%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO498+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 07:18:00 AM UTC 2026
% Result : Theorem 0.10s 0.47s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 4 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 10 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz7_7,axiom,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
file('theBenchmark.p',aSatz7_7) ).
fof(aSatz7_8,conjecture,
! [Xa,Xp,Xr,Xq] :
( Xp = Xq
| s(Xa,Xq) != Xr
| s(Xa,Xp) != Xr ),
file('theBenchmark.p',aSatz7_8) ).
fof(aSatz7_8_neg,negated_conjecture,
~ ! [Xa,Xp,Xr,Xq] :
( Xp = Xq
| s(Xa,Xq) != Xr
| s(Xa,Xp) != Xr ),
inference(assume_negation,[status(cth)],[aSatz7_8]) ).
cnf(c_264,plain,
s(A,s(A,B)) = B,
inference(clausify,[status(thm)],[aSatz7_7]) ).
fof(nnf_107,plain,
? [Xa,Xp,Xr,Xq] :
( Xq != Xp
& s(Xa,Xq) = Xr
& s(Xa,Xp) = Xr ),
inference(fof_nnf,[status(thm)],[aSatz7_8_neg]) ).
fof(sk_aSatz7_8_neg,plain,
( sK3 != sK1
& s(sK0,sK3) = sK2
& s(sK0,sK1) = sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(Xa,sK0),skolemize(Xp,sK1),skolemize(Xr,sK2),skolemize(Xq,sK3)],[nnf_107]) ).
cnf(c_284,negated_conjecture,
s(sK0,sK1) = sK2,
inference(split_conjunct,[status(thm)],[sk_aSatz7_8_neg]) ).
cnf(c_285,negated_conjecture,
s(sK0,sK3) = sK2,
inference(split_conjunct,[status(thm)],[sk_aSatz7_8_neg]) ).
cnf(c_286,negated_conjecture,
sK3 != sK1,
inference(split_conjunct,[status(thm)],[sk_aSatz7_8_neg]) ).
cnf(c_631,plain,
s(sK0,sK2) = sK1,
inference(paramod,[status(thm)],[c_284,c_264]) ).
cnf(c_634,plain,
s(sK0,sK2) = sK3,
inference(paramod,[status(thm)],[c_285,c_264]) ).
cnf(c_635,plain,
sK1 = sK3,
inference(paramod,[status(thm)],[c_631,c_634]) ).
cnf(c_636,plain,
sK3 = sK1,
inference(copy,[status(thm)],[c_635]) ).
cnf(c_633,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_286,c_636]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO498+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 13:36:44 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 882455 was started by sandbox on n010,
% 0.10/0.36 % Fri Sep 25 13:36:44 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.47
% 0.10/0.47 % SZS status Theorem for theBenchmark
% 0.10/0.47
% 0.10/0.47 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.10/0.47 % Length of proof is 8.
% 0.10/0.47 % Level of proof is 3.
% 0.10/0.47 % Maximum clause weight is 7.000.
% 0.10/0.47 % Given clauses 129.
% 0.10/0.47
% 0.10/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------