%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO148+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 : n013.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 07:17:11 AM UTC 2026
% Result : Theorem 0.15s 5.50s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 54 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 52 ( 23 ~; 13 |; 10 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 22 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(connect_defn,axiom,
! [X,Y,P] :
( connect(X,Y,P)
<=> once(at_the_same_time(at(X,P),at(Y,P))) ),
file('theBenchmark.p',connect_defn) ).
fof(trajectories_are_oriented_curves,axiom,
! [X] :
? [O] : trajectory_of(X) = O,
file('theBenchmark.p',trajectories_are_oriented_curves) ).
fof(homogeneous_behaviour,axiom,
! [P1,P2,Q1,Q2,X,Y] :
( ( once(at_the_same_time(at(X,Q1),at(Y,Q2)))
& once(at_the_same_time(at(X,P1),at(Y,P2))) )
=> ~ ( ordered_by(trajectory_of(Y),Q2,P2)
& ordered_by(trajectory_of(X),P1,Q1) ) ),
file('theBenchmark.p',homogeneous_behaviour) ).
fof(t14,conjecture,
! [P,X,Y] :
( connect(X,Y,P)
=> ! [Q1,Q2] :
( ( ordered_by(trajectory_of(X),P,Q1)
& ordered_by(trajectory_of(Y),Q2,P) )
=> ~ once(at_the_same_time(at(X,Q1),at(Y,Q2))) ) ),
file('theBenchmark.p',t14) ).
fof(t14_neg,negated_conjecture,
~ ! [P,X,Y] :
( connect(X,Y,P)
=> ! [Q1,Q2] :
( ( ordered_by(trajectory_of(X),P,Q1)
& ordered_by(trajectory_of(Y),Q2,P) )
=> ~ once(at_the_same_time(at(X,Q1),at(Y,Q2))) ) ),
inference(assume_negation,[status(cth)],[t14]) ).
cnf(c_79,plain,
( once(at_the_same_time(at(A,C),at(B,C)))
| ~ connect(A,B,C) ),
inference(clausify,[status(thm)],[connect_defn]) ).
fof(nnf_37,plain,
? [P,X,Y] :
( ? [Q1,Q2] :
( once(at_the_same_time(at(X,Q1),at(Y,Q2)))
& ordered_by(trajectory_of(X),P,Q1)
& ordered_by(trajectory_of(Y),Q2,P) )
& connect(X,Y,P) ),
inference(fof_nnf,[status(thm)],[t14_neg]) ).
fof(sk_t14_neg,plain,
( once(at_the_same_time(at(sK0,sK3),at(sK1,sK4)))
& ordered_by(trajectory_of(sK0),sK2,sK3)
& ordered_by(trajectory_of(sK1),sK4,sK2)
& connect(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK4,sK3]),skolemize(P,sK2),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Q1,sK3),skolemize(Q2,sK4)],[nnf_37]) ).
cnf(c_80,negated_conjecture,
connect(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t14_neg]) ).
cnf(c_81,negated_conjecture,
once(at_the_same_time(at(sK0,sK2),at(sK1,sK2))),
inference(resolve,[status(thm)],[c_80,c_79]) ).
cnf(c_113,negated_conjecture,
once(at_the_same_time(at(sK0,sK3),at(sK1,sK4))),
inference(split_conjunct,[status(thm)],[sk_t14_neg]) ).
cnf(c_114,negated_conjecture,
ordered_by(trajectory_of(sK0),sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t14_neg]) ).
cnf(c_115,negated_conjecture,
ordered_by(trajectory_of(sK1),sK4,sK2),
inference(split_conjunct,[status(thm)],[sk_t14_neg]) ).
cnf(c_117,plain,
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(trajectory_of(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ),
inference(clausify,[status(thm)],[homogeneous_behaviour]) ).
fof(nnf_34,plain,
! [X] :
? [O] : trajectory_of(X) = O,
inference(fof_nnf,[status(thm)],[trajectories_are_oriented_curves]) ).
fof(sk_trajectories_are_oriented_curves,plain,
! [X] : trajectory_of(X) = sK5(X),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(O,sK5(X))],[nnf_34]) ).
cnf(c_118,plain,
trajectory_of(A) = sK5(A),
inference(split_conjunct,[status(thm)],[sk_trajectories_are_oriented_curves]) ).
cnf(c_712,plain,
( ~ ordered_by(trajectory_of(C),F,D)
| ~ ordered_by(sK5(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ),
inference(paramod,[status(thm)],[c_118,c_117]) ).
cnf(c_211,plain,
( ~ ordered_by(sK5(C),F,D)
| ~ ordered_by(sK5(A),B,E)
| ~ once(at_the_same_time(at(A,E),at(C,F)))
| ~ once(at_the_same_time(at(A,B),at(C,D))) ),
inference(paramod,[status(thm)],[c_118,c_712]) ).
cnf(c_212,negated_conjecture,
ordered_by(sK5(sK1),sK4,sK2),
inference(paramod,[status(thm)],[c_118,c_115]) ).
cnf(c_213,negated_conjecture,
ordered_by(sK5(sK0),sK2,sK3),
inference(paramod,[status(thm)],[c_118,c_114]) ).
cnf(c_631,plain,
( ~ ordered_by(sK5(A),B,C)
| ~ once(at_the_same_time(at(A,C),at(sK1,sK4)))
| ~ once(at_the_same_time(at(A,B),at(sK1,sK2))) ),
inference(resolve,[status(thm)],[c_212,c_211]) ).
cnf(c_713,negated_conjecture,
( ~ once(at_the_same_time(at(sK0,sK3),at(sK1,sK4)))
| ~ once(at_the_same_time(at(sK0,sK2),at(sK1,sK2))) ),
inference(resolve,[status(thm)],[c_631,c_213]) ).
cnf(c_714,negated_conjecture,
~ once(at_the_same_time(at(sK0,sK3),at(sK1,sK4))),
inference(resolve,[status(thm)],[c_81,c_713]) ).
cnf(c_711,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_113,c_714]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO148+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n013.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 12:55:41 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 465761 was started by sandbox on n013,
% 0.10/5.38 % Fri Sep 25 12:55:41 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.50
% 0.15/5.50 % SZS status Theorem for theBenchmark
% 0.15/5.50
% 0.15/5.50 % Proof 1 at 0.09 (+ 0.01) seconds.
% 0.15/5.50 % Length of proof is 17.
% 0.15/5.50 % Level of proof is 4.
% 0.15/5.50 % Maximum clause weight is 26.000.
% 0.15/5.50 % Given clauses 158.
% 0.15/5.50
% 0.15/5.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------