%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO500+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 : n004.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 07:18:01 AM UTC 2026
% Result : Theorem 0.14s 24.50s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 23 unt; 0 def)
% Number of atoms : 73 ( 32 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 58 ( 29 ~; 25 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 31 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz7_4a,axiom,
! [Xp,Xa] : s_m(Xp,Xa,s(Xa,Xp)),
file('theBenchmark.p',aSatz7_4a) ).
fof(aSatz7_7,axiom,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
file('theBenchmark.p',aSatz7_7) ).
fof(aSatz7_10b,axiom,
! [Xa,Xp] :
( Xp != Xa
| s(Xa,Xp) = Xp ),
file('theBenchmark.p',aSatz7_10b) ).
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_16a,axiom,
! [Xp,Xq,Xr,Xcs,Xa] :
( s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs))
| ~ s_e(Xp,Xq,Xr,Xcs) ),
file('theBenchmark.p',aSatz7_16a) ).
fof(aSatz7_17,axiom,
! [Xp,Xa,Xq,Xb] :
( Xa = Xb
| ~ s_m(Xp,Xb,Xq)
| ~ s_m(Xp,Xa,Xq) ),
file('theBenchmark.p',aSatz7_17) ).
fof(aSatz7_18,axiom,
! [Xa,Xp,Xb] :
( Xa = Xb
| s(Xa,Xp) != s(Xb,Xp) ),
file('theBenchmark.p',aSatz7_18) ).
fof(d_Defn7_1,axiom,
! [Xa,Xm,Xb] :
( ( s_m(Xa,Xm,Xb)
| ~ s_e(Xm,Xa,Xm,Xb)
| ~ s_t(Xa,Xm,Xb) )
& ( s_e(Xm,Xa,Xm,Xb)
| ~ s_m(Xa,Xm,Xb) )
& ( s_t(Xa,Xm,Xb)
| ~ s_m(Xa,Xm,Xb) ) ),
file('theBenchmark.p',d_Defn7_1) ).
fof(aSatz7_19,conjecture,
! [Xa,Xb,Xp] :
( Xa = Xb
| s(Xa,s(Xb,Xp)) != s(Xb,s(Xa,Xp)) ),
file('theBenchmark.p',aSatz7_19) ).
fof(aSatz7_19_neg,negated_conjecture,
~ ! [Xa,Xb,Xp] :
( Xa = Xb
| s(Xa,s(Xb,Xp)) != s(Xb,s(Xa,Xp)) ),
inference(assume_negation,[status(cth)],[aSatz7_19]) ).
cnf(c_272,plain,
s_m(A,B,s(B,A)),
inference(clausify,[status(thm)],[aSatz7_4a]) ).
cnf(c_275,plain,
s(A,s(A,B)) = B,
inference(clausify,[status(thm)],[aSatz7_7]) ).
cnf(c_279,plain,
( B != A
| s(A,B) = B ),
inference(clausify,[status(thm)],[aSatz7_10b]) ).
cnf(c_281,plain,
( s_t(s(D,A),s(D,B),s(D,C))
| ~ s_t(A,B,C) ),
inference(clausify,[status(thm)],[aSatz7_15a]) ).
cnf(c_283,plain,
( s_e(s(E,A),s(E,B),s(E,C),s(E,D))
| ~ s_e(A,B,C,D) ),
inference(clausify,[status(thm)],[aSatz7_16a]) ).
cnf(c_285,plain,
( D = B
| ~ s_m(A,D,C)
| ~ s_m(A,B,C) ),
inference(clausify,[status(thm)],[aSatz7_17]) ).
cnf(c_286,plain,
( A = C
| s(A,B) != s(C,B) ),
inference(clausify,[status(thm)],[aSatz7_18]) ).
cnf(c_303,plain,
( s_t(A,B,C)
| ~ s_m(A,B,C) ),
inference(clausify,[status(thm)],[d_Defn7_1]) ).
cnf(c_304,plain,
( s_e(B,A,B,C)
| ~ s_m(A,B,C) ),
inference(clausify,[status(thm)],[d_Defn7_1]) ).
cnf(c_305,plain,
( s_m(A,B,C)
| ~ s_e(B,A,B,C)
| ~ s_t(A,B,C) ),
inference(clausify,[status(thm)],[d_Defn7_1]) ).
fof(nnf_118,plain,
? [Xa,Xb,Xp] :
( Xb != Xa
& s(Xb,s(Xa,Xp)) = s(Xa,s(Xb,Xp)) ),
inference(fof_nnf,[status(thm)],[aSatz7_19_neg]) ).
fof(sk_aSatz7_19_neg,plain,
( sK0 != sK1
& s(sK0,s(sK1,sK2)) = s(sK1,s(sK0,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(Xa,sK1),skolemize(Xb,sK0),skolemize(Xp,sK2)],[nnf_118]) ).
cnf(c_306,negated_conjecture,
s(sK0,s(sK1,sK2)) = s(sK1,s(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_aSatz7_19_neg]) ).
cnf(c_307,negated_conjecture,
sK0 != sK1,
inference(split_conjunct,[status(thm)],[sk_aSatz7_19_neg]) ).
cnf(c_50499,plain,
s(A,s(B,s(B,A))) = s(B,s(B,A)),
inference(resolve,[status(thm)],[c_279,c_275]) ).
cnf(c_50500,plain,
s(A,A) = s(B,s(B,A)),
inference(paramod,[status(thm)],[c_275,c_50499]) ).
cnf(c_642,plain,
s(A,A) = A,
inference(paramod,[status(thm)],[c_275,c_50500]) ).
cnf(c_712,plain,
( C = B
| ~ s_m(A,B,s(C,A)) ),
inference(resolve,[status(thm)],[c_285,c_272]) ).
cnf(c_725,plain,
s_t(A,B,s(B,A)),
inference(resolve,[status(thm)],[c_303,c_272]) ).
cnf(c_726,plain,
s_e(A,B,A,s(A,B)),
inference(resolve,[status(thm)],[c_304,c_272]) ).
cnf(c_731,plain,
s(sK0,s(sK1,s(sK0,sK2))) = s(sK1,sK2),
inference(paramod,[status(thm)],[c_306,c_275]) ).
cnf(c_906,plain,
( A = B
| s(A,B) != B ),
inference(paramod,[status(thm)],[c_642,c_286]) ).
cnf(c_939,plain,
s_t(s(A,B),s(A,C),s(A,s(C,B))),
inference(resolve,[status(thm)],[c_725,c_281]) ).
cnf(c_1182,plain,
s_e(s(A,B),s(A,C),s(A,B),s(A,s(B,C))),
inference(resolve,[status(thm)],[c_726,c_283]) ).
cnf(c_50501,plain,
s_t(s(sK0,s(sK0,sK2)),s(sK0,sK1),s(sK1,sK2)),
inference(paramod,[status(thm)],[c_731,c_939]) ).
cnf(c_37010,plain,
s_t(sK2,s(sK0,sK1),s(sK1,sK2)),
inference(paramod,[status(thm)],[c_275,c_50501]) ).
cnf(c_50502,plain,
s_e(s(sK0,sK1),s(sK0,s(sK0,sK2)),s(sK0,sK1),s(sK1,sK2)),
inference(paramod,[status(thm)],[c_731,c_1182]) ).
cnf(c_50293,plain,
s_e(s(sK0,sK1),sK2,s(sK0,sK1),s(sK1,sK2)),
inference(paramod,[status(thm)],[c_275,c_50502]) ).
cnf(c_50503,plain,
( s_m(sK2,s(sK0,sK1),s(sK1,sK2))
| ~ s_t(sK2,s(sK0,sK1),s(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_50293,c_305]) ).
cnf(c_50331,plain,
s_m(sK2,s(sK0,sK1),s(sK1,sK2)),
inference(resolve,[status(thm)],[c_37010,c_50503]) ).
cnf(c_50504,plain,
sK1 = s(sK0,sK1),
inference(resolve,[status(thm)],[c_50331,c_712]) ).
cnf(c_50341,plain,
s(sK0,sK1) = sK1,
inference(copy,[status(thm)],[c_50504]) ).
cnf(c_50505,plain,
sK0 = sK1,
inference(resolve,[status(thm)],[c_50341,c_906]) ).
cnf(c_50498,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_307,c_50505]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO500+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 13:36:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3278851 was started by sandbox on n004,
% 0.11/0.37 % Fri Sep 25 13:36:21 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.41
% 0.11/0.41 % From the command line: assign(max_seconds, 300).
% 0.14/24.50
% 0.14/24.50 % given #500 (A,wt=25): 430 -s_e(A,ext(B,C,C,D),A,D) | -s_t(A,C,E) | C = A | s_e(E,ext(B,C,C,D),E,D). [factor(426,d,e),unit_del(a,183),unit_del(b,183)].
% 0.14/24.50
% 0.14/24.50 % given #1000 (T,wt=11): 14075 le(A,B,s(A,ext(A,B,C,D)),A). [resolve(1508,b,174,a)].
% 0.14/24.50
% 0.14/24.50 % given #1500 (T,wt=11): 25687 s_col(ip(A,B,s(B,A),C,C),A,C). [resolve(17917,a,291,b)].
% 0.14/24.50
% 0.14/24.50 % given #2000 (T,wt=11): 33325 le(A,B,s(A,s(s(B,A),B)),B). [resolve(32460,a,239,a),unit_del(a,31343)].
% 0.14/24.50
% 0.14/24.50 % given #2500 (T,wt=12): 9472 s_t(ext(A,s(s(B,A),A),C,D),B,A). [resolve(5960,a,1000,a)].
% 0.14/24.50
% 0.14/24.50 % SZS status Theorem for theBenchmark
% 0.14/24.50
% 0.14/24.50 % Proof 1 at 12.89 (+ 4.19) seconds.
% 0.14/24.50 % Length of proof is 34.
% 0.14/24.50 % Level of proof is 7.
% 0.14/24.50 % Maximum clause weight is 18.000.
% 0.14/24.50 % Given clauses 2929.
% 0.14/24.50
% 0.14/24.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------