%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC421-1 : 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 : n001.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 05:19:36 PM UTC 2026
% Result : Unsatisfiable 1.62s 1.83s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of clauses : 62 ( 18 unt; 8 nHn; 60 RR)
% Number of literals : 196 ( 61 equ; 137 neg)
% Maximal clause size : 12 ( 3 avg)
% Maximal term depth : 4 ( 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 : 68 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_8,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk2
| app(app(X3,cons(X1,nil)),X2) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
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(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(co1_11,negated_conjecture,
( sk4 = X1
| ~ neq(sk4,nil)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| tl(sk3) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(sk3) != X4
| ~ neq(nil,sk3)
| ~ neq(nil,sk3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_7,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause116,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
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(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause100,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(co1_10,negated_conjecture,
( neq(sk3,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
cnf(clause76,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause115,axiom,
( X1 != X2
| ~ neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause115) ).
cnf(c_0_21,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk2
| app(app(X3,cons(X1,nil)),X2) != sk1 ),
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,
( app(app(X1,cons(X2,nil)),X3) != sk3
| app(app(X3,cons(X2,nil)),X1) != sk4
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_25,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
clause101 ).
cnf(c_0_26,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_27,negated_conjecture,
( app(app(X1,X2),X3) != sk3
| app(app(X3,X2),X1) != sk4
| ~ singletonP(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_28,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_29,axiom,
ssList(nil),
clause8 ).
cnf(c_0_30,negated_conjecture,
( sk4 = X1
| ~ neq(sk4,nil)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| tl(sk3) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(sk3) != X4
| ~ neq(nil,sk3)
| ~ neq(nil,sk3) ),
co1_11 ).
cnf(c_0_31,negated_conjecture,
neq(sk2,nil),
co1_7 ).
cnf(c_0_32,negated_conjecture,
( app(app(X1,X2),nil) != sk4
| app(X2,X1) != sk3
| ~ singletonP(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_33,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_34,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_35,negated_conjecture,
( sk4 = X1
| tl(sk3) != X2
| hd(sk3) != X4
| app(X2,X3) != X1
| cons(X4,nil) != X3
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ neq(nil,sk3)
| ~ neq(sk4,nil) ),
inference(cn,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
neq(sk4,nil),
inference(rw,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_37,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause116 ).
cnf(c_0_38,negated_conjecture,
( app(X1,X2) != sk4
| app(X2,X1) != sk3
| ~ singletonP(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( app(tl(sk3),cons(hd(sk3),nil)) = sk4
| ~ neq(nil,sk3)
| ~ ssItem(hd(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(tl(sk3)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])])])])])]),c_0_34]) ).
cnf(c_0_40,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_41,negated_conjecture,
( app(cons(hd(sk3),nil),tl(sk3)) != sk3
| ~ neq(nil,sk3)
| ~ ssItem(hd(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(tl(sk3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_42,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_43,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_44,negated_conjecture,
( cons(hd(sk3),tl(sk3)) != sk3
| ~ neq(nil,sk3)
| ~ ssItem(hd(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(tl(sk3)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_46,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_43,c_0_22]) ).
cnf(c_0_47,negated_conjecture,
( sk3 = nil
| ~ neq(nil,sk3)
| ~ ssItem(hd(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(tl(sk3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
cnf(c_0_48,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_49,negated_conjecture,
( sk3 = nil
| ~ neq(nil,sk3)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_29])]) ).
cnf(c_0_50,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_51,negated_conjecture,
( sk3 = nil
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_29]),c_0_46])]) ).
cnf(c_0_52,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_53,negated_conjecture,
( neq(sk3,nil)
| ~ neq(sk4,nil) ),
co1_10 ).
cnf(c_0_54,negated_conjecture,
( sk3 = nil
| ~ ssItem(hd(sk3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_46])]) ).
cnf(c_0_55,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_56,axiom,
( X1 != X2
| ~ neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause115 ).
cnf(c_0_57,negated_conjecture,
neq(sk3,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_36])]) ).
cnf(c_0_58,negated_conjecture,
sk3 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_46])]) ).
cnf(c_0_59,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_60,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWC421-1 : TPTP v9.2.1. Released v2.4.0.
% 0.11/0.13 % 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
% 0.17/0.35 % Computer : n001.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue May 5 04:50:48 EDT 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.36 % start to proof: theBenchmark
% 1.62/1.83 % Version : CSE_E---1.7
% 1.62/1.83 % Problem : theBenchmark.p
% 1.62/1.83 % SZS status Unsatisfiable for theBenchmark.p
% 1.62/1.83 % SZS output start CNFRefutation
% See solution above
% 1.62/1.83 % Total time : 1.377s
%------------------------------------------------------------------------------