TSTP Solution File: GEO168+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO168+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:09:34 EDT 2023
% Result : Theorem 30.55s 5.53s
% Output : Refutation 30.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 49
% Syntax : Number of formulae : 78 ( 4 unt; 22 typ; 0 def)
% Number of atoms : 156 ( 0 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 458 ( 2 ~; 8 |; 48 &; 356 @)
% ( 0 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 22 usr; 19 con; 0-4 aty)
% Number of variables : 123 ( 0 ^; 117 !; 6 ?; 123 :)
% Comments :
%------------------------------------------------------------------------------
thf(goal_type,type,
goal: $o ).
thf(point_equal_type,type,
point_equal: $i > $i > $o ).
thf(incident_type,type,
incident: $i > $i > $o ).
thf(line_equal_type,type,
line_equal: $i > $i > $o ).
thf(colinear_type,type,
colinear: $i > $i > $i > $i > $o ).
thf(b_type,type,
b: $i ).
thf(d_type,type,
d: $i ).
thf(h_type,type,
h: $i ).
thf(p_type,type,
p: $i ).
thf(a_type,type,
a: $i ).
thf(e_type,type,
e: $i ).
thf(q_type,type,
q: $i ).
thf(f_type,type,
f: $i ).
thf(g_type,type,
g: $i ).
thf(n_type,type,
n: $i ).
thf(c_type,type,
c: $i ).
thf(o_type,type,
o: $i ).
thf(i_type,type,
i: $i ).
thf(r_type,type,
r: $i ).
thf(s_type,type,
s: $i ).
thf(l_type,type,
l: $i ).
thf(m_type,type,
m: $i ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( line_equal @ C @ C )
& ( line_equal @ B @ B ) )
=> ? [D: $i] :
( ( incident @ D @ B )
& ( incident @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',point) ).
thf(42,plain,
! [A: $i,B: $i] :
( ( ( line_equal @ B @ B )
& ( line_equal @ A @ A ) )
=> ? [C: $i] :
( ( incident @ C @ A )
& ( incident @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26,axiom,
( ( incident @ e @ l )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goalel) ).
thf(84,plain,
( ( incident @ e @ l )
=> goal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i] :
( ( ( colinear @ A @ B @ C @ J )
& ( colinear @ D @ E @ F @ K )
& ( colinear @ B @ F @ G @ L )
& ( colinear @ C @ E @ G @ M )
& ( colinear @ B @ D @ H @ N )
& ( colinear @ A @ E @ H @ O )
& ( colinear @ C @ D @ I @ P )
& ( colinear @ A @ F @ I @ Q ) )
=> ( ? [R: $i] : ( colinear @ G @ H @ I @ R )
| ( line_equal @ L @ M )
| ( line_equal @ N @ O )
| ( line_equal @ P @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pappus1) ).
thf(38,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i] :
( ( ( colinear @ A @ B @ C @ J )
& ( colinear @ D @ E @ F @ K )
& ( colinear @ B @ F @ G @ L )
& ( colinear @ C @ E @ G @ M )
& ( colinear @ B @ D @ H @ N )
& ( colinear @ A @ E @ H @ O )
& ( colinear @ C @ D @ I @ P )
& ( colinear @ A @ F @ I @ Q ) )
=> ( ? [R: $i] : ( colinear @ G @ H @ I @ R )
| ( line_equal @ L @ M )
| ( line_equal @ N @ O )
| ( line_equal @ P @ Q ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( colinear @ A @ B @ C @ D )
=> ( incident @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity_elimination2) ).
thf(53,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( colinear @ A @ B @ C @ D )
=> ( incident @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(16,axiom,
( ( colinear @ c @ d @ i @ r )
& ( colinear @ a @ f @ i @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption4) ).
thf(59,plain,
( ( colinear @ c @ d @ i @ r )
& ( colinear @ a @ f @ i @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(27,axiom,
( ( incident @ a @ m )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goalam) ).
thf(86,plain,
( ( incident @ a @ m )
=> goal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(24,axiom,
( ( incident @ d @ l )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goaldl) ).
thf(80,plain,
( ( incident @ d @ l )
=> goal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( point_equal @ A @ A )
& ( point_equal @ B @ B ) )
=> ? [C: $i] :
( ( incident @ A @ C )
& ( incident @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',line) ).
thf(72,plain,
! [A: $i,B: $i] :
( ( ( point_equal @ A @ A )
& ( point_equal @ B @ B ) )
=> ? [C: $i] :
( ( incident @ A @ C )
& ( incident @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(20,axiom,
( ( colinear @ a @ b @ c @ l )
& ( colinear @ d @ e @ f @ m ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption1) ).
thf(69,plain,
( ( colinear @ a @ b @ c @ l )
& ( colinear @ d @ e @ f @ m ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(28,axiom,
( ( incident @ b @ m )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goalbm) ).
thf(88,plain,
( ( incident @ b @ m )
=> goal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( colinear @ A @ B @ C @ D )
=> ( incident @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity_elimination1) ).
thf(57,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( colinear @ A @ B @ C @ D )
=> ( incident @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(23,axiom,
( ( incident @ f @ l )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goalfl) ).
thf(78,plain,
( ( incident @ f @ l )
=> goal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).
thf(2,negated_conjecture,
~ goal,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ goal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( point_equal @ A @ B )
& ( incident @ B @ C ) )
=> ( incident @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pcon) ).
thf(45,plain,
! [A: $i,B: $i,C: $i] :
( ( ( point_equal @ A @ B )
& ( incident @ B @ C ) )
=> ( incident @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( incident @ A @ B )
=> ( point_equal @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_point_equal) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( incident @ A @ B )
=> ( point_equal @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( incident @ C @ A )
& ( incident @ C @ B )
& ( incident @ D @ A )
& ( incident @ D @ B ) )
=> ( ( point_equal @ C @ D )
| ( line_equal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique) ).
thf(32,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( incident @ C @ A )
& ( incident @ C @ B )
& ( incident @ D @ A )
& ( incident @ D @ B ) )
=> ( ( point_equal @ C @ D )
| ( line_equal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( line_equal @ A @ B )
=> ( line_equal @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_line_equal) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( line_equal @ A @ B )
=> ( line_equal @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
( ( colinear @ b @ f @ g @ n )
& ( colinear @ c @ e @ g @ o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption2) ).
thf(50,plain,
( ( colinear @ b @ f @ g @ n )
& ( colinear @ c @ e @ g @ o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( colinear @ A @ B @ C @ D )
=> ( incident @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity_elimination3) ).
thf(67,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( colinear @ A @ B @ C @ D )
=> ( incident @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( line_equal @ A @ B )
& ( line_equal @ B @ C ) )
=> ( line_equal @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_line_equal) ).
thf(40,plain,
! [A: $i,B: $i,C: $i] :
( ( ( line_equal @ A @ B )
& ( line_equal @ B @ C ) )
=> ( line_equal @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( incident @ A @ B )
=> ( line_equal @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_line_equal) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( incident @ A @ B )
=> ( line_equal @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
! [A: $i] :
( ( ( incident @ g @ A )
& ( incident @ h @ A )
& ( incident @ i @ A ) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal4) ).
thf(75,plain,
! [A: $i] :
( ( ( incident @ g @ A )
& ( incident @ h @ A )
& ( incident @ i @ A ) )
=> goal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(25,axiom,
( ( incident @ c @ m )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goalcm) ).
thf(82,plain,
( ( incident @ c @ m )
=> goal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( point_equal @ A @ B )
& ( point_equal @ B @ C ) )
=> ( point_equal @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_point_equal) ).
thf(36,plain,
! [A: $i,B: $i,C: $i] :
( ( ( point_equal @ A @ B )
& ( point_equal @ B @ C ) )
=> ( point_equal @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( point_equal @ A @ B )
=> ( point_equal @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_point_equal) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( point_equal @ A @ B )
=> ( point_equal @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
( ( colinear @ b @ d @ h @ p )
& ( colinear @ a @ e @ h @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption3) ).
thf(47,plain,
( ( colinear @ b @ d @ h @ p )
& ( colinear @ a @ e @ h @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( incident @ A @ B )
& ( line_equal @ B @ C ) )
=> ( incident @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lcon) ).
thf(62,plain,
! [A: $i,B: $i,C: $i] :
( ( ( incident @ A @ B )
& ( line_equal @ B @ C ) )
=> ( incident @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10820,plain,
$false,
inference(cvc4,[status(thm)],[42,84,38,53,59,86,80,72,69,88,57,78,29,45,64,32,34,50,67,40,55,75,82,36,30,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO168+1 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 03:58:18 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.96/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.98 % [INFO] Parsing done (135ms).
% 1.26/0.99 % [INFO] Running in sequential loop mode.
% 1.69/1.19 % [INFO] eprover registered as external prover.
% 1.69/1.19 % [INFO] cvc4 registered as external prover.
% 1.77/1.19 % [INFO] Scanning for conjecture ...
% 1.91/1.24 % [INFO] Found a conjecture and 26 axioms. Running axiom selection ...
% 1.91/1.28 % [INFO] Axiom selection finished. Selected 26 axioms (removed 0 axioms).
% 2.11/1.34 % [INFO] Problem is first-order (TPTP FOF).
% 2.11/1.34 % [INFO] Type checking passed.
% 2.11/1.35 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 30.55/5.53 % External prover 'cvc4' found a proof!
% 30.55/5.53 % [INFO] Killing All external provers ...
% 30.55/5.53 % Time passed: 5009ms (effective reasoning time: 4537ms)
% 30.55/5.53 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 30.55/5.53 % Axioms used in derivation (26): colinearity_elimination1, goal4, assumption3, transitivity_of_point_equal, colinearity_elimination3, lcon, colinearity_elimination2, assumption2, point, line, transitivity_of_line_equal, goaldl, goalfl, pappus1, goalam, goalbm, goalel, symmetry_of_point_equal, goalcm, pcon, assumption1, reflexivity_of_line_equal, symmetry_of_line_equal, reflexivity_of_point_equal, unique, assumption4
% 30.55/5.53 % No. of inferences in proof: 56
% 30.55/5.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5009 ms resp. 4537 ms w/o parsing
% 30.55/5.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.55/5.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------