%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC277+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 : n019.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 08:57:21 AM UTC 2026
% Result : Theorem 174.80s 23.83s
% Output : CNFRefutation 174.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 27 unt; 0 def)
% Number of atoms : 186 ( 43 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 192 ( 75 ~; 73 |; 26 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 23 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('theBenchmark.p',ax4) ).
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('theBenchmark.p',ax54) ).
fof(ax57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('theBenchmark.p',ax57) ).
fof(ax65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('theBenchmark.p',ax65) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ~ singletonP(W) )
| totalorderedP(U)
| ~ segmentP(X,W)
| 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)
=> ( ( neq(X,nil)
& ~ singletonP(W) )
| totalorderedP(U)
| ~ segmentP(X,W)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| singletonP(W) )
& ~ totalorderedP(U)
& segmentP(X,W)
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK1,nil)
| singletonP(sK0) )
& ~ totalorderedP(sK2)
& segmentP(sK1,sK0)
& sK0 = sK2
& sK1 = sK3
& ssList(sK1)
& ssList(sK0)
& ssList(sK3)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK0,sK1]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK0),skolemize(X,sK1)],[nnf_87]) ).
cnf(c_190,negated_conjecture,
( ~ neq(sK1,nil)
| singletonP(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
~ totalorderedP(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
segmentP(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
sK0 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_194,c_195]) ).
cnf(c_197,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
ssList(sK2),
inference(paramod,[status(thm)],[c_193,c_197]) ).
fof(ax66,axiom,
totalorderedP(nil),
file('theBenchmark.p',ax66) ).
cnf(c_237,plain,
totalorderedP(nil),
inference(clausify,[status(thm)],[ax66]) ).
cnf(c_238,plain,
( totalorderedP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax65]) ).
cnf(c_241,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax57]) ).
cnf(c_244,plain,
( B = A
| ~ segmentP(B,A)
| ~ segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax54]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_294,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_296,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_297,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
fof(nnf_4,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [X0] :
( cons(X0,nil) = U
& ssItem(X0) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(fof_nnf,[status(thm)],[ax4]) ).
fof(sk_ax4_sk,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4(U),nil) = U
& ssItem(sK4(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4(U))],[nnf_4]) ).
fof(sk_ax4,plain,
( ! [VAR_0,VAR_1] :
( cons(VAR_1,nil) != VAR_0
| ~ ssItem(VAR_1)
| singletonP(VAR_0)
| ~ ssList(VAR_0) )
& ! [VAR_0] :
( cons(sK4(VAR_0),nil) = VAR_0
| ~ singletonP(VAR_0)
| ~ ssList(VAR_0) )
& ! [VAR_0] :
( ssItem(sK4(VAR_0))
| ~ singletonP(VAR_0)
| ~ ssList(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_ax4_sk]) ).
cnf(c_325,plain,
( cons(sK4(A),nil) = A
| ~ singletonP(A)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_326,plain,
( ssItem(sK4(A))
| ~ singletonP(A)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_ax4]) ).
cnf(c_13254,negated_conjecture,
segmentP(sK3,sK0),
inference(paramod,[status(thm)],[c_194,c_192]) ).
cnf(c_543,negated_conjecture,
segmentP(sK3,sK2),
inference(paramod,[status(thm)],[c_193,c_13254]) ).
cnf(c_13255,negated_conjecture,
( ~ neq(sK1,nil)
| singletonP(sK2) ),
inference(paramod,[status(thm)],[c_193,c_190]) ).
cnf(c_544,negated_conjecture,
( ~ neq(sK3,nil)
| singletonP(sK2) ),
inference(paramod,[status(thm)],[c_194,c_13255]) ).
cnf(c_1701,plain,
segmentP(sK2,nil),
inference(resolve,[status(thm)],[c_241,c_198]) ).
cnf(c_13256,plain,
( A = nil
| neq(nil,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_296,c_294]) ).
cnf(c_1757,plain,
( nil = A
| neq(nil,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_13256]) ).
cnf(c_13257,negated_conjecture,
( A = sK3
| neq(sK3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_296,c_196]) ).
cnf(c_1759,negated_conjecture,
( sK3 = A
| neq(sK3,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_13257]) ).
cnf(c_13258,plain,
( sK2 = nil
| ~ segmentP(nil,sK2)
| ~ ssList(sK2)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_1701,c_244]) ).
cnf(c_13259,plain,
( sK2 = nil
| ~ segmentP(nil,sK2)
| ~ ssList(sK2) ),
inference(resolve,[status(thm)],[c_294,c_13258]) ).
cnf(c_4656,negated_conjecture,
( sK2 = nil
| ~ segmentP(nil,sK2) ),
inference(resolve,[status(thm)],[c_198,c_13259]) ).
cnf(c_13260,negated_conjecture,
( nil = sK2
| neq(nil,sK2) ),
inference(resolve,[status(thm)],[c_1757,c_198]) ).
cnf(c_5020,negated_conjecture,
( sK2 = nil
| neq(nil,sK2) ),
inference(copy,[status(thm)],[c_13260]) ).
cnf(c_13261,negated_conjecture,
( nil = sK3
| neq(nil,sK3) ),
inference(resolve,[status(thm)],[c_1757,c_196]) ).
cnf(c_5021,negated_conjecture,
( sK3 = nil
| neq(nil,sK3) ),
inference(copy,[status(thm)],[c_13261]) ).
cnf(c_13262,plain,
( ~ totalorderedP(nil)
| neq(nil,sK2) ),
inference(paramod,[status(thm)],[c_5020,c_191]) ).
cnf(c_5025,plain,
neq(nil,sK2),
inference(resolve,[status(thm)],[c_237,c_13262]) ).
cnf(c_13263,plain,
( sK2 != nil
| ~ ssList(sK2)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_5025,c_297]) ).
cnf(c_13264,plain,
( sK2 != nil
| ~ ssList(sK2) ),
inference(resolve,[status(thm)],[c_294,c_13263]) ).
cnf(c_5027,negated_conjecture,
sK2 != nil,
inference(resolve,[status(thm)],[c_198,c_13264]) ).
cnf(c_5030,negated_conjecture,
~ segmentP(nil,sK2),
inference(resolve,[status(thm)],[c_5027,c_4656]) ).
cnf(c_13265,plain,
( segmentP(nil,sK2)
| neq(nil,sK3) ),
inference(paramod,[status(thm)],[c_5021,c_543]) ).
cnf(c_5052,plain,
neq(nil,sK3),
inference(resolve,[status(thm)],[c_5030,c_13265]) ).
cnf(c_13266,plain,
( sK3 != nil
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_5052,c_297]) ).
cnf(c_13267,plain,
( sK3 != nil
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_294,c_13266]) ).
cnf(c_5054,negated_conjecture,
sK3 != nil,
inference(resolve,[status(thm)],[c_196,c_13267]) ).
cnf(c_13268,plain,
( sK3 = nil
| neq(sK3,nil) ),
inference(resolve,[status(thm)],[c_1759,c_294]) ).
cnf(c_5163,plain,
neq(sK3,nil),
inference(resolve,[status(thm)],[c_5054,c_13268]) ).
cnf(c_5165,negated_conjecture,
singletonP(sK2),
inference(resolve,[status(thm)],[c_5163,c_544]) ).
cnf(c_13269,negated_conjecture,
( ssItem(sK4(sK2))
| ~ ssList(sK2) ),
inference(resolve,[status(thm)],[c_5165,c_326]) ).
cnf(c_5166,negated_conjecture,
ssItem(sK4(sK2)),
inference(resolve,[status(thm)],[c_198,c_13269]) ).
cnf(c_13270,negated_conjecture,
( cons(sK4(sK2),nil) = sK2
| ~ ssList(sK2) ),
inference(resolve,[status(thm)],[c_5165,c_325]) ).
cnf(c_5167,negated_conjecture,
cons(sK4(sK2),nil) = sK2,
inference(resolve,[status(thm)],[c_198,c_13270]) ).
cnf(c_13271,plain,
totalorderedP(cons(sK4(sK2),nil)),
inference(resolve,[status(thm)],[c_5166,c_238]) ).
cnf(c_13272,plain,
totalorderedP(sK2),
inference(paramod,[status(thm)],[c_5167,c_13271]) ).
cnf(c_13253,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_191,c_13272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC277+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 12:40:18 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 1321361 was started by sandbox on n019,
% 0.10/0.38 % Sat Sep 26 12:40:18 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.41
% 0.10/0.41 % From the command line: assign(max_seconds, 300).
% 174.80/23.83
% 174.80/23.83 % given #500 (I,wt=52): 700 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,A)),cons(C,E)) != A | C != B | ssList(f36(A)). [factor(362,a,e)].
% 174.80/23.83
% 174.80/23.83 % given #1000 (I,wt=73): 1225 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(D,cons(B,D)),cons(C,D)) != A | C != B | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(717,d,e)].
% 174.80/23.83
% 174.80/23.83 % given #1500 (T,wt=13): 2868 -ssItem(A) | neq(c1,A) | c1 = A. [resolve(334,a,333,a),flip(c)].
% 174.80/23.83
% 174.80/23.83 % SZS status Theorem for theBenchmark
% 174.80/23.83
% 174.80/23.83 % Proof 1 at 6.28 (+ 0.67) seconds.
% 174.80/23.83 % Length of proof is 42.
% 174.80/23.83 % Level of proof is 12.
% 174.80/23.83 % Maximum clause weight is 25.000.
% 174.80/23.83 % Given clauses 1538.
% 174.80/23.83
% 174.80/23.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------