%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO526+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 : n016.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 07:18:03 AM UTC 2026
% Result : Theorem 92.11s 12.58s
% Output : CNFRefutation 92.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 23 unt; 0 def)
% Number of atoms : 99 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 96 ( 44 ~; 40 |; 12 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 41 !; 5 ?)
% 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_4,axiom,
! [Xa,Xb,Xc,Xd] :
( s_e(Xb,Xa,Xc,Xd)
| ~ s_e(Xa,Xb,Xc,Xd) ),
file('theBenchmark.p',aSatz2_4) ).
fof(aSatz2_14,axiom,
! [Xa,Xb,Xc,Xd] :
( s_e(Xb,Xa,Xd,Xc)
| ~ s_e(Xa,Xb,Xc,Xd) ),
file('theBenchmark.p',aSatz2_14) ).
fof(aSatz7_6,axiom,
! [Xp,Xa,Xq] :
( Xq = s(Xa,Xp)
| ~ s_m(Xp,Xa,Xq) ),
file('theBenchmark.p',aSatz7_6) ).
fof(aSatz8_2,axiom,
! [Xa,Xb,Xc] :
( s_r(Xc,Xb,Xa)
| ~ s_r(Xa,Xb,Xc) ),
file('theBenchmark.p',aSatz8_2) ).
fof(aSatz8_4,axiom,
! [Xa,Xb,Xc] :
( s_r(Xa,Xb,s(Xb,Xc))
| ~ s_r(Xa,Xb,Xc) ),
file('theBenchmark.p',aSatz8_4) ).
fof(aSatz8_22,axiom,
! [Xa,Xb] : s_m(Xa,midpoint(Xa,Xb),Xb),
file('theBenchmark.p',aSatz8_22) ).
fof(aSatz10_12b,axiom,
! [Xa,Xb,Xc,Xa1] :
( s_e(Xa,Xc,Xa1,Xc)
| ~ s_e(Xa,Xb,Xa1,Xb)
| ~ s_r(Xa1,Xb,Xc)
| ~ s_r(Xa,Xb,Xc) ),
file('theBenchmark.p',aSatz10_12b) ).
fof(aSatz10_12c,conjecture,
! [Xa,Xb,Xc,Xa1,Xc1] :
( Xc = Xc1
| Xb != midpoint(Xc,Xc1)
| s_e(Xa,Xc,Xa1,Xc1)
| ~ s_e(Xb,Xc,Xb,Xc1)
| ~ s_e(Xa,Xb,Xa1,Xb)
| ~ s_r(Xa1,Xb,Xc1)
| ~ s_r(Xa,Xb,Xc) ),
file('theBenchmark.p',aSatz10_12c) ).
fof(aSatz10_12c_neg,negated_conjecture,
~ ! [Xa,Xb,Xc,Xa1,Xc1] :
( Xc = Xc1
| Xb != midpoint(Xc,Xc1)
| s_e(Xa,Xc,Xa1,Xc1)
| ~ s_e(Xb,Xc,Xb,Xc1)
| ~ s_e(Xa,Xb,Xa1,Xb)
| ~ s_r(Xa1,Xb,Xc1)
| ~ s_r(Xa,Xb,Xc) ),
inference(assume_negation,[status(cth)],[aSatz10_12c]) ).
cnf(c_340,plain,
s_e(A,B,B,A),
inference(clausify,[status(thm)],[aA1]) ).
cnf(c_341,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_348,plain,
( s_e(B,A,C,D)
| ~ s_e(A,B,C,D) ),
inference(clausify,[status(thm)],[aSatz2_4]) ).
cnf(c_353,plain,
( s_e(B,A,D,C)
| ~ s_e(A,B,C,D) ),
inference(clausify,[status(thm)],[aSatz2_14]) ).
cnf(c_414,plain,
( s(B,A) = C
| ~ s_m(A,B,C) ),
inference(clausify,[status(thm)],[aSatz7_6]) ).
cnf(c_431,plain,
( s_r(C,B,A)
| ~ s_r(A,B,C) ),
inference(clausify,[status(thm)],[aSatz8_2]) ).
cnf(c_433,plain,
( s_r(A,B,s(B,C))
| ~ s_r(A,B,C) ),
inference(clausify,[status(thm)],[aSatz8_4]) ).
cnf(c_452,plain,
s_m(A,midpoint(A,B),B),
inference(clausify,[status(thm)],[aSatz8_22]) ).
cnf(c_495,plain,
( s_e(A,C,D,C)
| ~ s_e(A,B,D,B)
| ~ s_r(D,B,C)
| ~ s_r(A,B,C) ),
inference(clausify,[status(thm)],[aSatz10_12b]) ).
fof(nnf_206,plain,
? [Xa,Xb,Xc,Xa1,Xc1] :
( Xc1 != Xc
& midpoint(Xc,Xc1) = Xb
& ~ s_e(Xa,Xc,Xa1,Xc1)
& s_e(Xb,Xc,Xb,Xc1)
& s_e(Xa,Xb,Xa1,Xb)
& s_r(Xa1,Xb,Xc1)
& s_r(Xa,Xb,Xc) ),
inference(fof_nnf,[status(thm)],[aSatz10_12c_neg]) ).
fof(sk_aSatz10_12c_neg,plain,
( sK4 != sK2
& midpoint(sK2,sK4) = sK1
& ~ s_e(sK0,sK2,sK3,sK4)
& s_e(sK1,sK2,sK1,sK4)
& s_e(sK0,sK1,sK3,sK1)
& s_r(sK3,sK1,sK4)
& s_r(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(Xa,sK0),skolemize(Xb,sK1),skolemize(Xc,sK2),skolemize(Xa1,sK3),skolemize(Xc1,sK4)],[nnf_206]) ).
cnf(c_505,negated_conjecture,
s_r(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_aSatz10_12c_neg]) ).
cnf(c_506,negated_conjecture,
s_r(sK3,sK1,sK4),
inference(split_conjunct,[status(thm)],[sk_aSatz10_12c_neg]) ).
cnf(c_507,negated_conjecture,
s_e(sK0,sK1,sK3,sK1),
inference(split_conjunct,[status(thm)],[sk_aSatz10_12c_neg]) ).
cnf(c_508,negated_conjecture,
s_e(sK1,sK2,sK1,sK4),
inference(split_conjunct,[status(thm)],[sk_aSatz10_12c_neg]) ).
cnf(c_509,negated_conjecture,
~ s_e(sK0,sK2,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_aSatz10_12c_neg]) ).
cnf(c_510,negated_conjecture,
midpoint(sK2,sK4) = sK1,
inference(split_conjunct,[status(thm)],[sk_aSatz10_12c_neg]) ).
cnf(c_13898,negated_conjecture,
( s_e(sK1,sK4,A,B)
| ~ s_e(sK1,sK2,A,B) ),
inference(resolve,[status(thm)],[c_341,c_508]) ).
cnf(c_958,negated_conjecture,
s_e(sK1,sK4,sK2,sK1),
inference(resolve,[status(thm)],[c_13898,c_340]) ).
cnf(c_1331,plain,
s_e(sK4,sK1,sK2,sK1),
inference(resolve,[status(thm)],[c_958,c_348]) ).
cnf(c_4624,plain,
s_r(sK2,sK1,sK0),
inference(resolve,[status(thm)],[c_431,c_505]) ).
cnf(c_4931,plain,
s_m(sK2,sK1,sK4),
inference(paramod,[status(thm)],[c_510,c_452]) ).
cnf(c_4935,plain,
s(sK1,sK2) = sK4,
inference(resolve,[status(thm)],[c_4931,c_414]) ).
cnf(c_13899,negated_conjecture,
s_r(sK0,sK1,s(sK1,sK2)),
inference(resolve,[status(thm)],[c_433,c_505]) ).
cnf(c_5670,negated_conjecture,
s_r(sK0,sK1,sK4),
inference(paramod,[status(thm)],[c_4935,c_13899]) ).
cnf(c_5677,plain,
s_r(sK4,sK1,sK0),
inference(resolve,[status(thm)],[c_5670,c_431]) ).
cnf(c_13900,plain,
( s_e(sK4,sK0,A,sK0)
| ~ s_e(sK4,sK1,A,sK1)
| ~ s_r(A,sK1,sK0) ),
inference(resolve,[status(thm)],[c_495,c_5677]) ).
cnf(c_13901,plain,
( s_e(sK4,sK0,sK2,sK0)
| ~ s_e(sK4,sK1,sK2,sK1) ),
inference(resolve,[status(thm)],[c_13900,c_4624]) ).
cnf(c_12383,plain,
s_e(sK4,sK0,sK2,sK0),
inference(resolve,[status(thm)],[c_13901,c_1331]) ).
cnf(c_13902,plain,
( s_e(sK0,sK4,A,sK4)
| ~ s_e(sK0,sK1,A,sK1)
| ~ s_r(A,sK1,sK4) ),
inference(resolve,[status(thm)],[c_495,c_5670]) ).
cnf(c_13903,negated_conjecture,
( s_e(sK0,sK4,sK3,sK4)
| ~ s_e(sK0,sK1,sK3,sK1) ),
inference(resolve,[status(thm)],[c_13902,c_506]) ).
cnf(c_12385,negated_conjecture,
s_e(sK0,sK4,sK3,sK4),
inference(resolve,[status(thm)],[c_13903,c_507]) ).
cnf(c_12404,plain,
s_e(sK0,sK4,sK0,sK2),
inference(resolve,[status(thm)],[c_12383,c_353]) ).
cnf(c_13904,plain,
( s_e(sK0,sK2,A,B)
| ~ s_e(sK0,sK4,A,B) ),
inference(resolve,[status(thm)],[c_341,c_12404]) ).
cnf(c_13905,plain,
s_e(sK0,sK2,sK3,sK4),
inference(resolve,[status(thm)],[c_13904,c_12385]) ).
cnf(c_13897,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_509,c_13905]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO526+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.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 13:43:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2494567 was started by sandbox2 on n016,
% 0.09/0.36 % Fri Sep 25 13:43:44 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SInE: 161 to sos, 48 to usable, of 209 axioms (tolerance 2.00, depth 0 fixpoint).
% 92.11/12.58
% 92.11/12.58 % SZS status Theorem for theBenchmark
% 92.11/12.58
% 92.11/12.58 % Proof 1 at 3.38 (+ 0.71) seconds.
% 92.11/12.58 % Length of proof is 36.
% 92.11/12.58 % Level of proof is 8.
% 92.11/12.58 % Maximum clause weight is 113.000.
% 92.11/12.58 % Given clauses 419.
% 92.11/12.58
% 92.11/12.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------