%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC308-1 : 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 : n004.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 05:19:07 PM UTC 2026
% Result : Unsatisfiable 1.83s 1.87s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 25
% Syntax : Number of clauses : 74 ( 21 unt; 19 nHn; 59 RR)
% Number of literals : 237 ( 66 equ; 156 neg)
% Maximal clause size : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 112 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
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(clause169,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).
cnf(clause52,axiom,
ssList(skaf43(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).
cnf(clause53,axiom,
ssList(skaf42(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).
cnf(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
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(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(co1_8,negated_conjecture,
( ~ ssList(X1)
| sk1 != X1
| ~ ssList(X2)
| ~ ssList(X3)
| tl(sk2) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(sk2) != X4
| ~ neq(nil,sk2)
| ~ neq(nil,sk2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_9,negated_conjecture,
( app(X2,cons(X1,nil)) = sk3
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(clause138,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause138) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
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(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
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(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause115,axiom,
( X1 != X2
| ~ neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause115) ).
cnf(co1_7,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(c_0_25,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_26,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_25]) ).
cnf(c_0_27,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_28,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_29,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_30,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_31,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_32,plain,
( ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,cons(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_33,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_34,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_35,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_36,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_37,plain,
( ssItem(X1)
| duplicatefreeP(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_39,negated_conjecture,
( ~ ssList(X1)
| sk1 != X1
| ~ ssList(X2)
| ~ ssList(X3)
| tl(sk2) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(sk2) != X4
| ~ neq(nil,sk2)
| ~ neq(nil,sk2) ),
co1_8 ).
cnf(c_0_40,negated_conjecture,
( app(X2,cons(X1,nil)) = sk3
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != sk4 ),
co1_9 ).
cnf(c_0_41,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_42,plain,
( nil = X1
| ~ memberP(X2,skaf83(X1))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ duplicatefreeP(app(X2,X1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35])]),c_0_31]) ).
cnf(c_0_43,plain,
( skaf83(X1) = hd(X1)
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_34]),c_0_35])]) ).
cnf(c_0_44,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk2,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_46,negated_conjecture,
( sk1 != X1
| tl(sk2) != X2
| hd(sk2) != X4
| app(X2,X3) != X1
| cons(X4,nil) != X3
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ neq(nil,sk2) ),
inference(cn,[status(thm)],[c_0_39]) ).
cnf(c_0_47,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_48,negated_conjecture,
( app(X1,cons(X2,nil)) = sk3
| app(cons(X2,nil),X1) != sk2
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_50,plain,
( nil = X1
| ~ memberP(X2,hd(X1))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ duplicatefreeP(app(X2,X1)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk2,sk2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_38]) ).
cnf(c_0_52,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_53,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_54,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_55,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_56,negated_conjecture,
( app(tl(sk2),cons(hd(sk2),nil)) != sk3
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ~ ssList(tl(sk2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])])])])]),c_0_31]) ).
cnf(c_0_57,negated_conjecture,
( app(X1,cons(X2,nil)) = sk3
| cons(X2,X1) != sk2
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
( sk2 = nil
| ssItem(X1)
| ~ memberP(sk2,hd(sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_38])]) ).
cnf(c_0_59,plain,
( nil = X1
| memberP(X1,hd(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( cons(hd(sk2),tl(sk2)) != sk2
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ~ ssList(tl(sk2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,negated_conjecture,
( sk2 = nil
| ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_38])]) ).
cnf(c_0_62,negated_conjecture,
( sk2 = nil
| ~ neq(nil,sk2)
| ~ ssList(cons(hd(sk2),nil))
| ~ ssList(tl(sk2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_53]),c_0_38])]),c_0_61]) ).
cnf(c_0_63,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_64,axiom,
ssList(nil),
clause8 ).
cnf(c_0_65,negated_conjecture,
( sk2 = nil
| ~ ssList(cons(hd(sk2),nil))
| ~ ssList(tl(sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_38])]) ).
cnf(c_0_66,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_67,negated_conjecture,
( sk2 = nil
| ~ ssList(tl(sk2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_64])]),c_0_61]) ).
cnf(c_0_68,axiom,
( X1 != X2
| ~ neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause115 ).
cnf(c_0_69,negated_conjecture,
neq(sk2,nil),
co1_7 ).
cnf(c_0_70,negated_conjecture,
sk2 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_54]),c_0_38])]) ).
cnf(c_0_71,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_68]) ).
cnf(c_0_72,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_73,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_64])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC308-1 : 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
% 0.16/0.32 % Computer : n004.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 04:42:47 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.83/1.87 % Version : CSE_E---1.7
% 1.83/1.87 % Problem : theBenchmark.p
% 1.83/1.87 % SZS status Unsatisfiable for theBenchmark.p
% 1.83/1.87 % SZS output start CNFRefutation
% See solution above
% 1.83/1.88 % Total time : 1.371s
%------------------------------------------------------------------------------