%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC028+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 08:56:35 AM UTC 2026
% Result : Theorem 9.16s 2.04s
% Output : CNFRefutation 9.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 11 unt; 0 def)
% Number of atoms : 189 ( 104 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 212 ( 75 ~; 84 |; 38 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 22 ( 0 sgn 13 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax48,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( rearsegP(V,U)
& rearsegP(U,V) )
=> U = V ) ) ),
file('theBenchmark.p',ax48) ).
fof(ax51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('theBenchmark.p',ax51) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( nil = V
| nil != U )
& ( nil = U
| nil != V ) )
| 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)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( nil = V
| nil != U )
& ( nil = U
| nil != V ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_90,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( rearsegP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ( ( nil != V
& nil = U )
| ( nil != U
& nil = V ) )
& 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,
( ( ( rearsegP(sK0,sK1)
& neq(sK1,nil) )
| ( nil = sK1
& nil = sK0 ) )
& ( ( nil != sK3
& nil = sK2 )
| ( nil != sK2
& nil = sK3 ) )
& sK1 = sK2
& sK0 = sK3
& ssList(sK0)
& ssList(sK1)
& ssList(sK3)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK1,sK0]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK1),skolemize(X,sK0)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( rearsegP(sK0,sK1)
| nil = sK1 )
& ( neq(sK1,nil)
| nil = sK1 )
& ( rearsegP(sK0,sK1)
| nil = sK0 )
& ( neq(sK1,nil)
| nil = sK0 )
& ( nil != sK3
| nil != sK2 )
& ( nil = sK2
| nil = sK3 )
& sK1 = sK2
& sK0 = sK3
& ssList(sK0)
& ssList(sK1)
& ssList(sK3)
& ssList(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_92,negated_conjecture,
( neq(sK1,nil)
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_233,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_276,plain,
( B = A
| ~ rearsegP(B,A)
| ~ rearsegP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax48]) ).
cnf(c_279,plain,
( rearsegP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax51]) ).
cnf(c_329,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_330,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
sK0 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
sK1 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_335,negated_conjecture,
( nil = sK2
| nil = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2452,negated_conjecture,
( nil = sK2
| sK3 = nil ),
inference(copy,[status(thm)],[c_335]) ).
cnf(c_336,negated_conjecture,
( sK2 = nil
| sK3 = nil ),
inference(copy,[status(thm)],[c_2452]) ).
cnf(c_337,negated_conjecture,
( nil != sK3
| nil != sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2453,negated_conjecture,
( nil != sK3
| sK2 != nil ),
inference(copy,[status(thm)],[c_337]) ).
cnf(c_338,negated_conjecture,
( sK3 != nil
| sK2 != nil ),
inference(copy,[status(thm)],[c_2453]) ).
cnf(c_341,negated_conjecture,
( rearsegP(sK0,sK1)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2454,negated_conjecture,
( rearsegP(sK0,sK1)
| nil = sK2 ),
inference(paramod,[status(thm)],[c_334,c_341]) ).
cnf(c_2455,negated_conjecture,
( rearsegP(sK3,sK1)
| nil = sK2 ),
inference(paramod,[status(thm)],[c_333,c_2454]) ).
cnf(c_2456,negated_conjecture,
( rearsegP(sK3,sK2)
| nil = sK2 ),
inference(paramod,[status(thm)],[c_334,c_2455]) ).
cnf(c_342,negated_conjecture,
( rearsegP(sK3,sK2)
| sK2 = nil ),
inference(copy,[status(thm)],[c_2456]) ).
cnf(c_343,negated_conjecture,
( nil != sK1
| ~ ssList(nil)
| ~ ssList(sK1)
| nil = sK0 ),
inference(resolve,[status(thm)],[c_92,c_90]) ).
cnf(c_2457,negated_conjecture,
( nil != sK1
| ~ ssList(nil)
| ~ ssList(sK1)
| nil = sK3 ),
inference(paramod,[status(thm)],[c_333,c_343]) ).
cnf(c_2458,negated_conjecture,
( nil != sK1
| ~ ssList(nil)
| ~ ssList(sK2)
| nil = sK3 ),
inference(paramod,[status(thm)],[c_334,c_2457]) ).
cnf(c_2459,negated_conjecture,
( nil != sK2
| ~ ssList(nil)
| ~ ssList(sK2)
| nil = sK3 ),
inference(paramod,[status(thm)],[c_334,c_2458]) ).
cnf(c_2460,negated_conjecture,
( nil != sK2
| ~ ssList(nil)
| ~ ssList(sK2)
| sK3 = nil ),
inference(copy,[status(thm)],[c_2459]) ).
cnf(c_2461,negated_conjecture,
( sK2 != nil
| ~ ssList(nil)
| ~ ssList(sK2)
| sK3 = nil ),
inference(copy,[status(thm)],[c_2460]) ).
cnf(c_2462,negated_conjecture,
( sK2 != nil
| ~ ssList(nil)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_329,c_2461]) ).
cnf(c_344,negated_conjecture,
( sK2 != nil
| sK3 = nil ),
inference(resolve,[status(thm)],[c_233,c_2462]) ).
cnf(c_2013,plain,
rearsegP(sK2,nil),
inference(resolve,[status(thm)],[c_329,c_279]) ).
cnf(c_2463,negated_conjecture,
( sK3 = sK2
| ~ rearsegP(sK2,sK3)
| ~ ssList(sK3)
| ~ ssList(sK2)
| sK2 = nil ),
inference(resolve,[status(thm)],[c_342,c_276]) ).
cnf(c_2464,negated_conjecture,
( sK3 = sK2
| ~ rearsegP(sK2,sK3)
| ~ ssList(sK3)
| sK2 = nil ),
inference(resolve,[status(thm)],[c_329,c_2463]) ).
cnf(c_2435,negated_conjecture,
( sK3 = sK2
| ~ rearsegP(sK2,sK3)
| sK2 = nil ),
inference(resolve,[status(thm)],[c_330,c_2464]) ).
cnf(c_2465,negated_conjecture,
( sK3 = nil
| sK3 = nil ),
inference(resolve,[status(thm)],[c_344,c_336]) ).
cnf(c_2443,negated_conjecture,
sK3 = nil,
inference(copy,[status(thm)],[c_2465]) ).
cnf(c_2466,negated_conjecture,
( sK3 = sK2
| ~ rearsegP(sK2,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_2443,c_2435]) ).
cnf(c_2467,negated_conjecture,
( nil = sK2
| ~ rearsegP(sK2,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_2443,c_2466]) ).
cnf(c_2468,negated_conjecture,
( sK2 = nil
| ~ rearsegP(sK2,nil)
| sK2 = nil ),
inference(copy,[status(thm)],[c_2467]) ).
cnf(c_2469,negated_conjecture,
( ~ rearsegP(sK2,nil)
| sK2 = nil ),
inference(copy,[status(thm)],[c_2468]) ).
cnf(c_2450,negated_conjecture,
sK2 = nil,
inference(resolve,[status(thm)],[c_2013,c_2469]) ).
cnf(c_2470,negated_conjecture,
( sK3 != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_2450,c_338]) ).
cnf(c_2471,negated_conjecture,
( nil != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_2443,c_2470]) ).
cnf(c_2472,negated_conjecture,
nil != nil,
inference(copy,[status(thm)],[c_2471]) ).
cnf(c_2451,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_2472]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC028+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 12:07:25 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2822858 was started by sandbox on n003,
% 0.10/0.36 % Sat Sep 26 12:07:25 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 9.16/2.04
% 9.16/2.04 % SZS status Theorem for theBenchmark
% 9.16/2.04
% 9.16/2.04 % Proof 1 at 1.08 (+ 0.11) seconds.
% 9.16/2.04 % Length of proof is 26.
% 9.16/2.04 % Level of proof is 6.
% 9.16/2.04 % Maximum clause weight is 15.000.
% 9.16/2.04 % Given clauses 165.
% 9.16/2.04
% 9.16/2.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------