%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC112+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 08:56:52 AM UTC 2026
% Result : Theorem 34.26s 26.03s
% Output : CNFRefutation 34.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 19 unt; 0 def)
% Number of atoms : 274 ( 101 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 337 ( 121 ~; 118 |; 78 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 41 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('theBenchmark.p',ax7) ).
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('theBenchmark.p',ax58) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ( segmentP(V,U)
& neq(U,nil) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( lt(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ strictorderedP(W)
| app(app(Y,W),Z) != 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)
=> ( ( ( ( segmentP(V,U)
& neq(U,nil) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( lt(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ strictorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( nil != W
| nil = X )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != W
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != Z
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ lt(X1,X3)
| app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& strictorderedP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& 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,
( ( ( ( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( nil != sK3
| nil = sK2 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != sK3
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != sK5
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ lt(X1,X3)
| app(cons(X3,nil),X4) != sK3
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != sK4
| ~ ssList(X2) )
| ~ ssItem(X1) )
& strictorderedP(sK3)
& app(app(sK4,sK3),sK5) = sK2
& ssList(sK5)
& 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,sK5]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK2),skolemize(Y,sK4),skolemize(Z,sK5)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil)
| nil != sK0 )
& ( neq(sK1,nil)
| nil != sK0 )
& ( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil)
| nil = sK1 )
& ( neq(sK1,nil)
| nil = sK1 )
& ( nil != sK3
| nil = sK2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ lt(VAR_2,VAR_0)
| app(VAR_3,cons(VAR_2,nil)) != sK3
| ~ ssList(VAR_3)
| ~ ssItem(VAR_2)
| app(cons(VAR_0,nil),VAR_1) != sK5
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ lt(VAR_0,VAR_2)
| app(cons(VAR_2,nil),VAR_3) != sK3
| ~ ssList(VAR_3)
| ~ ssItem(VAR_2)
| app(VAR_1,cons(VAR_0,nil)) != sK4
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& strictorderedP(sK3)
& app(app(sK4,sK3),sK5) = sK2
& ssList(sK5)
& 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_192,negated_conjecture,
( neq(sK1,nil)
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( neq(sK1,nil)
| sK0 != nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_194,negated_conjecture,
( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil)
| sK1 = nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_198,negated_conjecture,
( nil != sK3
| nil = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_15026,negated_conjecture,
( nil != sK3
| sK2 = nil ),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_199,negated_conjecture,
( sK3 != nil
| sK2 = nil ),
inference(copy,[status(thm)],[c_15026]) ).
cnf(c_203,negated_conjecture,
app(app(sK4,sK3),sK5) = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_204,negated_conjecture,
ssList(sK5),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
ssList(sK4),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_206,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_207,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_208,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_209,negated_conjecture,
ssList(sK1),
inference(paramod,[status(thm)],[c_207,c_208]) ).
cnf(c_210,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_211,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_206,c_210]) ).
cnf(c_253,plain,
( nil = A
| ~ segmentP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax58]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_307,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_309,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_310,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_327,plain,
( app(app(C,B),D) != A
| ~ ssList(D)
| ~ ssList(C)
| segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax7]) ).
cnf(c_15027,negated_conjecture,
app(app(sK4,sK0),sK5) = sK2,
inference(paramod,[status(thm)],[c_206,c_203]) ).
cnf(c_558,negated_conjecture,
app(app(sK4,sK0),sK5) = sK1,
inference(paramod,[status(thm)],[c_207,c_15027]) ).
cnf(c_15028,negated_conjecture,
( sK3 != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_207,c_199]) ).
cnf(c_562,negated_conjecture,
( sK0 != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_206,c_15028]) ).
cnf(c_15029,plain,
( A != A
| ~ neq(A,A)
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_310]) ).
cnf(c_603,plain,
( ~ neq(A,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_15029]) ).
cnf(c_15030,negated_conjecture,
( nil = sK0
| ~ segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_253,c_211]) ).
cnf(c_5319,negated_conjecture,
( sK0 = nil
| ~ segmentP(nil,sK0) ),
inference(copy,[status(thm)],[c_15030]) ).
cnf(c_15031,negated_conjecture,
( A = sK0
| neq(sK0,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_309,c_211]) ).
cnf(c_6455,negated_conjecture,
( sK0 = A
| neq(sK0,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_15031]) ).
cnf(c_15032,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK1,sK0)
| ~ ssList(sK0)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_558,c_327]) ).
cnf(c_15033,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK1,sK0)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_209,c_15032]) ).
cnf(c_15034,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_211,c_15033]) ).
cnf(c_15035,negated_conjecture,
( ~ ssList(sK5)
| segmentP(sK1,sK0) ),
inference(resolve,[status(thm)],[c_205,c_15034]) ).
cnf(c_11701,negated_conjecture,
segmentP(sK1,sK0),
inference(resolve,[status(thm)],[c_204,c_15035]) ).
cnf(c_11711,negated_conjecture,
( ~ neq(sK0,nil)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_11701,c_195]) ).
cnf(c_11949,plain,
~ neq(nil,nil),
inference(resolve,[status(thm)],[c_603,c_307]) ).
cnf(c_14874,plain,
( sK0 = nil
| neq(sK0,nil) ),
inference(resolve,[status(thm)],[c_6455,c_307]) ).
cnf(c_14878,plain,
( sK1 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_14874,c_11711]) ).
cnf(c_14918,plain,
( segmentP(nil,sK0)
| sK0 = nil ),
inference(paramod,[status(thm)],[c_14878,c_11701]) ).
cnf(c_15036,plain,
( sK0 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_14918,c_5319]) ).
cnf(c_14957,plain,
sK0 = nil,
inference(copy,[status(thm)],[c_15036]) ).
cnf(c_15037,negated_conjecture,
( nil != nil
| sK1 = nil ),
inference(paramod,[status(thm)],[c_14957,c_562]) ).
cnf(c_15018,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_15037]) ).
cnf(c_15038,negated_conjecture,
( neq(sK1,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_14957,c_193]) ).
cnf(c_15039,negated_conjecture,
( neq(nil,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_15018,c_15038]) ).
cnf(c_15040,negated_conjecture,
neq(nil,nil),
inference(copy,[status(thm)],[c_15039]) ).
cnf(c_15025,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_11949,c_15040]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC112+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.15/21.11 % CPULimit : 300
% 0.15/21.11 % WCLimit : 300
% 0.15/21.11 % DateTime : Sat Sep 26 12:16:44 UTC 2026
% 0.15/21.11 % CPUTime :
% 0.15/21.12 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/21.12 % Process 558931 was started by sandbox2 on n012,
% 0.15/21.12 % Sat Sep 26 12:16:44 2026
% 0.15/21.12 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/21.13
% 0.15/21.13 % From the command line: assign(max_seconds, 300).
% 34.26/26.03
% 34.26/26.03 % given #500 (I,wt=52): 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(371,d,f)].
% 34.26/26.03
% 34.26/26.03 % given #1000 (I,wt=73): 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)].
% 34.26/26.03
% 34.26/26.03 % given #1500 (A,wt=70): 1691 -ssList(app(app(A,cons(B,A)),cons(C,D))) | ssList(f22(app(app(A,cons(B,A)),cons(C,D)))) | -ssItem(B) | -ssItem(C) | -ssList(A) | -ssList(D) | lt(B,C) | lt(C,B). [factor(1689,e,f)].
% 34.26/26.03
% 34.26/26.03 % SZS status Theorem for theBenchmark
% 34.26/26.03
% 34.26/26.03 % Proof 1 at 4.42 (+ 0.44) seconds.
% 34.26/26.03 % Length of proof is 38.
% 34.26/26.03 % Level of proof is 9.
% 34.26/26.03 % Maximum clause weight is 38.000.
% 34.26/26.03 % Given clauses 1536.
% 34.26/26.03
% 34.26/26.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------