%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO085+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 07:17:01 AM UTC 2026
% Result : Theorem 0.15s 5.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 6 unt; 0 def)
% Number of atoms : 60 ( 11 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 68 ( 31 ~; 20 |; 13 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 24 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(open_defn,axiom,
! [C] :
( open(C)
<=> ? [P] : end_point(P,C) ),
file('theBenchmark.p',open_defn) ).
fof(c6,axiom,
! [C,P] :
( end_point(P,C)
=> ? [Q] :
( P != Q
& end_point(Q,C) ) ),
file('theBenchmark.p',c6) ).
fof(theorem_2_7_1,conjecture,
! [C] :
( open(C)
=> ? [P,Q] :
( end_point(Q,C)
& end_point(P,C)
& P != Q ) ),
file('theBenchmark.p',theorem_2_7_1) ).
fof(theorem_2_7_1_neg,negated_conjecture,
~ ! [C] :
( open(C)
=> ? [P,Q] :
( end_point(Q,C)
& end_point(P,C)
& P != Q ) ),
inference(assume_negation,[status(cth)],[theorem_2_7_1]) ).
fof(nnf_7,plain,
! [C] :
( ( ! [P] : ~ end_point(P,C)
| open(C) )
& ( ? [X0] : end_point(X0,C)
| ~ open(C) ) ),
inference(fof_nnf,[status(thm)],[open_defn]) ).
fof(sk_open_defn_sk,plain,
! [C] :
( ( ! [P] : ~ end_point(P,C)
| open(C) )
& ( end_point(sK0(C),C)
| ~ open(C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(C))],[nnf_7]) ).
fof(sk_open_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ end_point(VAR_1,VAR_0)
| open(VAR_0) )
& ! [VAR_0] :
( end_point(sK0(VAR_0),VAR_0)
| ~ open(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_open_defn_sk]) ).
cnf(c_28,plain,
( end_point(sK0(A),A)
| ~ open(A) ),
inference(split_conjunct,[status(thm)],[sk_open_defn]) ).
fof(nnf_17,plain,
? [C] :
( ! [P,Q] :
( ~ end_point(Q,C)
| ~ end_point(P,C)
| Q = P )
& open(C) ),
inference(fof_nnf,[status(thm)],[theorem_2_7_1_neg]) ).
fof(sk_theorem_2_7_1_neg,plain,
( ! [P,Q] :
( ~ end_point(Q,sK1)
| ~ end_point(P,sK1)
| Q = P )
& open(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(C,sK1)],[nnf_17]) ).
cnf(c_30,negated_conjecture,
open(sK1),
inference(split_conjunct,[status(thm)],[sk_theorem_2_7_1_neg]) ).
cnf(c_31,negated_conjecture,
end_point(sK0(sK1),sK1),
inference(resolve,[status(thm)],[c_30,c_28]) ).
cnf(c_40,negated_conjecture,
( ~ end_point(A,sK1)
| ~ end_point(B,sK1)
| A = B ),
inference(split_conjunct,[status(thm)],[sk_theorem_2_7_1_neg]) ).
fof(nnf_13,plain,
! [C,P] :
( ? [Q] :
( Q != P
& end_point(Q,C) )
| ~ end_point(P,C) ),
inference(fof_nnf,[status(thm)],[c6]) ).
fof(sk_c6_sk,plain,
! [C,P] :
( ( sK2(C,P) != P
& end_point(sK2(C,P),C) )
| ~ end_point(P,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(Q,sK2(C,P))],[nnf_13]) ).
fof(sk_c6,plain,
( ! [VAR_0,VAR_1] :
( sK2(VAR_1,VAR_0) != VAR_0
| ~ end_point(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( end_point(sK2(VAR_1,VAR_0),VAR_1)
| ~ end_point(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_c6_sk]) ).
cnf(c_45,plain,
( sK2(B,A) != A
| ~ end_point(A,B) ),
inference(split_conjunct,[status(thm)],[sk_c6]) ).
cnf(c_46,plain,
( end_point(sK2(B,A),B)
| ~ end_point(A,B) ),
inference(split_conjunct,[status(thm)],[sk_c6]) ).
cnf(c_94,plain,
sK2(sK1,sK0(sK1)) != sK0(sK1),
inference(resolve,[status(thm)],[c_45,c_31]) ).
cnf(c_95,plain,
end_point(sK2(sK1,sK0(sK1)),sK1),
inference(resolve,[status(thm)],[c_46,c_31]) ).
cnf(c_365,negated_conjecture,
( ~ end_point(sK2(sK1,sK0(sK1)),sK1)
| ~ end_point(sK0(sK1),sK1) ),
inference(resolve,[status(thm)],[c_40,c_94]) ).
cnf(c_366,negated_conjecture,
~ end_point(sK2(sK1,sK0(sK1)),sK1),
inference(resolve,[status(thm)],[c_365,c_31]) ).
cnf(c_364,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_95,c_366]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO085+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n001.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Fri Sep 25 12:47:16 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 3309018 was started by sandbox on n001,
% 0.11/5.39 % Fri Sep 25 12:47:16 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/5.41
% 0.15/5.41 % From the command line: assign(max_seconds, 300).
% 0.15/5.46
% 0.15/5.46 % SZS status Theorem for theBenchmark
% 0.15/5.46
% 0.15/5.46 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.15/5.46 % Length of proof is 12.
% 0.15/5.46 % Level of proof is 4.
% 0.15/5.46 % Maximum clause weight is 22.000.
% 0.15/5.46 % Given clauses 54.
% 0.15/5.46
% 0.15/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------