%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC331+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 : n012.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 08:57:30 AM UTC 2026
% Result : Theorem 47.08s 6.37s
% Output : CNFRefutation 47.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 19 unt; 0 def)
% Number of atoms : 145 ( 43 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 165 ( 55 ~; 48 |; 45 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 25 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('theBenchmark.p',ax28) ).
fof(ax55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('theBenchmark.p',ax55) ).
fof(ax56,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(U,V)
=> segmentP(app(app(W,U),X),V) ) ) ) ) ),
file('theBenchmark.p',ax56) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( equalelemsP(U)
& segmentP(V,U) )
| ( 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)
=> ( ( equalelemsP(U)
& segmentP(V,U) )
| ( 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] :
( ( ~ equalelemsP(U)
| ~ segmentP(V,U) )
& ( 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,
( ( ~ equalelemsP(sK1)
| ~ segmentP(sK0,sK1) )
& ( nil != sK2
| nil = sK4 )
& ! [Z] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(Z,nil)) != sK2
| ~ ssList(X2) )
| app(cons(Z,nil),X1) != sK3
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(sK2)
& app(sK2,sK3) = sK4
& ssList(sK3)
& sK2 = sK1
& sK4 = sK0
& ssList(sK4)
& ssList(sK2)
& ssList(sK0)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2,sK4,sK3]),skolemize(U,sK1),skolemize(V,sK0),skolemize(W,sK2),skolemize(X,sK4),skolemize(Y,sK3)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ equalelemsP(sK1)
| ~ segmentP(sK0,sK1) )
& ( nil != sK2
| nil = sK4 )
& ! [VAR_0,VAR_1,VAR_2] :
( app(VAR_2,cons(VAR_0,nil)) != sK2
| ~ ssList(VAR_2)
| app(cons(VAR_0,nil),VAR_1) != sK3
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& equalelemsP(sK2)
& app(sK2,sK3) = sK4
& ssList(sK3)
& sK2 = sK1
& sK4 = sK0
& ssList(sK4)
& ssList(sK2)
& ssList(sK0)
& ssList(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_169,negated_conjecture,
( ~ equalelemsP(sK1)
| ~ segmentP(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_173,negated_conjecture,
equalelemsP(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_174,negated_conjecture,
app(sK2,sK3) = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_175,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_176,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_177,negated_conjecture,
sK4 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_180,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_181,negated_conjecture,
ssList(sK1),
inference(paramod,[status(thm)],[c_176,c_180]) ).
cnf(c_227,plain,
( segmentP(app(app(C,A),D),B)
| ~ segmentP(A,B)
| ~ ssList(D)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax56]) ).
cnf(c_228,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax55]) ).
cnf(c_265,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax28]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_279,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_4627,negated_conjecture,
app(sK1,sK3) = sK4,
inference(paramod,[status(thm)],[c_176,c_174]) ).
cnf(c_490,negated_conjecture,
app(sK1,sK3) = sK0,
inference(paramod,[status(thm)],[c_177,c_4627]) ).
cnf(c_491,negated_conjecture,
equalelemsP(sK1),
inference(paramod,[status(thm)],[c_176,c_173]) ).
cnf(c_507,plain,
( segmentP(app(app(B,A),C),A)
| ~ segmentP(A,A)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_227]) ).
cnf(c_908,negated_conjecture,
~ segmentP(sK0,sK1),
inference(resolve,[status(thm)],[c_491,c_169]) ).
cnf(c_1652,plain,
segmentP(sK1,sK1),
inference(resolve,[status(thm)],[c_228,c_181]) ).
cnf(c_1673,plain,
app(nil,sK1) = sK1,
inference(resolve,[status(thm)],[c_265,c_181]) ).
cnf(c_4628,negated_conjecture,
( segmentP(app(app(A,sK1),B),sK1)
| ~ segmentP(sK1,sK1)
| ~ ssList(B)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_507,c_181]) ).
cnf(c_4629,negated_conjecture,
( segmentP(app(app(nil,sK1),A),sK1)
| ~ segmentP(sK1,sK1)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_4628,c_279]) ).
cnf(c_4630,negated_conjecture,
( segmentP(app(app(nil,sK1),sK3),sK1)
| ~ segmentP(sK1,sK1) ),
inference(resolve,[status(thm)],[c_4629,c_175]) ).
cnf(c_4631,negated_conjecture,
segmentP(app(app(nil,sK1),sK3),sK1),
inference(resolve,[status(thm)],[c_4630,c_1652]) ).
cnf(c_4632,negated_conjecture,
segmentP(app(sK1,sK3),sK1),
inference(paramod,[status(thm)],[c_1673,c_4631]) ).
cnf(c_4633,negated_conjecture,
segmentP(sK0,sK1),
inference(paramod,[status(thm)],[c_490,c_4632]) ).
cnf(c_4626,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_908,c_4633]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC331+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sat Sep 26 12:48:50 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/0.31 % Process 635027 was started by sandbox on n012,
% 0.05/0.31 % Sat Sep 26 12:48:50 2026
% 0.05/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.05/0.32
% 0.05/0.32 % From the command line: assign(max_seconds, 300).
% 47.08/6.37
% 47.08/6.37 % given #500 (I,wt=57): 685 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,A)),cons(C,E)) != A | lt(B,C) | lt(C,B) | -lt(f19(A),f18(A)). [factor(358,a,e)].
% 47.08/6.37
% 47.08/6.37 % given #1000 (I,wt=56): 1192 -ssList(cons(A,nil)) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(D,cons(B,D)),cons(C,D)) != cons(A,nil) | lt(B,C) | lt(C,B) | -ssItem(A). [factor(696,d,e)].
% 47.08/6.37
% 47.08/6.37 % SZS status Theorem for theBenchmark
% 47.08/6.37
% 47.08/6.37 % Proof 1 at 5.65 (+ 0.12) seconds.
% 47.08/6.37 % Length of proof is 23.
% 47.08/6.37 % Level of proof is 4.
% 47.08/6.37 % Maximum clause weight is 38.000.
% 47.08/6.37 % Given clauses 1329.
% 47.08/6.37
% 47.08/6.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------