%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC018+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:56:33 AM UTC 2026
% Result : Theorem 53.29s 8.11s
% Output : CNFRefutation 53.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 71 ( 19 unt; 0 def)
% Number of atoms : 280 ( 98 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 335 ( 126 ~; 126 |; 60 &)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 32 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('theBenchmark.p',ax5) ).
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax40,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( frontsegP(V,W)
& frontsegP(U,V) )
=> frontsegP(U,W) ) ) ) ),
file('theBenchmark.p',ax40) ).
fof(ax42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('theBenchmark.p',ax42) ).
fof(ax46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> nil = U ) ),
file('theBenchmark.p',ax46) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ? [X3] :
( frontsegP(U,X3)
& frontsegP(V,X3)
& neq(X3,nil)
& ssList(X3) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(W)
| app(W,Y) != X ) )
| U != W
| V != X ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ? [X3] :
( frontsegP(U,X3)
& frontsegP(V,X3)
& neq(X3,nil)
& ssList(X3) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(W)
| app(W,Y) != X ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [X3] :
( ~ frontsegP(U,X3)
| ~ frontsegP(V,X3)
| ~ neq(X3,nil)
| ~ ssList(X3) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(Z,nil)) != W
| ~ ssList(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(W)
& app(W,Y) = X
& ssList(Y) )
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg_sk,plain,
( ( ( ! [X3] :
( ~ frontsegP(sK0,X3)
| ~ frontsegP(sK1,X3)
| ~ neq(X3,nil)
| ~ ssList(X3) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( nil != sK3
| nil = sK2 )
& ! [Z] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(Z,nil)) != sK3
| ~ ssList(X2) )
| app(cons(Z,nil),X1) != sK4
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(sK3)
& app(sK3,sK4) = sK2
& ssList(sK4)
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK2,sK4]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK2),skolemize(Y,sK4)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0] :
( ~ frontsegP(sK0,VAR_0)
| ~ frontsegP(sK1,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil != sK0 )
& ( neq(sK1,nil)
| nil != sK0 )
& ! [VAR_0] :
( ~ frontsegP(sK0,VAR_0)
| ~ frontsegP(sK1,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sK1 )
& ( neq(sK1,nil)
| nil = sK1 )
& ( nil != sK3
| nil = sK2 )
& ! [VAR_0,VAR_1,VAR_2] :
( app(VAR_2,cons(VAR_0,nil)) != sK3
| ~ ssList(VAR_2)
| app(cons(VAR_0,nil),VAR_1) != sK4
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& equalelemsP(sK3)
& app(sK3,sK4) = sK2
& ssList(sK4)
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_194,negated_conjecture,
( neq(sK1,nil)
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( neq(sK1,nil)
| sK0 != nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_196,negated_conjecture,
( ~ frontsegP(sK0,A)
| ~ frontsegP(sK1,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
( ~ frontsegP(sK0,A)
| ~ frontsegP(sK1,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sK1 = nil ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_200,negated_conjecture,
( nil != sK3
| nil = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_15474,negated_conjecture,
( nil != sK3
| sK2 = nil ),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_201,negated_conjecture,
( sK3 != nil
| sK2 = nil ),
inference(copy,[status(thm)],[c_15474]) ).
cnf(c_203,negated_conjecture,
app(sK3,sK4) = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_204,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_206,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_207,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_208,negated_conjecture,
ssList(sK1),
inference(paramod,[status(thm)],[c_206,c_207]) ).
cnf(c_209,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_210,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_205,c_209]) ).
cnf(c_265,plain,
( nil != A
| frontsegP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax46]) ).
cnf(c_266,plain,
( nil = A
| ~ frontsegP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax46]) ).
cnf(c_272,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax42]) ).
cnf(c_274,plain,
( frontsegP(A,C)
| ~ frontsegP(B,C)
| ~ frontsegP(A,B)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax40]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_306,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_308,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_309,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_333,plain,
( app(B,C) != A
| ~ ssList(C)
| frontsegP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_15475,negated_conjecture,
app(sK0,sK4) = sK2,
inference(paramod,[status(thm)],[c_205,c_203]) ).
cnf(c_559,negated_conjecture,
app(sK0,sK4) = sK1,
inference(paramod,[status(thm)],[c_206,c_15475]) ).
cnf(c_15476,negated_conjecture,
( sK3 != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_206,c_201]) ).
cnf(c_561,negated_conjecture,
( sK0 != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_205,c_15476]) ).
cnf(c_15477,plain,
( A != A
| ~ neq(A,A)
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_309]) ).
cnf(c_603,plain,
( ~ neq(A,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_15477]) ).
cnf(c_3501,plain,
( ~ frontsegP(sK0,sK0)
| ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_210,c_197]) ).
cnf(c_15478,negated_conjecture,
( nil != sK1
| frontsegP(nil,sK1) ),
inference(resolve,[status(thm)],[c_265,c_208]) ).
cnf(c_4578,negated_conjecture,
( sK1 != nil
| frontsegP(nil,sK1) ),
inference(copy,[status(thm)],[c_15478]) ).
cnf(c_15479,negated_conjecture,
( nil = sK0
| ~ frontsegP(nil,sK0) ),
inference(resolve,[status(thm)],[c_266,c_210]) ).
cnf(c_4581,negated_conjecture,
( sK0 = nil
| ~ frontsegP(nil,sK0) ),
inference(copy,[status(thm)],[c_15479]) ).
cnf(c_4635,plain,
frontsegP(sK0,sK0),
inference(resolve,[status(thm)],[c_272,c_210]) ).
cnf(c_4639,plain,
( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_4635,c_3501]) ).
cnf(c_15480,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_308,c_210]) ).
cnf(c_5503,negated_conjecture,
( sK0 = A
| neq(sK0,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_15480]) ).
cnf(c_15481,negated_conjecture,
( ~ ssList(sK4)
| frontsegP(sK1,sK0)
| ~ ssList(sK0)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_559,c_333]) ).
cnf(c_15482,negated_conjecture,
( ~ ssList(sK4)
| frontsegP(sK1,sK0)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_208,c_15481]) ).
cnf(c_15483,negated_conjecture,
( ~ ssList(sK4)
| frontsegP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_210,c_15482]) ).
cnf(c_12073,negated_conjecture,
frontsegP(sK1,sK0),
inference(resolve,[status(thm)],[c_204,c_15483]) ).
cnf(c_12075,plain,
( ~ neq(sK0,nil)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_12073,c_4639]) ).
cnf(c_12259,plain,
~ neq(nil,nil),
inference(resolve,[status(thm)],[c_603,c_306]) ).
cnf(c_15484,plain,
( frontsegP(A,sK0)
| ~ frontsegP(A,sK1)
| ~ ssList(sK0)
| ~ ssList(sK1)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_12073,c_274]) ).
cnf(c_15485,negated_conjecture,
( frontsegP(A,sK0)
| ~ frontsegP(A,sK1)
| ~ ssList(sK0)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_208,c_15484]) ).
cnf(c_14887,negated_conjecture,
( frontsegP(A,sK0)
| ~ frontsegP(A,sK1)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_210,c_15485]) ).
cnf(c_14910,plain,
( sK0 = nil
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_5503,c_306]) ).
cnf(c_14914,plain,
( sK1 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_14910,c_12075]) ).
cnf(c_14917,plain,
( frontsegP(nil,sK1)
| sK0 = nil ),
inference(resolve,[status(thm)],[c_14914,c_4578]) ).
cnf(c_15486,plain,
( sK0 = nil
| frontsegP(nil,sK0)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_14887,c_14917]) ).
cnf(c_15422,plain,
( sK0 = nil
| frontsegP(nil,sK0) ),
inference(resolve,[status(thm)],[c_306,c_15486]) ).
cnf(c_15487,plain,
( sK0 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_15422,c_4581]) ).
cnf(c_15436,plain,
sK0 = nil,
inference(copy,[status(thm)],[c_15487]) ).
cnf(c_15488,negated_conjecture,
( nil != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_15436,c_561]) ).
cnf(c_15468,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_15488]) ).
cnf(c_15489,negated_conjecture,
( neq(sK1,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_15436,c_195]) ).
cnf(c_15490,negated_conjecture,
( neq(nil,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_15468,c_15489]) ).
cnf(c_15491,negated_conjecture,
neq(nil,nil),
inference(copy,[status(thm)],[c_15490]) ).
cnf(c_15473,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_12259,c_15491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC018+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n003.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 12:06:24 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 2820443 was started by sandbox on n003,
% 0.15/0.43 % Sat Sep 26 12:06:24 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.22/0.47
% 0.22/0.47 % From the command line: assign(max_seconds, 300).
% 53.29/8.11
% 53.29/8.11 % given #500 (I,wt=49): 708 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,D)) != A | C != B | ssItem(f34(A)). [factor(370,d,f)].
% 53.29/8.11
% 53.29/8.11 % given #1000 (I,wt=67): 1239 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(D,cons(B,D)),cons(C,A)) != A | C != B | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(733,d,e)].
% 53.29/8.11
% 53.29/8.11 % given #1500 (A,wt=76): 1671 -ssList(app(app(A,cons(B,A)),cons(C,D))) | -lt(f19(app(app(A,cons(B,A)),cons(C,D))),f18(app(app(A,cons(B,A)),cons(C,D)))) | -ssItem(B) | -ssItem(C) | -ssList(A) | -ssList(D) | lt(B,C) | lt(C,B). [factor(1669,e,f)].
% 53.29/8.11
% 53.29/8.11 % SZS status Theorem for theBenchmark
% 53.29/8.11
% 53.29/8.11 % Proof 1 at 6.86 (+ 0.68) seconds.
% 53.29/8.11 % Length of proof is 48.
% 53.29/8.11 % Level of proof is 11.
% 53.29/8.11 % Maximum clause weight is 24.000.
% 53.29/8.11 % Given clauses 1649.
% 53.29/8.11
% 53.29/8.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------