%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO504+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 : n014.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 24.29s 9.01s
% Output : CNFRefutation 24.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 16 unt; 0 def)
% Number of atoms : 46 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 18 ~; 14 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aA1,axiom,
! [X,Y] : s_e(X,Y,Y,X),
file('theBenchmark.p',aA1) ).
fof(aA2,axiom,
! [X,Y,Z,V,Z2,V2] :
( s_e(Z,V,Z2,V2)
| ~ s_e(X,Y,Z2,V2)
| ~ s_e(X,Y,Z,V) ),
file('theBenchmark.p',aA2) ).
fof(aSatz2_2,axiom,
! [Xa,Xb,Xc,Xd] :
( s_e(Xc,Xd,Xa,Xb)
| ~ s_e(Xa,Xb,Xc,Xd) ),
file('theBenchmark.p',aSatz2_2) ).
fof(aSatz7_7,axiom,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
file('theBenchmark.p',aSatz7_7) ).
fof(aSatz7_13,axiom,
! [Xp,Xq,Xa] : s_e(Xp,Xq,s(Xa,Xp),s(Xa,Xq)),
file('theBenchmark.p',aSatz7_13) ).
fof(d_Defn8_1,axiom,
! [Xa,Xb,Xc] :
( ( ~ s_e(Xa,Xc,Xa,s(Xb,Xc))
| s_r(Xa,Xb,Xc) )
& ( s_e(Xa,Xc,Xa,s(Xb,Xc))
| ~ s_r(Xa,Xb,Xc) ) ),
file('theBenchmark.p',d_Defn8_1) ).
fof(aSatz8_2,conjecture,
! [Xa,Xb,Xc] :
( s_r(Xc,Xb,Xa)
| ~ s_r(Xa,Xb,Xc) ),
file('theBenchmark.p',aSatz8_2) ).
fof(aSatz8_2_neg,negated_conjecture,
~ ! [Xa,Xb,Xc] :
( s_r(Xc,Xb,Xa)
| ~ s_r(Xa,Xb,Xc) ),
inference(assume_negation,[status(cth)],[aSatz8_2]) ).
cnf(c_207,plain,
s_e(A,B,B,A),
inference(clausify,[status(thm)],[aA1]) ).
cnf(c_208,plain,
( s_e(C,D,E,F)
| ~ s_e(A,B,E,F)
| ~ s_e(A,B,C,D) ),
inference(clausify,[status(thm)],[aA2]) ).
cnf(c_213,plain,
( s_e(C,D,A,B)
| ~ s_e(A,B,C,D) ),
inference(clausify,[status(thm)],[aSatz2_2]) ).
cnf(c_282,plain,
s(A,s(A,B)) = B,
inference(clausify,[status(thm)],[aSatz7_7]) ).
cnf(c_287,plain,
s_e(A,B,s(C,A),s(C,B)),
inference(clausify,[status(thm)],[aSatz7_13]) ).
cnf(c_305,plain,
( s_e(A,C,A,s(B,C))
| ~ s_r(A,B,C) ),
inference(clausify,[status(thm)],[d_Defn8_1]) ).
cnf(c_306,plain,
( ~ s_e(A,C,A,s(B,C))
| s_r(A,B,C) ),
inference(clausify,[status(thm)],[d_Defn8_1]) ).
fof(nnf_128,plain,
? [Xa,Xb,Xc] :
( ~ s_r(Xc,Xb,Xa)
& s_r(Xa,Xb,Xc) ),
inference(fof_nnf,[status(thm)],[aSatz8_2_neg]) ).
fof(sk_aSatz8_2_neg,plain,
( ~ s_r(sK2,sK1,sK0)
& s_r(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(Xa,sK0),skolemize(Xb,sK1),skolemize(Xc,sK2)],[nnf_128]) ).
cnf(c_317,negated_conjecture,
s_r(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_aSatz8_2_neg]) ).
cnf(c_318,negated_conjecture,
~ s_r(sK2,sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_aSatz8_2_neg]) ).
cnf(c_403,plain,
( s_e(C,D,B,A)
| ~ s_e(A,B,C,D) ),
inference(resolve,[status(thm)],[c_208,c_207]) ).
cnf(c_771,plain,
s_e(sK0,sK2,sK0,s(sK1,sK2)),
inference(resolve,[status(thm)],[c_305,c_317]) ).
cnf(c_772,plain,
s_e(sK0,s(sK1,sK2),sK2,sK0),
inference(resolve,[status(thm)],[c_771,c_403]) ).
cnf(c_858,plain,
s_e(sK2,sK0,s(sK1,sK2),sK0),
inference(resolve,[status(thm)],[c_772,c_403]) ).
cnf(c_973,plain,
s_e(s(sK1,sK2),sK0,sK2,sK0),
inference(resolve,[status(thm)],[c_213,c_858]) ).
cnf(c_1026,plain,
( s_e(sK2,sK0,A,B)
| ~ s_e(s(sK1,sK2),sK0,A,B) ),
inference(resolve,[status(thm)],[c_973,c_208]) ).
cnf(c_9154,plain,
s_e(s(A,B),C,B,s(A,C)),
inference(paramod,[status(thm)],[c_282,c_287]) ).
cnf(c_9850,plain,
s_e(sK2,sK0,sK2,s(sK1,sK0)),
inference(resolve,[status(thm)],[c_9154,c_1026]) ).
cnf(c_10013,plain,
s_r(sK2,sK1,sK0),
inference(resolve,[status(thm)],[c_9850,c_306]) ).
cnf(c_10012,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_318,c_10013]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO504+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/5.46 % Computer : n014.cluster.edu
% 0.20/5.46 % Model : x86_64 x86_64
% 0.20/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.46 % Memory : 8046.5625MB
% 0.20/5.46 % OS : Linux 6.8.0-71-generic
% 0.20/5.46 % CPULimit : 300
% 0.20/5.46 % WCLimit : 300
% 0.20/5.46 % DateTime : Fri Sep 25 13:36:53 UTC 2026
% 0.20/5.47 % CPUTime :
% 0.20/5.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/5.47 % Process 342852 was started by sandbox2 on n014,
% 0.20/5.47 % Fri Sep 25 13:36:53 2026
% 0.20/5.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.24/5.52
% 0.24/5.52 % From the command line: assign(max_seconds, 300).
% 0.24/5.52
% 0.24/5.52 % SInE: 99 to sos, 31 to usable, of 130 axioms (tolerance 2.00, depth 0 fixpoint).
% 24.29/9.01
% 24.29/9.01 % given #500 (W,wt=9): 8819 -s_m(s(A,B),A,C) | B = C. [resolve(280,a,8782,a)].
% 24.29/9.01
% 24.29/9.01 % SZS status Theorem for theBenchmark
% 24.29/9.01
% 24.29/9.01 % Proof 1 at 2.63 (+ 0.60) seconds.
% 24.29/9.01 % Length of proof is 25.
% 24.29/9.01 % Level of proof is 8.
% 24.29/9.01 % Maximum clause weight is 115.000.
% 24.29/9.01 % Given clauses 562.
% 24.29/9.01
% 24.29/9.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------