%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO499+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 66.67s 9.20s
% Output : CNFRefutation 66.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 9 unt; 0 def)
% Number of atoms : 21 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 4 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 14 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz7_7,axiom,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
file('theBenchmark.p',aSatz7_7) ).
fof(aSatz7_15a,axiom,
! [Xp,Xq,Xr,Xa] :
( s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr))
| ~ s_t(Xp,Xq,Xr) ),
file('theBenchmark.p',aSatz7_15a) ).
fof(aSatz7_15b,conjecture,
! [Xp,Xq,Xr,Xa] :
( ~ s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr))
| s_t(Xp,Xq,Xr) ),
file('theBenchmark.p',aSatz7_15b) ).
fof(aSatz7_15b_neg,negated_conjecture,
~ ! [Xp,Xq,Xr,Xa] :
( ~ s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr))
| s_t(Xp,Xq,Xr) ),
inference(assume_negation,[status(cth)],[aSatz7_15b]) ).
cnf(c_270,plain,
s(A,s(A,B)) = B,
inference(clausify,[status(thm)],[aSatz7_7]) ).
cnf(c_276,plain,
( s_t(s(D,A),s(D,B),s(D,C))
| ~ s_t(A,B,C) ),
inference(clausify,[status(thm)],[aSatz7_15a]) ).
fof(nnf_113,plain,
? [Xp,Xq,Xr,Xa] :
( s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr))
& ~ s_t(Xp,Xq,Xr) ),
inference(fof_nnf,[status(thm)],[aSatz7_15b_neg]) ).
fof(sk_aSatz7_15b_neg,plain,
( s_t(s(sK3,sK0),s(sK3,sK1),s(sK3,sK2))
& ~ s_t(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(Xp,sK0),skolemize(Xq,sK1),skolemize(Xr,sK2),skolemize(Xa,sK3)],[nnf_113]) ).
cnf(c_296,negated_conjecture,
~ s_t(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_aSatz7_15b_neg]) ).
cnf(c_297,negated_conjecture,
s_t(s(sK3,sK0),s(sK3,sK1),s(sK3,sK2)),
inference(split_conjunct,[status(thm)],[sk_aSatz7_15b_neg]) ).
cnf(c_711,plain,
s_t(s(A,s(sK3,sK0)),s(A,s(sK3,sK1)),s(A,s(sK3,sK2))),
inference(resolve,[status(thm)],[c_297,c_276]) ).
cnf(c_31521,plain,
s_t(sK0,s(sK3,s(sK3,sK1)),s(sK3,s(sK3,sK2))),
inference(paramod,[status(thm)],[c_270,c_711]) ).
cnf(c_31522,plain,
s_t(sK0,sK1,s(sK3,s(sK3,sK2))),
inference(paramod,[status(thm)],[c_270,c_31521]) ).
cnf(c_31523,plain,
s_t(sK0,sK1,sK2),
inference(paramod,[status(thm)],[c_270,c_31522]) ).
cnf(c_31520,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_296,c_31523]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO499+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 13:36:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3029711 was started by sandbox2 on n006,
% 0.10/0.37 % Fri Sep 25 13:36:26 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 66.67/9.20
% 66.67/9.20 % given #500 (T,wt=10): 8284 s_col(s(A,s(s(B,A),A)),B,A). [resolve(5553,a,280,b)].
% 66.67/9.20
% 66.67/9.20 % given #1000 (T,wt=11): 14336 s_t(A,B,A) | s_t(c63(A,B,A),B,A). [resolve(1962,b,190,a)].
% 66.67/9.20
% 66.67/9.20 % given #1500 (T,wt=11): 26618 s_col(A,B,ip(C,B,s(B,C),A,A)). [resolve(18185,a,280,b)].
% 66.67/9.20
% 66.67/9.20 % SZS status Theorem for theBenchmark
% 66.67/9.20
% 66.67/9.20 % Proof 1 at 6.77 (+ 1.69) seconds.
% 66.67/9.20 % Length of proof is 9.
% 66.67/9.20 % Level of proof is 3.
% 66.67/9.20 % Maximum clause weight is 16.000.
% 66.67/9.20 % Given clauses 1644.
% 66.67/9.20
% 66.67/9.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------