%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO146+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 07:17:10 AM UTC 2026
% Result : Theorem 46.78s 7.21s
% Output : CNFRefutation 46.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 6 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 11 ~; 12 |; 2 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 11 !; 3 ?)
% 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(symmetry_of_at_the_same_time,axiom,
! [A,B] :
( once(at_the_same_time(A,B))
<=> once(at_the_same_time(B,A)) ),
file('theBenchmark.p',symmetry_of_at_the_same_time) ).
fof(t12,conjecture,
! [X,Y,P] :
( connect(X,Y,P)
<=> connect(Y,X,P) ),
file('theBenchmark.p',t12) ).
fof(t12_neg,negated_conjecture,
~ ! [X,Y,P] :
( connect(X,Y,P)
<=> connect(Y,X,P) ),
inference(assume_negation,[status(cth)],[t12]) ).
cnf(c_149,plain,
( once(at_the_same_time(at(A,C),at(B,C)))
| ~ connect(A,B,C) ),
inference(clausify,[status(thm)],[connect_defn]) ).
cnf(c_150,plain,
( ~ once(at_the_same_time(at(A,C),at(B,C)))
| connect(A,B,C) ),
inference(clausify,[status(thm)],[connect_defn]) ).
cnf(c_151,plain,
( once(at_the_same_time(B,A))
| ~ once(at_the_same_time(A,B)) ),
inference(clausify,[status(thm)],[symmetry_of_at_the_same_time]) ).
fof(nnf_37,plain,
? [X,Y,P] :
( ( ~ connect(Y,X,P)
| ~ connect(X,Y,P) )
& ( connect(Y,X,P)
| connect(X,Y,P) ) ),
inference(fof_nnf,[status(thm)],[t12_neg]) ).
fof(sk_t12_neg,plain,
( ( ~ connect(sK1,sK0,sK2)
| ~ connect(sK0,sK1,sK2) )
& ( connect(sK1,sK0,sK2)
| connect(sK0,sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(P,sK2)],[nnf_37]) ).
cnf(c_163,negated_conjecture,
( connect(sK1,sK0,sK2)
| connect(sK0,sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t12_neg]) ).
cnf(c_164,negated_conjecture,
( ~ connect(sK1,sK0,sK2)
| ~ connect(sK0,sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t12_neg]) ).
cnf(c_453,plain,
( once(at_the_same_time(at(sK1,sK2),at(sK0,sK2)))
| connect(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_163,c_149]) ).
cnf(c_2708,plain,
( once(at_the_same_time(at(sK0,sK2),at(sK1,sK2)))
| once(at_the_same_time(at(sK1,sK2),at(sK0,sK2))) ),
inference(resolve,[status(thm)],[c_453,c_149]) ).
cnf(c_26552,plain,
( once(at_the_same_time(at(sK0,sK2),at(sK1,sK2)))
| once(at_the_same_time(at(sK0,sK2),at(sK1,sK2))) ),
inference(resolve,[status(thm)],[c_2708,c_151]) ).
cnf(c_26413,plain,
once(at_the_same_time(at(sK0,sK2),at(sK1,sK2))),
inference(copy,[status(thm)],[c_26552]) ).
cnf(c_26418,plain,
once(at_the_same_time(at(sK1,sK2),at(sK0,sK2))),
inference(resolve,[status(thm)],[c_26413,c_151]) ).
cnf(c_26419,plain,
connect(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_26413,c_150]) ).
cnf(c_26420,negated_conjecture,
~ connect(sK1,sK0,sK2),
inference(resolve,[status(thm)],[c_26419,c_164]) ).
cnf(c_26553,plain,
connect(sK1,sK0,sK2),
inference(resolve,[status(thm)],[c_26418,c_150]) ).
cnf(c_26551,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_26420,c_26553]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO146+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.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 12:50:47 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 2314301 was started by sandbox2 on n017,
% 0.11/0.38 % Fri Sep 25 12:50:47 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 46.78/7.21
% 46.78/7.21 % given #500 (A,wt=39): 353 meet(f2(A,B,C),A,D) | -incident_c(f2(A,B,C),D) | incident_c(f5(f2(A,B,C),A,D),D) | sum(B,C) = A | incident_c(f2(A,B,C),B) | incident_c(f2(A,B,C),C). [resolve(125,b,109,b)].
% 46.78/7.21
% 46.78/7.21 % given #1000 (A,wt=23): 558 A = B | -incident_c(B,B) | -incident_c(A,B) | incident_o(C,f21(B,A,B)) | -incident_c(C,B) | incident_c(f1(A,B),B). [factor(557,a,f)].
% 46.78/7.21
% 46.78/7.21 % given #1500 (T,wt=14): 21814 once(at(A,f6(underlying_curve(B)))) | incident_o(f1(underlying_curve(f25(A)),underlying_curve(B)),B). [resolve(7617,a,5501,b)].
% 46.78/7.21
% 46.78/7.21 % given #2000 (T,wt=15): 23796 underlying_curve(A) != sum(sum(B,C),D) | incident_o(f6(f9(B,f8(B))),A). [resolve(23794,a,146,c)].
% 46.78/7.21
% 46.78/7.21 % SZS status Theorem for theBenchmark
% 46.78/7.21
% 46.78/7.21 % Proof 1 at 5.31 (+ 1.33) seconds.
% 46.78/7.21 % Length of proof is 15.
% 46.78/7.21 % Level of proof is 7.
% 46.78/7.21 % Maximum clause weight is 16.000.
% 46.78/7.21 % Given clauses 2155.
% 46.78/7.21
% 46.78/7.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------