_44,negated_conjecture,
( hd(sk1) = hd(sk4)
| sk4 = nil
| ~ neq(nil,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_45,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_46,negated_conjecture,
( sk4 = nil
| sk1 != nil
| ~ neq(nil,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_39]),c_0_40])]) ).
cnf(c_0_47,negated_conjecture,
( sk4 = nil
| X1 = nil
| cons(X2,X1) != sk1
| ~ ssItem(hd(sk4))
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_32]),c_0_40])]) ).
cnf(c_0_48,negated_conjecture,
( sk4 = nil
| ssItem(hd(sk4))
| ~ neq(nil,sk4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_44]),c_0_45])]),c_0_46]) ).
cnf(c_0_49,negated_conjecture,
( sk4 = nil
| X1 = nil
| cons(X2,X1) != sk1
| ~ neq(nil,sk4)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,negated_conjecture,
( sk4 = nil
| X1 = nil
| cons(X2,X1) != sk1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_43]),c_0_32]),c_0_40])]) ).
cnf(c_0_51,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_52,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_53,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_54,negated_conjecture,
( sk4 = nil
| sk1 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_43]),c_0_32]),c_0_40])]) ).
cnf(c_0_55,negated_conjecture,
( skaf82(sk1) = nil
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53])])]),c_0_45])]),c_0_54]) ).
cnf(c_0_56,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_57,negated_conjecture,
( cons(skaf83(sk1),nil) = sk1
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_55]),c_0_45])]),c_0_54]) ).
cnf(c_0_58,axiom,
( frontsegP(cons(X3,X1),cons(X4,X2))
| ~ frontsegP(X1,X2)
| X3 != X4
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ ssItem(X3) ),
clause178 ).
cnf(c_0_59,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_60,negated_conjecture,
( tl(sk1) = nil
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_52]),c_0_32])]) ).
cnf(c_0_61,negated_conjecture,
( skaf83(sk1) = hd(sk1)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_57]),c_0_52]),c_0_32])]) ).
cnf(c_0_62,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( cons(hd(sk1),nil) = sk1
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_45])]),c_0_54]) ).
cnf(c_0_64,negated_conjecture,
( sk4 = nil
| ssItem(hd(sk1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_61]) ).
cnf(c_0_65,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
clause60 ).
cnf(c_0_66,negated_conjecture,
( sk4 = nil
| frontsegP(cons(hd(sk1),X1),sk1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_32])]),c_0_64]),c_0_65]) ).
cnf(c_0_67,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ frontsegP(sk2,X1)
| ~ frontsegP(sk1,X1)
| ~ neq(sk4,nil) ),
co1_11 ).
cnf(c_0_68,negated_conjecture,
( sk4 = nil
| frontsegP(cons(hd(sk4),X1),sk1)
| ~ neq(nil,sk4)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_44]) ).
cnf(c_0_69,negated_conjecture,
( ~ neq(X1,nil)
| ~ frontsegP(sk1,X1)
| ~ frontsegP(sk4,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_26]),c_0_29])]) ).
cnf(c_0_70,negated_conjecture,
( sk4 = nil
| frontsegP(sk4,sk1)
| ~ neq(nil,sk4)
| ~ ssList(tl(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_59]),c_0_40])]) ).
cnf(c_0_71,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_72,negated_conjecture,
( nil = X1
| ~ frontsegP(sk1,X1)
| ~ frontsegP(sk4,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_43]),c_0_32])]) ).
cnf(c_0_73,axiom,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
clause61 ).
cnf(c_0_74,negated_conjecture,
( sk4 = nil
| frontsegP(sk4,sk1)
| ~ neq(nil,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_40])]) ).
cnf(c_0_75,negated_conjecture,
( sk1 = nil
| ~ frontsegP(sk4,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_45])]) ).
cnf(c_0_76,negated_conjecture,
( sk4 = nil
| frontsegP(sk4,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_43]),c_0_32]),c_0_40])]) ).
cnf(c_0_77,axiom,
( frontsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
clause83 ).
cnf(c_0_78,negated_conjecture,
( ~ frontsegP(sk1,sk4)
| ~ frontsegP(sk4,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_29]),c_0_40])]) ).
cnf(c_0_79,negated_conjecture,
sk4 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_54]) ).
cnf(c_0_80,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_77]),c_0_32])]) ).
cnf(c_0_81,negated_conjecture,
~ frontsegP(sk1,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79]),c_0_79]),c_0_79]),c_0_80])]) ).
cnf(c_0_82,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_65]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC022-1 : 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
% 0.15/0.33 % Computer : n010.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:15:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.50/1.79 % Version : CSE_E---1.7
% 1.50/1.79 % Problem : theBenchmark.p
% 1.50/1.79 % SZS status Unsatisfiable for theBenchmark.p
% 1.50/1.79 % SZS output start CNFRefutation
% See solution above
% 1.50/1.79 % Total time : 1.372s
%------------------------------------------------------------------------------