%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC005-1 : 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 : 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 05:17:51 PM UTC 2026
% Result : Unsatisfiable 1.12s 1.87s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of clauses : 53 ( 17 unt; 12 nHn; 53 RR)
% Number of literals : 143 ( 51 equ; 88 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 46 ( 0 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_11,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X1,X2),X3) != sk2
| app(X1,X3) != sk1
| ~ neq(X2,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
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_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(clause100,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(co1_12,negated_conjecture,
( sk3 = X1
| ~ ssList(X1)
| tl(sk4) != X1
| ~ 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(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
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(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause99,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
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_17,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_18,negated_conjecture,
neq(sk2,nil),
c_0_17 ).
cnf(c_0_19,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_20,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X1,X2),X3) != sk2
| app(X1,X3) != sk1
| ~ neq(X2,nil)
| ~ neq(sk4,nil) ),
co1_11 ).
cnf(c_0_21,negated_conjecture,
neq(sk4,nil),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( app(app(X1,X2),X3) != sk4
| app(X1,X3) != sk1
| ~ neq(X2,nil)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_19]),c_0_21])]) ).
cnf(c_0_23,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_24,axiom,
ssList(nil),
clause8 ).
cnf(c_0_25,negated_conjecture,
( app(nil,X1) != sk1
| app(X2,X1) != sk4
| ~ neq(X2,nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_26,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_27,negated_conjecture,
( app(X1,sk1) != sk4
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23])]),c_0_26])]) ).
cnf(c_0_28,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_29,negated_conjecture,
( sk3 = X1
| ~ ssList(X1)
| tl(sk4) != X1
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
co1_12 ).
cnf(c_0_30,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_31,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_32,negated_conjecture,
( nil = X1
| app(X1,sk1) != sk4
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24])]) ).
cnf(c_0_33,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_34,negated_conjecture,
( tl(sk4) = sk1
| ~ neq(nil,sk4)
| ~ ssList(tl(sk4)) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_21])])]) ).
cnf(c_0_35,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_36,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_37,negated_conjecture,
( cons(X1,nil) = nil
| cons(X1,sk1) != sk4
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_26])]) ).
cnf(c_0_38,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_39,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_40,negated_conjecture,
( tl(sk4) = sk1
| sk4 = nil
| ~ neq(nil,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_41,negated_conjecture,
( cons(X1,nil) = nil
| cons(X1,sk1) != sk4
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_24])]) ).
cnf(c_0_42,negated_conjecture,
( cons(hd(sk4),sk1) = sk4
| sk4 = nil
| ~ neq(nil,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_36])]) ).
cnf(c_0_43,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_44,negated_conjecture,
( cons(hd(sk4),nil) = nil
| sk4 = nil
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
( sk4 = nil
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_24])]) ).
cnf(c_0_46,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_47,negated_conjecture,
( sk4 = nil
| ~ neq(nil,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_36])]) ).
cnf(c_0_48,axiom,
( X1 != X2
| ~ neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause115 ).
cnf(c_0_49,negated_conjecture,
sk4 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_28]),c_0_24]),c_0_36])]) ).
cnf(c_0_50,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_51,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_21,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.23 % Problem : SWC005-1 : TPTP v9.2.1. Released v2.4.0.
% 0.03/0.23 % 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
% 0.13/0.45 % Computer : n007.cluster.edu
% 0.13/0.45 % Model : x86_64 x86_64
% 0.13/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.45 % Memory : 8042.1875MB
% 0.13/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.45 % CPULimit : 300
% 0.13/0.45 % WCLimit : 300
% 0.13/0.45 % DateTime : Tue May 5 04:13:09 EDT 2026
% 0.13/0.45 % CPUTime :
% 0.13/0.46 % start to proof: theBenchmark
% 1.12/1.87 % Version : CSE_E---1.7
% 1.12/1.87 % Problem : theBenchmark.p
% 1.12/1.87 % SZS status Unsatisfiable for theBenchmark.p
% 1.12/1.87 % SZS output start CNFRefutation
% See solution above
% 1.12/1.87 % Total time : 1.389s
%------------------------------------------------------------------------------