%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC316-1 : 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 05:19:10 PM UTC 2026
% Result : Unsatisfiable 1.32s 1.71s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of clauses : 53 ( 20 unt; 3 nHn; 53 RR)
% Number of literals : 144 ( 48 equ; 98 neg)
% Maximal clause size : 13 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 44 ( 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_16,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
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(co1_14,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_15,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
cnf(co1_18,negated_conjecture,
( ~ ssList(X1)
| sk2 != X1
| ~ ssList(X2)
| ~ ssList(X3)
| tl(sk1) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(sk1) != X4
| ~ neq(nil,sk1)
| ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
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(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(co1_17,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
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(clause98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
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(c_0_18,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_19,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk3
| ~ neq(sk4,nil) ),
co1_16 ).
cnf(c_0_20,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_21,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_22,negated_conjecture,
neq(sk2,nil),
c_0_18 ).
cnf(c_0_23,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
co1_14 ).
cnf(c_0_24,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
co1_15 ).
cnf(c_0_25,negated_conjecture,
( ~ ssList(X1)
| sk2 != X1
| ~ ssList(X2)
| ~ ssList(X3)
| tl(sk1) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(sk1) != X4
| ~ neq(nil,sk1)
| ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ neq(sk4,nil) ),
co1_18 ).
cnf(c_0_26,negated_conjecture,
app(cons(sk5,nil),sk6) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_27,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_28,negated_conjecture,
ssItem(sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_21]),c_0_22])]) ).
cnf(c_0_29,negated_conjecture,
ssList(sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_21]),c_0_22])]) ).
cnf(c_0_30,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_31,negated_conjecture,
( sk2 != X1
| tl(sk1) != X2
| hd(sk1) != X4
| app(X2,X3) != X1
| cons(X4,nil) != X3
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ neq(sk4,nil) ),
inference(cn,[status(thm)],[c_0_25]) ).
cnf(c_0_32,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_33,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_34,negated_conjecture,
cons(sk5,sk6) = sk1,
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_35,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_36,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk4
| ~ neq(sk4,nil) ),
co1_17 ).
cnf(c_0_37,negated_conjecture,
( cons(sk5,nil) = nil
| sk1 != nil
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_26]),c_0_29])]) ).
cnf(c_0_38,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_39,axiom,
ssList(nil),
clause8 ).
cnf(c_0_40,negated_conjecture,
( app(tl(sk1),cons(hd(sk1),nil)) != sk2
| ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ ssItem(hd(sk1))
| ~ ssList(cons(hd(sk1),nil))
| ~ ssList(tl(sk1)) ),
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)],[inference(rw,[status(thm)],[c_0_31,c_0_21]),c_0_22])])])])])]),c_0_32]) ).
cnf(c_0_41,negated_conjecture,
tl(sk1) = sk6,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_28]),c_0_29])]) ).
cnf(c_0_42,negated_conjecture,
hd(sk1) = sk5,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_34]),c_0_28]),c_0_29])]) ).
cnf(c_0_43,negated_conjecture,
app(sk6,cons(sk5,nil)) = sk2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_21]),c_0_21]),c_0_22])]) ).
cnf(c_0_44,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_45,negated_conjecture,
( cons(sk5,nil) = nil
| sk1 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_28]),c_0_39])]) ).
cnf(c_0_46,negated_conjecture,
( ~ neq(nil,sk1)
| ~ neq(sk1,nil)
| ~ ssList(cons(sk5,nil)) ),
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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_41]),c_0_29])]),c_0_42]),c_0_43]),c_0_42]),c_0_28]),c_0_42])]) ).
cnf(c_0_47,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_48,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_49,negated_conjecture,
sk1 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_28]),c_0_39])]) ).
cnf(c_0_50,negated_conjecture,
( ~ neq(nil,sk1)
| ~ ssList(cons(sk5,nil)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_39])]),c_0_49]) ).
cnf(c_0_51,negated_conjecture,
~ ssList(cons(sk5,nil)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_47]),c_0_39]),c_0_48])]),c_0_49]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_38]),c_0_28]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC316-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % 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
% 0.14/0.31 % Computer : n001.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Tue May 5 04:44:33 EDT 2026
% 0.14/0.31 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.32/1.71 % Version : CSE_E---1.7
% 1.32/1.71 % Problem : theBenchmark.p
% 1.32/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.32/1.71 % SZS output start CNFRefutation
% See solution above
% 1.32/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------